diff --git a/404.html b/404.html index 4f77c66b..1867bc24 100644 --- a/404.html +++ b/404.html @@ -4,13 +4,13 @@ math.gl - +
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tokens.")),(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},(0,r.kt)("img",{alt:"quadkey",src:a(4749).Z,title:"quadkey",width:"1252",height:"636"})),(0,r.kt)("td",{parentName:"tr",align:null},(0,r.kt)("strong",{parentName:"td"},(0,r.kt)("inlineCode",{parentName:"strong"},"@math.gl/dggs-quadkey"))),(0,r.kt)("td",{parentName:"tr",align:null},"Get geometry of QuadKey tokens")),(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},(0,r.kt)("img",{alt:"s2",src:a(8477).Z,title:"s2",width:"1124",height:"588"})),(0,r.kt)("td",{parentName:"tr",align:null},(0,r.kt)("strong",{parentName:"td"},(0,r.kt)("inlineCode",{parentName:"strong"},"@math.gl/dggs-s2"))),(0,r.kt)("td",{parentName:"tr",align:null},"Get geometry of S2 tokens.")))),(0,r.kt)("br",null),"In addition, math.gl provides a few deprecated legacy modules, to avoid breaking older applications.",(0,r.kt)("br",null),(0,r.kt)("br",null),(0,r.kt)("table",null,(0,r.kt)("thead",{parentName:"table"},(0,r.kt)("tr",{parentName:"thead"},(0,r.kt)("th",{parentName:"tr",align:null},"Legacy Module"),(0,r.kt)("th",{parentName:"tr",align:null},"Description"))),(0,r.kt)("tbody",{parentName:"table"},(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},(0,r.kt)("strong",{parentName:"td"},(0,r.kt)("inlineCode",{parentName:"strong"},"math.gl"))),(0,r.kt)("td",{parentName:"tr",align:null},"Re-exports the API from ",(0,r.kt)("strong",{parentName:"td"},(0,r.kt)("inlineCode",{parentName:"strong"},"@math.gl/core")),'. An "alias" for ',(0,r.kt)("strong",{parentName:"td"},(0,r.kt)("inlineCode",{parentName:"strong"},"@math.gl/core"))," to avoid breaking old applications.")),(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},(0,r.kt)("strong",{parentName:"td"},(0,r.kt)("inlineCode",{parentName:"strong"},"viewport-mercator-project"))),(0,r.kt)("td",{parentName:"tr",align:null},"Re-exports the Web Mercator projection utilities in ",(0,r.kt)("strong",{parentName:"td"},(0,r.kt)("inlineCode",{parentName:"strong"},"@math.gl/web-mercator")),". 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The goal was to independently usable set of 3D and Geospatial math modules.")),(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},"2018"),(0,r.kt)("td",{parentName:"tr",align:null},"v2.0"),(0,r.kt)("td",{parentName:"tr",align:null},"The math.gl API started to mature.")),(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},"2019"),(0,r.kt)("td",{parentName:"tr",align:null},"v3.0"),(0,r.kt)("td",{parentName:"tr",align:null},"A collaboration with the Cesium team around 3D Tiles led to parts of the Cesium math library were ported into the ",(0,r.kt)("inlineCode",{parentName:"td"},"math.gl/geospatial")," and ",(0,r.kt)("inlineCode",{parentName:"td"},"@math.gl/culling")," modules.")),(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},"2020+"),(0,r.kt)("td",{parentName:"tr",align:null},"v3.x"),(0,r.kt)("td",{parentName:"tr",align:null},"Additional geospatial modules have gradually been added to support more advanced use cases for deck.gl.")),(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},"2022"),(0,r.kt)("td",{parentName:"tr",align:null},"v3.6"),(0,r.kt)("td",{parentName:"tr",align:null},"Code base fully rewritten in TypeScript.")),(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},"2023"),(0,r.kt)("td",{parentName:"tr",align:null},"v4.0"),(0,r.kt)("td",{parentName:"tr",align:null},"ES module support. gl-matrix was removed as a dependency and math.gl became fully stand-alone.")))),(0,r.kt)("h2",{id:"attributions"},"Attributions"),(0,r.kt)("p",null,"math.gl was inspired by and built upon some of the most proven open source JavaScript math libraries:"),(0,r.kt)("ul",null,(0,r.kt)("li",{parentName:"ul"},(0,r.kt)("a",{parentName:"li",href:"http://glmatrix.net/"},(0,r.kt)("inlineCode",{parentName:"a"},"gl-matrix"))," - math.gl classes use gl-matrix under the hood"),(0,r.kt)("li",{parentName:"ul"},"THREE.js math library - math.gl classes are API-compatible with a subset of the THREE.js classes and pass THREE.js test suites."),(0,r.kt)("li",{parentName:"ul"},"The CesiumJS math library (Apache2) - The geospatial and culling modules were ported from Cesium code base.")),(0,r.kt)("h2",{id:"license"},"License"),(0,r.kt)("p",null,"MIT license. 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-

Introduction

Welcome to math.gl! math.gl is JavaScript (TypeScript) math library focused on geospatial and 3D use cases. Designed as a composable, modular toolbox. math.gl provides a core module with classic vector and matrix classes, and a suite of optional modules implementing various aspects of geospatial and 3D math.

While math.gl is highly optimized for use with the WebGL and WebGPU APIs, it has no WebGL dependencies and is designed to be usable in any application.

Features

  • 3D math - Basic vectors and matrices, as well as 3D primitives and culling: @math.gl/types, @math.gl/core, @math.gl/culling
  • Geospatial projections - Support for a variety of geospatial projections @math.gl/geospatial, @math.gl/geoid, @math.gl/proj4, @math.gl/web-mercator
  • Geospatial utilities - Cutting polygons and calculating sun position and direction @math.gl/polygon, @math.gl/sun
  • Discrete Global Grids - Standardized interfaces to a number of the major discrete global grids. @math.gl/dggs-geohash, @math.gl/dggs-quadkey, @math.gl/dggs-s2

Modules

math.gl is a toolbox that offers a suite of composable modules.

Core math librariesModule Description
@math.gl/typesBasic math type helpers (NumericArray etc)
core@math.gl/core3D math classes (vectors, matrices, etc)
culling@math.gl/cullingBounding volumes and intersection testing.
Geospatial math librariesModule Description
geospatial@math.gl/geospatialEllipsoidal math for WGS84 coordinates.
geoid@math.gl/geoidEarth Gravity Model support .
@math.gl/polygonPolygon math, including geospatial cutting etc.
@math.gl/proj4Conversion between coordinate reference systems.
@math.gl/sunSolar position / direction from position and time.
@math.gl/web-mercatorSupports 3D Web Mercator (spherical) projections.
DGGS (Discrete global grid support) librariesModule Description
geohash@math.gl/dggs-geohashGet geometry of GeoHash tokens.
quadkey@math.gl/dggs-quadkeyGet geometry of QuadKey tokens
s2@math.gl/dggs-s2Get geometry of S2 tokens.

In addition, math.gl provides a few deprecated legacy modules, to avoid breaking older applications.

Legacy ModuleDescription
math.glRe-exports the API from @math.gl/core. An "alias" for @math.gl/core to avoid breaking old applications.
viewport-mercator-projectRe-exports the Web Mercator projection utilities in @math.gl/web-mercator. The viewport-mercator-project repository was moved to math.gl in Oct 2019.

Supported Browsers and Node Versions

math.gl is fully supported on:

  • Evergreen browsers: Recent versions of Chrome, Safari, Firefox, Edge etc.
  • Node.js: Active and Maintenance LTS releases

History

YearVersionDescription
2015N/A@math.gl/core classes were created as part of luma.gl v4, as a set of class wrappers for gl-matrix for luma.gl and deck.gl frameworks.
2017v1.0math.gl was broken out into its own repository to manage luma.gl growth. The goal was to independently usable set of 3D and Geospatial math modules.
2018v2.0The math.gl API started to mature.
2019v3.0A collaboration with the Cesium team around 3D Tiles led to parts of the Cesium math library were ported into the math.gl/geospatial and @math.gl/culling modules.
2020+v3.xAdditional geospatial modules have gradually been added to support more advanced use cases for deck.gl.
2022v3.6Code base fully rewritten in TypeScript.
2023v4.0ES module support. gl-matrix was removed as a dependency and math.gl became fully stand-alone.

Attributions

math.gl was inspired by and built upon some of the most proven open source JavaScript math libraries:

  • gl-matrix - math.gl classes use gl-matrix under the hood
  • THREE.js math library - math.gl classes are API-compatible with a subset of the THREE.js classes and pass THREE.js test suites.
  • The CesiumJS math library (Apache2) - The geospatial and culling modules were ported from Cesium code base.

License

MIT license. The libraries that the core @math.gl/core module are built on (e.g. gl-matrix) are also all open source and MIT licensed.

The @math.gl/geospatial and @math.gl/culling modules include Cesium-derived code which is Apache2 licensed.

math.gl will never include any code that is not under permissive license.

- +

Introduction

Welcome to math.gl!

math.gl is TypeScript math library focused on geospatial and 3D use cases. Designed as a composable, modular toolbox. math.gl provides a core module with the standard complement of vector and matrix classes, and a suite of optional modules implementing various aspects of geospatial and 3D math.

math.gl is optimized for use with WebGL and WebGPU, however it is not a GPU math library, meaning that it has no GPU dependencies and is designed to be usable in any application.

Features

  • Core classes - Basic vectors and matrices: @math.gl/types, @math.gl/core
  • Geospatial projections - Support for a variety of geospatial projections @math.gl/geospatial, @math.gl/geoid, @math.gl/proj4, @math.gl/web-mercator
  • Geospatial utilities - Cutting polygons and calculating sun position and direction @math.gl/polygon, @math.gl/sun
  • Discrete Global Grids - Standardized interfaces to a number of the major discrete global grids. @math.gl/dggs-geohash, @math.gl/dggs-quadkey, @math.gl/dggs-s2
  • 3D math - 3D primitives and culling: @math.gl/culling

Modules

math.gl is a toolbox that offers a suite of composable modules.

Core math librariesModule Description
@math.gl/typesBasic math type helpers (NumericArray etc)
core@math.gl/coreBasic math classes (vectors, matrices, etc)
Geospatial math librariesModule Description
geospatial@math.gl/geospatialEllipsoidal math for WGS84 coordinates.
geoid@math.gl/geoidEarth Gravity Model support .
@math.gl/polygonPolygon math, including geospatial cutting etc.
@math.gl/proj4Conversion between coordinate reference systems.
@math.gl/sunSolar position / direction from position and time.
@math.gl/web-mercatorSupports 3D Web Mercator (spherical) projections.
DGGS (Discrete global grid support) librariesModule Description
geohash@math.gl/dggs-geohashGet geometry of GeoHash tokens.
quadkey@math.gl/dggs-quadkeyGet geometry of QuadKey tokens
s2@math.gl/dggs-s2Get geometry of S2 tokens.
3D math librariesModule Description
culling@math.gl/cullingBounding volumes and intersection testing.

In addition, math.gl provides a few deprecated legacy modules, to avoid breaking older applications.

Legacy ModuleDescription
math.glRe-exports the API from @math.gl/core. An "alias" for @math.gl/core to avoid breaking old applications.
viewport-mercator-projectRe-exports the Web Mercator projection utilities in @math.gl/web-mercator. The viewport-mercator-project repository was moved to math.gl in Oct 2019.

Supported Browsers and Node Versions

math.gl is fully supported on:

  • Evergreen browsers: Recent versions of Chrome, Safari, Firefox, Edge etc.
  • Node.js: Active and Maintenance LTS releases

History

YearVersionDescription
2015N/A@math.gl/core classes were created as part of luma.gl v4, as a set of class wrappers for gl-matrix for luma.gl and deck.gl frameworks.
2017v1.0math.gl was broken out into its own repository to manage luma.gl growth. The goal was to independently usable set of 3D and Geospatial math modules.
2018v2.0The math.gl API started to mature.
2019v3.0A collaboration with the Cesium team around 3D Tiles led to parts of the Cesium math library were ported into the math.gl/geospatial and @math.gl/culling modules.
2020+v3.xAdditional geospatial modules have gradually been added to support more advanced use cases for deck.gl.
2022v3.6Code base fully rewritten in TypeScript.
2023v4.0ES module support. gl-matrix was removed as a dependency and math.gl became fully stand-alone.

Attributions

math.gl was inspired by and built upon some of the most proven open source JavaScript math libraries:

  • gl-matrix - math.gl classes use gl-matrix under the hood
  • THREE.js math library - math.gl classes are API-compatible with a subset of the THREE.js classes and pass THREE.js test suites.
  • The CesiumJS math library (Apache2) - The geospatial and culling modules were ported from Cesium code base.

License

MIT license. The libraries that the core @math.gl/core module are built on (e.g. gl-matrix) are also all open source and MIT licensed.

The @math.gl/geospatial and @math.gl/culling modules include Cesium-derived code which is Apache2 licensed.

math.gl will never include any code that is not under permissive license.

+ \ No newline at end of file diff --git a/docs/developer-guide/debugging.html b/docs/developer-guide/debugging.html index f975dd7c..2503da31 100644 --- a/docs/developer-guide/debugging.html +++ b/docs/developer-guide/debugging.html @@ -4,13 +4,13 @@ Debugging | math.gl - +

Debugging

This article is a work in progress.

About Validation and Debug Support

TBA:

  • Turning on an off
  • performance implications

About "Printing"

Generating a string representation of a math.gl object with desired precision and formatting.

Every math.gl object has a formatString({...opts}) method that allows you to stringify an object with special options set. Each object also defines the built-in JavaScript function toString() to call formatString() with the global printing options in the math.gl config object.

  • toString and formatString methods print with controllable precision
Print ParameterDefaultDescription
printPrecision4Number of significant digits
printTypesfalsePrints the name of the math.gl type (e.g. Vector3[...] instead of [...]
printDegreesfalsePrints degrees instead of radians (e.g. for Euler and SphericalCoordinates)
printRowMajortruePrints matrices as row major which makes them look more familiar instead of as column major (which is how they are stored internally for WebGL compatibility).
- + \ No newline at end of file diff --git a/docs/developer-guide/external-frameworks.html b/docs/developer-guide/external-frameworks.html index 9ef8ff89..e7f5a573 100644 --- a/docs/developer-guide/external-frameworks.html +++ b/docs/developer-guide/external-frameworks.html @@ -4,13 +4,13 @@ Using with Other Frameworks | math.gl - +

Using with Other Frameworks

math.gl has made some efforts to be "interoperable" with other major JavaScript math frameworks.

Using with gl-matrix

API comparison

The math.gl Matrix and Vector class APIs are inspired by the popular gl-matrix library, and it is possible to use gl-matrix together with math.gl.

Sometimes, in code that is very frequently executed, working with directly with gl-matrix can sometimes provide better performance than math.gl, mainly by avoiding object creation. However in such cases you may also be able to use pre-created "scratch objects" in math.gl to achieve similar performance.

To learn more about gl-matrix, the gl-matrix docs are a good start.

Using with THREE.js

math.gl is partially compatible with the THREE.js math API. In fact, math.gl includes a fork of the math test suite from THREE.js, parts of which pass cleanly when run using the math.gl core classes (admittedly with a few disabled cases).

Method Interoperability

In particular, the basic math.gl math classes have implementations of most of the methods that THREE.js defines.

math.glTHREE.jsNotable differences
Vector2THREE.Vector2length() => len()
Vector3THREE.Vector3ditto
Vector4THREE.Vector4ditto
Matrix3THREE.Matrix3Math.gl stores in column-major order by default
Matrix4THREE.Matrix4ditto

Colum-Major vs. Row-Major Matrices

By default, math.gl stores matrices in column-major order internally (while exposing a row-major friendly interface), whereas THREE.js stores matrices in row-major order.

Array.length()

Since math.gl's classes are subclasses of JavaScripts built-in Array class, the length property has the special meaning defined by Array, so it is not possible to implement the Vector.length() method defined by THREE.js. Instead a Vector.len() method is offered on math.gl Vector classes.

Cross-Library Convenience Methods

A complication with THREE.js is that the framework is not strict about separating the library into independent layers. Thus the THREE math classes have convenience methods that accept other THREE.js objects such Geometries and BufferAttributes. These methods can not be implemented in math.gl.

- + \ No newline at end of file diff --git a/docs/developer-guide/geospatial/dggs.html b/docs/developer-guide/geospatial/dggs.html index 60a49831..86366d53 100644 --- a/docs/developer-guide/geospatial/dggs.html +++ b/docs/developer-guide/geospatial/dggs.html @@ -4,7 +4,7 @@ Discrete Global Grids | math.gl - + @@ -12,7 +12,7 @@

Discrete Global Grids

Discrete global grid systems are powerful tools that enables us to convert geospatial data into a common, easy-to-analyze form.

Why DGGS in math.gl

Today there are multiple DGGS grid systems, and it is not unusual for an application to have to work with more than one DGGS. This can require working with a set of independent DGGS libraries with large API surfaces and subtly different API conventions, which can be taxing for implementors and maintainers.

We found that there is a value in having a common set of small, easy-to-use DGGS libraries that work with common API conventions.

Goals

The DGGS support in math.gl is currently focused on decoding cell indexes or tokens into center points (lng/lat) or cell boundary polygons.

Encoding (lng/lat to cell index) and advanced operations (child/neighbor calculation, polygon fills etc) are not currently included. Some basic encoding may be included in the future, however it is a goal to keep these libraries fairly small, and the intention is not to eventually fully duplicate large existing DGGS libraries.

Supported Grid Systems

DGGSModuleFunctionality
GeoHash@math.gl/dggs-geohashGet geometry of GeoHash tokens.
QuadKey@math.gl/dggs-quadkeyGet geometry of QuadKey tokens
S2@math.gl/dggs-s2Get geometry of S2 tokens.
H3h3-js *Get geometry of H3 tokens.

Note that h3-js is not a math.gl library. For H3 it is recommended to work directly with the H3 JavaScript bindings.

H3 API Conventions

In terms of API design and nomenclature, the golden standard for DGGS systems at this time is arguably H3, in terms of functionality, number of languages and platforms supported, community activity etc.

Rather than expose the original function names as in the existing JavaScript libraries for each DGGS, math.gl applies API naming convention based on the H3 API.

FunctionH3S2QuadKeyGeoHash
Get cell centergetH3LngLatgetS2LngLatgetQuadKeyLngLatgetGeoHashLngLat
Get cell boundarygetH3BoundarygetS2BoundarygetQuadKeyBoundarygetGeoHashBoundary
Get cell boundary flatgetH3BoundaryFlatgetS2BoundaryFlatgetQuadKeyBoundaryFlatgetGeoHashBoundaryFlat

Comparison of DGGS Systems

CharacteristicH3S2QuadKeyGeoHash
Cell shapeHexagon"square"squaresquare
Cell area"constant"variesvariesvaries
Neighbor distance"constant"1 or 1.4...1 or 1.4...1 or 1.4...
Child cells7444
Exact hierarchyNoYesYesYes

H3

H3 is now widely used across the geospatial industry (it was initially developed at Uber). While not directly supported by math.gl, H3 is in fact the DGGS we would recommend for most applications.

  • Extensive, optimized, evolving API.
  • Superb cross-language support.
  • Equal distance between neighboring cells
  • Similar size between all cells.
  • K-ring formation for filtering and convolutions

Downsides:

  • More complex projection math.

S2

S2 works well when exact aggregation and subdivision are needed but has some disadvantages when e.g. neighbor cell calculations are important

GeoHash

Geohash is common choice in the open source word.

Good cross-language support.

QuadKey

Bing Maps uses a quadkey structure as their tiling scheme. Here is an overview of the concept

  • Quadtrees are more predictable in that each level spans a square (at least in terms of coordinates), whereas in geohash representation sometimes squares sometimes rectangles are spanned.
- + \ No newline at end of file diff --git a/docs/developer-guide/geospatial/geospatial-models.html b/docs/developer-guide/geospatial/geospatial-models.html index 10219cc1..ffb70456 100644 --- a/docs/developer-guide/geospatial/geospatial-models.html +++ b/docs/developer-guide/geospatial/geospatial-models.html @@ -4,13 +4,13 @@ Geospatial Models | math.gl - +

Geospatial Models

This section introduces some basic concepts used when modeling the Earth. The terminology and descriptions align with the WGS (World Geodetic System).

Earth Models

Earth ModelModeled ByDescription
SphereWeb MercatorEarth is a sphere. Permits fast visualization. Mainly used in the web mercator projection to quickly project ellipsoidal coordinates on a flat surface, with less than 0.5% error.
EllipsoidWGS84Earth is a (rotationally) flattened ellipsoid centered at Earth's center of gravity. This model is normally used to express WGS coordinates.
GeoidEarth Gravity ModelThe shape that the ocean surface (extended through the continents) would take because of gravity and rotation of the Earth (ignoring winds, tides etc). It is a lumpy, roughly spherical object.

Earth Gravity Models

The Earth geoid can be calculated as an additive refinement of the elevation at each point on the ellipsoid.

ModelResolutionSizeNotes
EGM84-300.5 degreesPart of WGS84. Combined old GRS 80 with Doppler, satellite laser ranging and Very Long Baseline Interferometry (VLBI).
EGM840.5 degrees.
EGM9615'x15'Airborne gravity surveys
EGM20082.5'x2.5'GRACE Satellite missions

The additive refinement is calculated using spherical harmonics using big coefficent files.

Newer models do provide additional precision, at the expense of considerable memory size for the coefficient files (and additional computational cost).

- + \ No newline at end of file diff --git a/docs/developer-guide/geospatial/web-mercator-coordinates.html b/docs/developer-guide/geospatial/web-mercator-coordinates.html index 70de79b4..f5c02368 100644 --- a/docs/developer-guide/geospatial/web-mercator-coordinates.html +++ b/docs/developer-guide/geospatial/web-mercator-coordinates.html @@ -4,7 +4,7 @@ Web Mercator Coordinates | math.gl - + @@ -16,7 +16,7 @@ web mercator projection see, so scaling will depend on the viewport center and any linear scale factor should only be expected to be locally correct.

- + \ No newline at end of file diff --git a/docs/developer-guide/geospatial/web-mercator-offset-accuracy.html b/docs/developer-guide/geospatial/web-mercator-offset-accuracy.html index c3989be2..0c12164f 100644 --- a/docs/developer-guide/geospatial/web-mercator-offset-accuracy.html +++ b/docs/developer-guide/geospatial/web-mercator-offset-accuracy.html @@ -4,13 +4,13 @@ Accuracy of Offset Projection | math.gl - +

Accuracy of Offset Projection

getDistanceScales offers a cheap way to project lng/lat or meter offset to pixels. It is useful when using the GPU to project a cluster of coordinates near an origin point, without suffering the precision loss of WebGL.

This article discusses the usage and accuracy of the distance scales.

Meter offset to pixels

Regular meter offset to pixels projection:

uniform vec3 unitsPerMeter;
vec3 meters_offset_to_pixels_offset(vec3 meters) {
return meters * unitsPerMeter;
}

When getDistanceScales is called with flag highPrecision: true, it generates additional multipliers to compensate for precision loss over latitude change. More precise meter offset to pixels projection:

uniform vec3 unitsPerMeter;
uniform vec3 unitsPerMeter2;
vec3 meters_offset_to_pixels_offset_adjusted(vec3 meters) {
return meters * (unitsPerMeter + unitsPerMeter2 * meters.y);
}

Accuracy at San Francisco (37N, z = 12):

RX unadjustedX adjusted
100 metersoff by -0.000 pixels, 0.001%off by 0.000 pixels, 0.001%
1000 metersoff by -0.008 pixels, 0.012%off by 0.000 pixels, 0.001%
5000 metersoff by -0.200 pixels, 0.060%off by 0.002 pixels, 0.001%
10000 metersoff by -0.804 pixels, 0.121%off by 0.003 pixels, 0.000%
30000 metersoff by -7.277 pixels, 0.366%off by -0.021 pixels, 0.001%

Accuracy at high latitude (75N, z = 12):

RX unadjustedX adjusted
100 metersoff by -0.001 pixels, 0.006%off by 0.000 pixels, 0.001%
1000 metersoff by -0.130 pixels, 0.061%off by 0.001 pixels, 0.001%
5000 metersoff by -3.290 pixels, 0.309%off by -0.001 pixels, 0.000%
10000 metersoff by -13.200 pixels, 0.620%off by -0.044 pixels, 0.002%
30000 metersoff by -119.884 pixels, 1.877%off by -1.473 pixels, 0.023%

LngLat offset to pixels

Regular lng_lat offset to pixels projection:

uniform vec3 unitsPerDegree;
vec3 lnglat_offset_to_pixels_offset(vec3 lngLatZ) {
return lngLatZ * unitsPerDegree;
}

When getDistanceScales is called with flag highPrecision: true, it generates additional multipliers to compensate for precision loss over latitude change. More precise meter offset to pixels projection:

uniform vec3 unitsPerDegree;
uniform vec3 unitsPerDegree2;
vec3 lnglat_offset_to_pixels_offset_adjusted(vec3 lngLatZ) {
return lngLatZ * (unitsPerDegree + unitsPerDegree2 * lngLatZ.y);
}

Accuracy at San Francisco (37N, z = 12):

RY unadjustedY adjusted
0.001 degreesoff by -0.000 pixels, 0.001%off by -0.000 pixels, 0.000%
0.01 degreesoff by -0.005 pixels, 0.007%off by -0.000 pixels, 0.000%
0.05 degreesoff by -0.125 pixels, 0.034%off by -0.000 pixels, 0.000%
0.1 degreesoff by -0.499 pixels, 0.068%off by -0.001 pixels, 0.000%
0.3 degreesoff by -4.508 pixels, 0.204%off by -0.022 pixels, 0.001%

Accuracy at high latitude (75N, z = 12):

RY unadjustedY adjusted
0.001 degreesoff by -0.001 pixels, 0.003%off by -0.000 pixels, 0.000%
0.01 degreesoff by -0.081 pixels, 0.034%off by -0.000 pixels, 0.000%
0.05 degreesoff by -2.038 pixels, 0.172%off by -0.005 pixels, 0.000%
0.1 degreesoff by -8.172 pixels, 0.345%off by -0.039 pixels, 0.002%
0.3 degreesoff by -74.258 pixels, 1.046%off by -1.055 pixels, 0.015%
- + \ No newline at end of file diff --git a/docs/developer-guide/get-started.html b/docs/developer-guide/get-started.html index 914813c4..f64dccd8 100644 --- a/docs/developer-guide/get-started.html +++ b/docs/developer-guide/get-started.html @@ -4,13 +4,13 @@ Get Started | math.gl - +

Get Started

Installation

If using a bundler like webpack to build your app with npm modules, use npm or yarn to install @math.gl/core and any other math.gl modules you need.

npm install @math.gl/core

TypeScript

Type definitions are provided with each module. There is no need to install any separate types.

ESM modules

Since v4.0, math.gl is published as ES modules, but with a CommonJS named export. This setup should work automatically for most applications and bundlers.

- + \ No newline at end of file diff --git a/docs/developer-guide/math/coordinate-systems.html b/docs/developer-guide/math/coordinate-systems.html index 60c25129..e7fa4467 100644 --- a/docs/developer-guide/math/coordinate-systems.html +++ b/docs/developer-guide/math/coordinate-systems.html @@ -4,13 +4,13 @@ 3D Coordinate Systems | math.gl - +

3D Coordinate Systems

This article is a work in progress.

There are many possible ways to represent points in space using coordinates, e.g. rectangular, elliptical, polar/spherical, etc. Which coordinate system is the best depends entirely on the problem at hand. When working with specific geometrical problems, it is often the case that the required mathematical operations become more simple in a certain coordinate system which means that it is worth being familiar both with a few different coordinate system and also how to convert between them.

math.gl provides support for a couple of 3D coordinate systems:

  • Rectilinear (Vector3) - Typically used to represent standard Cartesian space
  • Spherical (SpericalCoordinates) - Two angles representing point on sphere and a distance from center
  • Projective/Homogeneous (Vector4) - These are coordinates in "projective" 3-space. The purpose of these is explained in link

Converting between Coordinate Systems

Note that each coordinate system ultimately specifies the same point

Converting within Coordinate Systems

Remarks

  • Note that a similar situation applies for rotations, where different representations are possible (e.g. Euler angles, Quaternions, Axis/angle, 4x4 matrices) and the choice of a "best" representation often depends on the problem at hand.
- + \ No newline at end of file diff --git a/docs/developer-guide/math/floating-point.html b/docs/developer-guide/math/floating-point.html index a2b68d08..e642431a 100644 --- a/docs/developer-guide/math/floating-point.html +++ b/docs/developer-guide/math/floating-point.html @@ -4,13 +4,13 @@ Floating Point | math.gl - +

Floating Point

This article is a work in progress.

Precision

About Comparisons

Due to small rounding errors, exact equality is often not a reliable way to compare floating point numbers. Therefore the default equals operation checks that two numbers are within a small delta.

There is also an exactEquals method that compares the floating point values directly.

return Math.abs(a - b) <= config.EPSILON * Math.max(1.0, Math.abs(a), Math.abs(b));
  • Floating point comparison implementation in gl-matrix and alternatives (links)
  • Comparisons
- + \ No newline at end of file diff --git a/docs/developer-guide/math/homogeneous-coordinates.html b/docs/developer-guide/math/homogeneous-coordinates.html index dcaa0ad5..931d8076 100644 --- a/docs/developer-guide/math/homogeneous-coordinates.html +++ b/docs/developer-guide/math/homogeneous-coordinates.html @@ -4,13 +4,13 @@ Homogeneous Coordinates | math.gl - +

Homogeneous Coordinates

This article is a work in progress.

The math.gl Vector4 class is not normally used to represent four dimensonal points. Instead it is intended to be used to calculate with 3 dimensonal homogeneous coordinates, as defined by projective geometry.

Mathematically, in projective geometry, each Vector4 is interpreted as a point on a 3D line through the origin. And it is this line that is the primary object, in the sense that the point is only considered to be one of infinintely many "representatives" of that a line through the origin. Dividing xyz with the same number will generate another point, or 'representative' of the same line

The main reason homogeneous coordinates and projective geometry are used in 3D graphics programming is that they allow perspective projection and translations to be represented as linear transformations using 4x4 matrices.

The W Coordinate

Mathematically, homogeneous coordinates add one extra dimension to represent a number. In the 3 dimensional computer graphics case, it is customary to refer to the extra (4th) components as w. Mathematically, the w coordinate indicates which representative along the projective line.

There is a straightforward graphical interpretation of the w coordinate: During projection of a set of homogeneous vectors onto a plane at distance 1 from the origin, all the vectors are normalized so that their w coordinates are 1 by dividing xyz with w. which leads to the following graphical interpretation:

wGraphical Interpretation
> 1your object will look smaller
< 1your object will look bigger
= 0will cause a crash or undefined behavior
< 0will flip your object (upside-down, back-to-front, ...)

Both math.gl and typical GPUs do not support calculations on homogeneous coordinates with a w component of zero. (However, zero wcoordinates play a very important role in general projective geometry, see "Background" below).

Practical Usage

Projective Transformation

A general projective transformation matrix has the following format

c0c1c2projxc1c2c3projyc2c3c4projztransxtransytranszscaleglobal
<mo>.</mo>

<mfenced open="[" close="]">
<mtable>
<mtr><mtd columnalign="center"><mi>x</mi></mtd></mtr>
<mtr><mtd columnalign="center"><mi>y</mi></mtd></mtr>
<mtr><mtd columnalign="center"><mi>z</mi></mtd></mtr>
<mtr><mtd columnalign="center"><mi>w</mi></mtd></mtr>
</mtable>
</mfenced>

Translation of 3D coordinates

Linear transformations on a vector space can not move the origin, they can only scale and rotate.

Translations leave the w coordinate unchanged.

As can be seen in the general format of the projection matrix, setting w to 0 prevents a vector from picking up the translations when multiplied with a 4x4 matrix. (easy to see as the translations are stored in the final column of the transposed matrix)

Perspective Transformation

Note that in general, a perspective transformation (i.e. multipliying) do change the w coordinate of the Vector4, so vectors must be "scaled" after transformation when used in JavaScript.

GPU Note: the GPU automatically divides vec4 xyz components with w when they are returned from the vertex shader (when homogeneous coordinates are returned from the vertex shader (typically by assigning a vec4 to gl_Position). This can be an important detail to be aware of when comparing JavaScript and GLSL code, and also when working in screen space (post-projection) in the vertex shader, in which case you typically do need to perform the w scaling yourself.

Background Information

Some fun facts to provide additional context around homogeneous coordinates.

Projective geometry was coordinatized (in the form or homogeneous coordinates) in the early 1800s by Plücker and Möbius, almost 200 years after the coordinatization of "affine" geometry by Descartes.

There is a special notation for homogeneous coordinate vectors that emphasizes the relative aspect of the values:

xyz

However, in mathematics, one of the most important aspects of projective geometry is that it can be used to avoid handling of special cases (this aspect is not used in math.gl). Essentially, in contrast to line equations in affine geometry, projective geometry allows parallel lines to be represented by adding a set of additional points in the form of a "plane at infinity" (which is represented by w=0). This is powerful as it makes it possible to e.g. make statements about geometry (such as two lines always meet in one point) without having to make tedious exceptions for parallel lines.

- + \ No newline at end of file diff --git a/docs/developer-guide/math/rotations.html b/docs/developer-guide/math/rotations.html index 04fafa40..da2e2fb6 100644 --- a/docs/developer-guide/math/rotations.html +++ b/docs/developer-guide/math/rotations.html @@ -4,7 +4,7 @@ 3D Rotations | math.gl - + @@ -13,7 +13,7 @@ RR = I

Note that a matrix R satisfying this can also include an inversion (improper rotation matrix)

Converting between Rotation Representations

new Euler();
new Euler();

Executing Rotation Transformations

While Euler angles are often a good way to specify 3D rotations, they can not directly be used to transfor points or vectors. To do that, they have to be converted to .

Rotations using Rotation Matrices

A rotation matrix

T RR = I

Combining Rotations

The fact that rotations. They can either be combined as w

Math with Euler Angles

Math with Quaternions

Interpolating Rotations

To avoid issues with gimbal locks and flips, it is recommended to use quaternions when interpolating rotations.

Calculate the quaternion that represents the rotation you want to apply (e.g. moves the start rotation to the target rotation), and then just interpolate q with the identity quaternion using slerp(). The resulting quaternion can then be used directly to transform Vectors or it can be transformed into a Matrix4 transformation matrix.

  const qUnit = new Quaternion();
const qTarget = new Quaternion(...);

for (let ratio = 0; ratio < 1.0; ratio += 0.1) {
const qInterpolated = new Quaternion().slerp(qUnit, qTarget, ratio);
}

Background: Rotations are Complicated

If you are new to working with 3D rotations it can be good to have an awareness of how they differ mathematically from 2D rotations

In two dimensions, rotations represent a highly structured and intuitive set of operations:

  • A series of 2D rotations can be applied in any order (they commute).
  • The combination of two 2D rotations can always be expressed as another single rotation (simply by taking the sum of the angles of the two rotations).
  • Any 2D rotation can be fully parametrized by a single value (the "angle").

However, in three dimensions, rotations start to loose some "structure":

  • In 3D, rotations are no longer order-independent (they are not commutative), meaning that applying the same two rotations in different order will often yield different results.
  • However, by Euler's Rotation Theorem, two 3D rotations around the origin can still always be expressed as (combined into) another single 3D rotation around the origin.
  • Also, a 3D rotation requires not two, but three values to be fully specified.

While math.gl does not support rotations in four and higher dimensions, it should be no surprised that rotations continue to "loose structure" as the number of dimensions increase:

  • Higher dimension rotations are also not commutative.
  • Euler's Rotation Theorem no longer holds. There are now two different "types" of basic rotations, and the combination of two rotations will in general not even result in another "rotation", but another, more complex transformation.
  • In addition, the number of parameters (degrees of freedom) required to fully specify a rotation grows with mind-boggling rapidity, as 2^(n-1) - 1, (meaning that e.g. a "21 dimensional rotation" would require over one million values to be fully specified).

Background: More on Euler Angles

Euler angle values

  • Axis Order - the order of rotations needs to be defined. There are 6 ways to order rotations around the three axis.
  • Choice of Axes - "Classic Euler" angles follow a Z-Y-Z, convention, rotating around the same angle first and last. However, in modern applications (e.g. Aerospace and Nautical), the "Tait-Brya"
  • Intrinsic or Extrinsic - One one also needs to define whether the angles are intrinsic or extrinsic. As a comparison:
  • three.js Euler class uses intrinsic Tait-Bryan angles. "Intrinsic" means that rotations are performed with respect to the local coordinate system. That is, for order 'XYZ', the rotation is first around the local-X axis (which is the same as the world-X axis), then around local-Y (which may now be different from the world Y-axis), then local-Z (which may be different from the world Z-axis).

Remarks

  • In this article, the word "axes" represents the plural of a (coordinate) "axis" (normally, the word "axes" refers to the X, Y and Z coordinate axes).
  • Note that one of the most efficient way to specify rotations is to use the Euler-Rodrigues parameters, which has some of the quaternion representation without requiring the introduction of quaternion algebra. math.gl does not directly support this representation although the vector/angle can easily be converted.
- + \ No newline at end of file diff --git a/docs/developer-guide/math/transformations.html b/docs/developer-guide/math/transformations.html index 8220801f..9363d7f8 100644 --- a/docs/developer-guide/math/transformations.html +++ b/docs/developer-guide/math/transformations.html @@ -4,13 +4,13 @@ Transformations | math.gl - +

Transformations

math.gl allows you to create mathematical objects and then apply transformations on those objects. Objects are typically vectors but can also be more complex object such as spheres, planes, boxes etc, and transformations are typically represented by matrices and quaternions.

Representing Transformations

Transformations can be represented in many different notations but for computational purposes it is efficient to express them as matrices, or in some cases as quaternions.

The most general transform is a 4x4 matrix. See the article on homogeneous coordinates for some advantages in using 4x4 matrices to represent transformations.

Applying transformations

Most math.gl classes offer a transform method that accepts matrices and quaternions.

// prettier-ignore
const transformedVector1 = new Vector4(1, 0, 0, 1).transform([
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1
]);
// or
const transformedVector2 = new Vector4(1, 0, 0, 1).transform(
new Matrix4([1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1])
);

The various vector classes also offer methods to transform with smaller matrices

const transformedVector1 = new Vector4(1, 0, 0, 1).transformByMatrix3([1, 0, 0, 0, 1, 0, 0, 0, 1]);
// or
const transformedVector2 = new Vector3(1, 0, 0).transformByMatrix2(new Matrix2([1, 0, 0, 1]));

Quaternion transformations are also supported on some objects

const transformedVector1 = new Vector4(1, 0, 0).transformByQuaternion([0, 0, 0, 1]);
// or
const transformedVector2 = new Vector3(1, 0, 0).transformByQuaternion(new Quaternion([1, 0, 0, 1]));

Note that <object>.transform() operations modify the object being transformed (and also return the modified object to enable "chaining" of calls).

Alternatively, transformations can also be performed via the matrix and quaternion classes. In this case, the transformation is stored in the result parameters (a new array is allocated if it result is not supplied.)

const transformedVector1 = new Vector4(1, 0, 0).transformByQuaternion([0, 0, 0, 1]);
// or
const result = new Vector3();
const transformedVector2 = new Quaternion([1, 0, 0, 1]).transformByQuaternion([1, 0, 0], result);

Types of Transformations

The basic transformations are rotations, scalings, and translations.

Composing Transformations

One of the most powerful aspects of using matrices to manage transformations is that matrices can be multiplied together using linear algebra.

This allows us to build up a complex transformation by multiplying together component parts.

Matrix4 provides a number of transformation methods ('scale', 'rotate', 'translate', ...) that allow us to build transformation matrices. These can be applied to an identity matrix (e.g. a newly created Matrix4) or to a matrix that already contains other transformations.

Order Matters

When composing (i.e. multiplying) matrices it is critical to consider the order in which they are being applied, as changing the order of component will in most cases change the resulting composite transformation. It is not hard to verify that this is consistent with geometric intuition by composing a few operations on paper.

Because of this the Matrix4 class provides two matrix multiplication methods: multiplyLeft and multiplyRight that force you to make explicit what you intend when multiplying two matrices.

All Matrix4 transformation methods ('scale', 'rotate', 'translate', ...) conceptually correspond to multiplying in a new transformation matrix from the right (although these methods internally are more efficient in that they don't create any temporary objects and they only do the minimal amount of changes to the matrix required for that specific transformation).

In the end, the point or vector to be transformed will be multiplied in from the right, which means that a typical composed transformation needs to be read in reverse order. I.e. in the example below, the vector will first be rotated, then transformed by the partialTransform, then scaled.

// Illustrates that transformations are applied in reverse order
const partialTransform = new Matrix4(...);
const fullTransform = new Matrix4()
.scale([1, -1, 1])
.multiplyRight(partialTransform)
.rotateX({radians: Math.PI});
const v = fullTransform.transformVector(new Vector4(...));

About Rotations

For more in-depth background about rotations, see the separate article on rotations.

If you have a vector with 3 elements you can rotate it around an axis and a point like so:

const v = new Vector3([1, 2, 3]).rotateZ({radians: ..., origin: [1, 1, 0]});

Decomposing Transformations

The ability to compose transformations naturally leads to the possibility of decomposing a composite transformations into its constituent parts. This is possible, with certain caveats (not all matrices are directly decomposable into rotation, translation and scale. Shear is currently not handled).

Sepcifically, the math.gl Matrix4 object exposes the getScale, getTranslation and getRotation (or getRotationMatrix3) methods are provided for this purpose:

const transform = new Matrix4()
.translate([10, 10, 0])
.rotateX(Math.PI / 4)
.scale(5);
transform.getScale(); // [5, 5, 5]
transform.getTranslation(); // [ 10, 10, 0]
- + \ No newline at end of file diff --git a/docs/developer-guide/math/view-and-projection.html b/docs/developer-guide/math/view-and-projection.html index a0c4697e..0f6787c0 100644 --- a/docs/developer-guide/math/view-and-projection.html +++ b/docs/developer-guide/math/view-and-projection.html @@ -4,13 +4,13 @@ View and Projection Matrices | math.gl - +

View and Projection Matrices

One of the major functions of any 3D math library is to let applications create view and projection matrices to enable positioning of the viewer in a 3D world and projection of 3D geometries via a field-of-view onto a flat "screen".

To set up a 4x4 view projection matrix you need a view matrix (specifying the position, direction and orientation of the camera) and a projection matrix (specifying the characteristics of the camera such as its field of view etc).

View Matrices

The purpose of the view matrix is to translate and rotate your world coordinates so that the eye is located in the origin [0, 0, 0], looking down the positive Z axis, rotated so that the right direction is up. This is called the "view coordinate system".

The purpose of the projection matrix is to transform from view coordinates to "clipspace" coordinates (which is the only coordinate system that the GPU can work directly with). If a point is between -1 and 1 (after w scaling) in clipspace, it will be rendered. The z coordinate in clipspace is also scaled (using 'near' and 'far' planes) and if between -1 and 1 it is used for depth test.

Note: while a projection matrix may generate coordinates with w !== 1, the GPU will automatically divide the xyzw coordinates with the w coordinateof any positions it receives thus and "normalize" the w coordinate. Thus, there is no need to do this scaling manually in shaders unless doing additional arithmetic in clipspace.

Creating a View Matrix

To create a view matrix

  • Matrix4.lookAt({...})

Normally positions are transformed by the view matrix. If doing work (e.g. lighting) in view space you will also want to transform other geometry such as normals.

Projection Matrices

A perspective projection typically shows everything inside a frustum (truncated pyramid) or a cube in the view space. Their job is to "scale" or "skew" the geometry inside this virtual shape into the clipspace cube, which is the coordinate system the GPU takes as input.

This projection matrices map your geometry into a "normalized box" where x and y values of -1 and 1 represent the bounds of your screen or frame buffer.

Projection matrices can also be ortographic, meaning that 3D objects are mapped via parallel lines onto the screen, rather than via a frustum.

Perspective Projection Matrix

To create a projection matrix use:

  • Matrix4.perspective({fov, aspect, near, far})

Orthographic Projection Matrix

math.gl provides the traditional function create an orhtographic projection matrix by providing the "box" extents:

  • Matrix4.ortho({right, left, top, bottom, near, far})

The extents are specified in "view space" (which is typically translated and rotated, but not scaled, world space).

Switching between Perspective and Orthographic Views

In applications it is not unusual to want to offer both perspective and orthographic views. To support this case, math.gl offers an additional method for creating orthographic projection matrix, that takes the same parameters as Matrix4.perspective(), with the addition of one additional parameter, focalDistance that selects which plane in the perspective view frustum should be used to calculate the size of the orthographic view box.

  • Matrix4.orthographic({fovy, aspect, focalDistance, near, far})

About Projection Matrices

An ortograhic projection matrix scales your view to show everything within a box. As can be seen in the matrix below, it centers your view between the bounds of the box, and scales your positions so that the box limits fall on -1 and +1 in each direction. It also does an inversion of the X and Y coordinates.

scalex......translatex...scaley...translatey......scaleztranslatez.........scaleglobal
<mo>=</mo>

<mfenced open="[" close="]">
<mtable>
<mtr>
<mtd columnalign="center"><mfrac><mn>-2</mn><mi>left - right</mi></mfrac></mtd>
<mtd columnalign="center"><mn>0</mn></mtd>
<mtd columnalign="center"><mn>0</mn></mtd>
<mtd columnalign="center"><mfrac><mi>left + right</mi><mi>left - right</mi></mfrac></mtd>
</mtr>
<mtr>
<mtd columnalign="center"><mn>0</mn></mtd>
<mtd columnalign="center"><mfrac><mn>-2</mn><mi>bottom - top</mi></mfrac></mtd>
<mtd columnalign="center"><mn>0</mn></mtd>
<mtd columnalign="center"><mfrac><mi>bottom + top</mi><mi>bottom - top</mi></mfrac></mtd>
</mtr>
<mtr>
<mtd columnalign="center"><mn>0</mn></mtd>
<mtd columnalign="center"><mn>0</mn></mtd>
<mtd columnalign="center"><mfrac><mn>2</mn><mi>near - far</mi></mfrac></mtd>
<mtd columnalign="center"><mfrac><mi>near + far</mi><mi>near - far</mi></mfrac></mtd>
</mtr>
<mtr>
<mtd columnalign="center"><mn>0</mn></mtd>
<mtd columnalign="center"><mn>0</mn></mtd>
<mtd columnalign="center"><mn>0</mn></mtd>
<mtd columnalign="center"><mn>1</mn></mtd>
</mtr>
</mtable>
</mfenced>

Decomposing a ViewProjection Matrix

TBA

Remarks

  • As always, matrices are presented here in row major notation, however math.gl stores them internally in column major format to match WebGL conventions.
- + \ No newline at end of file diff --git a/docs/developer-guide/performance.html b/docs/developer-guide/performance.html index 42833885..19715f60 100644 --- a/docs/developer-guide/performance.html +++ b/docs/developer-guide/performance.html @@ -4,13 +4,13 @@ Performance | math.gl - +

Performance

The code vector and matrix operations in math.gl are based on gl-matrix which is designed as a high performance JavaScript 3D math library.

Since math.gl uses gl-matrix functions under the hood, math.gl's performance is usually very close to gl-matrix, but the additional conveniences in math.gl do come with a certain overhead. Understanding this overhead can help you write more performant code and work around performance issues.

In cases where javascript math calculations are performance critical, you can always use gl-matrix operations directly. See (./docs/get-started/using-with-gl-matrix.md). Essentially, since all math.gl classes inherit from Arrays they work directly as arguments to gl-matrix functions, no copying necessary.

Disabling Debug Checks

If debug mode has been turned on, math.gl checks that objects after every operation. Enabling the checks has a modest impact on performance.

import {configure, Vector2} from '@math.gl/core';
configure({debug: false});
let vector = new Vector2(NaN, NaN); // Initializes an "invalid" vector

configure({debug: true});
let vector = new Vector2(NaN, NaN); // Now throws an error. The check

Verifying that error checks are not turned on.

import {configure} from '@math.gl/core';
console.log('Debug status', configure().debug);

Minimizing Object Creation

The biggest performance issue in math.gl (and essentially all other JavaScript math libraries) is object creation cost. Creating new Vector3 and Matrix4 instances every time a calculation is made incurs significant overhead.

There are two standard techniques to avoid object creation costs.

Resuing Objects

Therefore, reusing objects where possible is an important technique to optimize performance. A typical technique is to allocate a global object in the file.

Replace

for (...) {
const v = new Vector3(x, y, z);
}

with

const tempVector = new Vector3();
for (...) {
v.set(x, y, z);
}

Note that while creating objects can be slow, copying data into a temo object (e.g. vector4.copy([1, 1, 1, 1]) or vector4.copy([1, 1, 1, 1])) is very fast.

Supplying result Objects

A number of methods, such as Matrix4.transformVector(), allocate new objects as return values. These methods typically accept an optional result argument which can be populated and returned. By providing a result value, you revent the allocation of a new object and instead reuse an object you have already allocated.

for (...) {
const v = matrix4.transformVector([x, y, z]);
// v now contains a reference to a newly allocated `Vector3` which was updated with the result of the `tranformVector` operation.
}

vs.

const tempVector = new Vector3();
for (...) {
const v = matrix4.transformVector([x, y, z], tempVector);
// v now contains a reference to `tempVector` which was updated with the result of the `tranformVector` operation.
}

Browser, OS version etc

The JavaScript engine powering Chrome and Node is still improving. The performance difference between some older Node versions was dramatic.

Benchmarking

The math.gl repository comes with a benchmark suite that you can run to see what operations are fast and which take more time in your environment.

You can run the benchmarks both in Node.js and in the browser

yarn bench
yarn bench browser

JavaScript Engine Optimizations

This section should be considered advanced, and is not required reading for the normal math.gl user. However if you are writing your own math code it can be useful to have an understanding.

To get good performance it is important to structure code so that it can be compiled and optimized by the JavaScript engine in use. math.gl focuses on optimizing for the V8 engine, since it is used both by Chrome and Node.js, however the optimizations are general and should also be relevant to other optimizing JavaScript engines.

In particular, math.gl makes efforts to ensure that the engine knows that fields in math classes contain numbers, which allows for important optimizations that can result in a ~5x performance difference for simple operations.

A good introduction to the topic can be found in JavaScript Performance Pitfalls in V8.

- + \ No newline at end of file diff --git a/docs/modules/core.html b/docs/modules/core.html index d4f6a698..5c2b9a53 100644 --- a/docs/modules/core.html +++ b/docs/modules/core.html @@ -4,13 +4,13 @@ Overview | math.gl - +

Overview

Basic 3D math classes (vectors, matrices, quaternions etc) for JavaScript.

Installation

npm install @math.gl/core

Classes

ClassDescription
Vector2Two element vector, inherits from Array
Vector3Three element vector, inherits from Array
Vector4Four element vector, inherits from Array
Matrix33x3 matrix, inherits from Array
Matrix44x4 matrix, inherits from Array
QuaternionQuaternion in [x,y,z,w] form, inherits from Array
Euler3 Euler angles and rotation order
SphericalCoordinates2 rotations and a radius

Usage

import {Vector2} from '@math.gl/core';
const vector = new Vector2(1, 2);
const x = vector[0];
const y = vector[1];

Design Goals

Some of the design goals for the math.gl core library

  • Performance - The core math.gl classes are built on top of gl-matrix. gl-matrix has a reputation for being the most performant and battle-tested JavaScript math library around.

  • Array-Based - math.gl classes (like Vector3, Matrix4) are subclasses of the built-in JavaScript Array which enables applications to use them interchangeably with plain (or typed) arrays.

  • Debug Friendly - math.gl offers optional error checking after every math operation which makes quick work of locating coding errors and bad input data. Printing support for objects (toString) also simplifies debugging.

  • Size Conscious - math.gl is published as multiple modules to let applications cherry-pick required functionality, and is optimizes dependencies for tree-shaking to make sure you only pay for (bundle) what you use.

- + \ No newline at end of file diff --git a/docs/modules/core/api-reference/euler.html b/docs/modules/core/api-reference/euler.html index 825721bc..2a21e117 100644 --- a/docs/modules/core/api-reference/euler.html +++ b/docs/modules/core/api-reference/euler.html @@ -4,13 +4,13 @@ Euler | math.gl - +

Euler

class Euler extends MathArray extends Array

A class to handle Euler rotation. More information on rotation using a Euler vector can be found here. Generally speaking the three components of the Euler object represents the roll, pitch and yaw angles and the rotation is applied according to a specific rotation order.

Usage

import {Euler} from '@math.gl/core';

Constants

  • Euler.ZYX

  • Euler.YXZ

  • Euler.XZY

  • Euler.ZXY

  • Euler.YZX

  • Euler.XYZ

  • Euler.RollPitchYaw

  • Euler.DefaultOrder (= Euler.ZYX)

  • Euler.RotationOrders = ['ZYX', 'YXZ', 'XZY', 'ZXY', 'YZX', 'XYZ'];

Members

x, y z

x, y, z angle notation (note: only corresponds to axis in XYZ orientation)

roll, pitch, yaw

roll, pitch, yaw angle notation

alpha, beta, gamma

alpha, beta, gamma angle notation

phi, theta, psi

phi, theta, psi angle notation

order

rotation order in all notations

Methods

constructor

(x = 0, y = 0, z = 0, order = Euler.DefaultOrder)

  • Number|Number[], Number, Number, Number

fromRollPitchYaw

Common ZYX rotation order

euler.fromRollPitchYaw(roll, pitch, yaw)

fromRotationMatrix

euler.fromRotationMatrix(m, order = Euler.DefaultOrder)

fromQuaternion

euler.fromQuaternion(q, order)

copy

If copied array does contain fourth element, preserves currently set order.

euler.copy(array)

set

Sets the three angles, and optionally sets the rotation order. If order is not specified, preserves currently set order.

euler.set(x = 0, y = 0, z = 0, order)

toArray

Does not copy the orientation element

euler.toArray(array = [], offset = 0)

toArray4

Copies the orientation element

euler.toArray4(array = [], offset = 0)

toVector3

euler.toVector3(optionalResult)

fromVector3

euler.fromVector3(v, order)

fromArray

euler.fromArray(array, offset = 0)

getRotationMatrix

euler.getRotationMatrix(m = new Matrix4())

Returns Matrix4 - a rotation matrix corresponding to rotations per the specified euler angles

getQuaternion

euler.getQuaternion()

Remarks

  • Attribution: inspired by THREE.js THREE.Euler class
- + \ No newline at end of file diff --git a/docs/modules/core/api-reference/math-array.html b/docs/modules/core/api-reference/math-array.html index 0c58c1ea..3b86d17a 100644 --- a/docs/modules/core/api-reference/math-array.html +++ b/docs/modules/core/api-reference/math-array.html @@ -4,13 +4,13 @@ MathArray | math.gl - +

MathArray

class MathArray extends Array

Usage

MathArray is a base class, and should not be instantiated directly.

Cloning an object

const clone = vector.clone();

Scaling with constants

const u = v.scale(-1); // Reverse direction vector

Scaling with vectors is very flexible, you can e.g. set a component to zero, or flip a component's sign.

const u = v.scale([1, 1, 0]); // Set z component to zero
const w = v.scale([1, -1, 1]); // Flip y component

Methods

clone

array.clone()

copy

array.copy(array)

set

array.set(...args)

fromArray

array.fromArray(array, offset = 0)

toString

Calls formatString with the global math.gl config.

array.toString()

formatString

array.formatString(config)

toArray

array.toArray(array = [], offset = 0)

toFloat32Array

array.toFloat32Array()

equals

array.equals(array)

exactEquals

array.exactEquals(array)

length

array.length()

lengthSquared

array.lengthSquared()

distance

array.distance(mathArray)

distanceSquared

array.distanceSquared(mathArray)

normalize

array.normalize()

validate

Checks if a MathArray contains valid values.

array.validate(array = this)

Returns false if any value fails Number.isFinite test.

check

If config.debug is true, validates the MathArray and throws an error if it does not contains valid values.

array.check(array = this)

Mote: This method is called by all mutating methods.

- + \ No newline at end of file diff --git a/docs/modules/core/api-reference/matrix.html b/docs/modules/core/api-reference/matrix.html index 552dbfcc..eac576d8 100644 --- a/docs/modules/core/api-reference/matrix.html +++ b/docs/modules/core/api-reference/matrix.html @@ -4,13 +4,13 @@ Matrix | math.gl - +

Matrix

Matrix is a base class for Matrix3 and Matrix4, providing common methods to those classes.

Methods

toString()

Returns a string representation of the matrix

setElement(): this

Sets the element at "conceptual position" M[i][j], row major indices by default

matrix3.set(i, j, value, columnMajor = false)

getElement(): number

Gets the element at "conceptual position" M[i][j], row major indices by default

matrix3.get(i, j, columnMajor = false)

getColumn(columnIndex: number [ , result: number[3]]): number[3]

Extracts a column from the matrix

setColumn(columnIndex: number, columnVector: number[3]): Matrix

Copies a column into the matrix

- + \ No newline at end of file diff --git a/docs/modules/core/api-reference/matrix3.html b/docs/modules/core/api-reference/matrix3.html index ec986e2f..028db4d9 100644 --- a/docs/modules/core/api-reference/matrix3.html +++ b/docs/modules/core/api-reference/matrix3.html @@ -4,14 +4,14 @@ Matrix3 | math.gl - +

Matrix3

A 3x3 matrix. Any arguments can be plain JavaScript arrays or other math.gl objects.

Usage

import {Matrix3} from `math.gl`;

Copy a matrix to a Matrix3 so that it can be manipulated (and mutated) with Matrix3 methods:

const IDENTITY = [1, 0, ..., 1];
const m = new Matrix3(IDENTITY).translate([1, 0]);

Invert a matrix

const inverse = matrix.invert();

Transform a vector as a point (including translations)

const transform = new Matrix3();
const vector2 = transform.transformPoint([1, 2]);
const vector3 = transform.transformPoint([1, 2, 1]);

Transform a vector as a direction (NOT including translations)

const transform = new Matrix3();
const vector2 = transform.transformDirection([1, 2]);
const vector3 = transform.transformDirection([1, 2, 1]);

Inheritance

class Matrix3 extends [Matrix](./docs/api-reference/matrix) extends [MathArray](./docs/api-reference/math-array) extends [Array](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array)

Methods

Many of the most commonly used methods are inherited from MathArray:

  • matrix3.clone()
  • matrix3.copy(array)
  • matrix3.set(...args)
  • matrix3.fromArray(array, offset = 0)
  • matrix3.toString()
  • matrix3.toArray(array = [], offset = 0)
  • matrix3.equals(array)
  • matrix3.exactEquals(array)
  • matrix3.validate(array = this)
  • matrix3.check(array = this)
  • matrix3.normalize()

Note that Matrix3 is a subclass of the built in JavaScript Array and can thus e.g. be supplied as a parameter to any function expecting an Array.

constructor()

Creates an empty Matrix3

new Matrix3()

identity(): this

Sets the matrix to the multiplicative identity matrix.

matrix3.identity()

set(...number): this

Sets the elements of the matrix.

matrix3.set(m00, m01, m02, m10, m11, m12, m20, m21, m22)

fromQuaternion(q: Quaternion): this

Sets the matrix to a transformation corresponding to the rotations represented by the given quaternion.

matrix3.fromQuaternion(quaternion)

  • quaternion (Quaternion) - the quaternion to create matrix from

determinant(): number

Returns the determinant of the matrix (does not modify the matrix).

const determinant = matrix3.determinant()

Returns (Number) - the determinant

  • If the determinant is zero, the matrix is not invertible.
  • Determinant calculation is somewhat expensive.

transpose(): this

Sets this matrix to its transpose matrix.

matrix3.transpose()

  • The transpose matrix mirrors the original matrix elements in the diagonal.

invert(): this

Sets this matrix to its inverse matrix.

matrix3.invert()

  • The inverse matrix times its original matrix is an identity matrix of the same size.

multiplyLeft(matrix: number[9]): this

Multiplies in another matrix from the left

matrix3.multiplyLeft(matrix3)

  • When using Matrix3 to transform vectors, the vectors are multiplied in from the right. This means that the multiplying in a matrix from the left will cause it to be applied last during transformation (unless additional matrices are multiplied in from the left of course).

multiplyRight(matrix: number[9]): this

matrix3.multiplyRight(matrix3)

  • When using Matrix3 to transform vectors, the vectors are multiplied in from the right. This means that the multiplying in a matrix from the left will cause it to be applied last during transformation (unless additional matrices are multiplied in from the left of course).

rotate(): this

Adds a rotation by the given angle. Equivalent to right multiplying the new transform into the matrix but more performant.

matrix3.rotate(radians)

scale(factor: number[2]): this

Adds a scaling transform, each axis can be scaled independently.

matrix3.scale(factor)

  • factor (Number) - scale factor to be applied to each axis.

matrix3.scale([x, y])

  • x (Number) - scale factor to be multiplied into x component
  • y (Number) - scale factor to be multiplied into y component

Equivalent to right multiplying the new transform into the matrix but more performant.

  • During vector transformation all coordinates will be multiplied with the given factors.
  • Scale with -1 will flip the coordinate system in that axis.
  • Scale with 0 will drop that component.

translate(offset: number[2]): this

Adds a translation to the matrix.

matrix3.translate([x, y])

  • x (Number) - translation to be added to the x component
  • y (Number) - translation to be added to the y component

Equivalent to right multiplying the new transform into the matrix but more performant.

During vector transformation the given translation values are added to each component of the vector being transformed.

transformVector()

transformVector(vector, out)

  • vector (Array|Vector2|Vector3)
  • out - unless supplied, will be a Vector2 or Vector3, matching the length of input vector. Returns out, or a newly minted Vector2 or Vector3.

Remarks

  • All transforms are effectively "right multiplied" onto the matrix (meaning that during transform they will be applied in opposite order).
  • Matrix3 is stored internally in column major format (per WebGL conventions). This only matters when you read out the matrix to use it with other software.
- + \ No newline at end of file diff --git a/docs/modules/core/api-reference/matrix4.html b/docs/modules/core/api-reference/matrix4.html index 4c9b2cde..6a578fac 100644 --- a/docs/modules/core/api-reference/matrix4.html +++ b/docs/modules/core/api-reference/matrix4.html @@ -4,7 +4,7 @@ Matrix4 | math.gl - + @@ -12,7 +12,7 @@

Matrix4

A 4x4 matrix. Any arguments to Matrix4 methods can be plain JavaScript arrays or other math.gl objects.

Usage

import {Matrix4} from `math.gl`;

Copy a matrix to a Matrix4 so that it can be manipulated (and mutated) with Matrix4 methods:

const IDENTITY = [1, 0, ..., 1];
const m = new Matrix4(IDENTITY).translate([1, 0, 0]);

Create a perspective projection matrix

const projectionMatrix = new Matrix4().perspective({fov, aspect, near, far});

Create an orthograhic projection matrix


Invert a matrix

const inverse = matrix.invert();

Transform a vector as a point (including translations)

const transform = new Matrix4();
const vector2 = transform.transformPoint([0, 0]);
const vector3 = transform.transformPoint([0, 1, 2]);
const vector4 = transform.transformPoint([0, 1, 2, 1]);

Transform a vector as a direction (NOT including translations)

const transform = new Matrix4();
const vector2 = transform.transformDirection([0, 0]);
const vector3 = transform.transformDirection([0, 1, 2]);
const vector4 = transform.transformDirection([0, 1, 2, 1]);

Inheritance

class Matrix4 extends Matrix extends MathArray extends Array`

Many basic methods are inherited:

  • matrix4.clone()
  • matrix4.copy(array)
  • matrix4.set(...args)
  • matrix4.fromArray(array, offset = 0)
  • matrix4.toString()
  • matrix4.toArray(array = [], offset = 0)
  • matrix4.equals(array)
  • matrix4.exactEquals(array)
  • matrix4.validate(array = this)
  • matrix4.check(array = this)
  • matrix4.normalize()

Since Matrix4 is a subclass of the built in JavaScript Array it can be used directly as a parameter to any function expecting an Array.

Methods

constructor()

Creates an empty Matrix4

new Matrix4()

identity(): this

Sets the matrix to the multiplicative identity matrix.

matrix4.identity()

set(...number): this

Sets the elements of the matrix.

matrix4.set(m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33)

fromQuaternion(quaternion: Quaternion): this

Sets the matrix to a transformation corresponding to the rotations represented by the given quaternion.

matrix4.fromQuaternion(quaternion)

  • quaternion (Quaternion) - the quaternion to create matrix from
frustum(options: {left: number, right: number, bottom: number, top: number, near: number, far: number}): this

Generates a frustum matrix with the given bounds. The frustum far plane can be infinite.

matrix4.frustum({left, right, bottom, top, near, far})

  • left (number) - Left bound of the frustum
  • right (number) - Right bound of the frustum
  • bottom (number) - Bottom bound of the frustum
  • top (number) - Top bound of the frustum
  • near (number) - Near bound of the frustum
  • far (number|Infinity) - Far bound of the frustum
lookAt(options?: {eye: number, center: number, up: number}): this

Generates a look-at matrix with the given eye position, focal point, and up axis

matrix4.lookAt({eye, center, up})

  • eye (Vector3|number[3]) - Position of the viewer
  • center=[0, 0, 0] (Vector3|number[3]) vec3 Point the viewer is looking at
  • up=[0, 1, 0] (Vector3|number[3]) vec3 vec3 pointing up
ortho(options: {left: number, right: number, bottom: number, top: number, near?: number, far: number}): this

Generates a orthogonal projection matrix with the given bounds

matrix4.ortho({left, right, bottom, top, near = 0.1, far = 500})

  • left (number) - Left bound of the frustum
  • right (number) - Right bound of the frustum
  • bottom (number) - Bottom bound of the frustum
  • top (number) - Top bound of the frustum
  • near (number) - Near bound of the frustum
  • far (number) - Far bound of the frustum
orthographic

Generates an orthogonal projection matrix with the same parameters as a perspective matrix (plus focalDistance).

  • Matrix4.orthographic({fovy, aspect, focalDistance, near, far})

  • fovy (number) - Vertical field of view in radians

  • aspect (number) - Aspect ratio. typically viewport width/height

  • focalDistance (number) - selects which plane in the perspective view frustum should be used to calculate the size of the orthographic view box.

  • near=0.1 (number) - Near bound of the frustum

  • far=500 (number) - Far bound of the frustum

In applications it is not unusual to want to offer both perspective and orthographic views and this method is supplied to make this as simple as possible.

perspective

Generates a perspective projection matrix with the given bounds. The frustum far plane can be infinite.

matrix4.perspective({ fovy = 45 * Math.PI - / 180, aspect = 1, near = 0.1, far = 500 })

  • fovy=45 (number) - Vertical field of view in radians (default is 45 degrees specified in radians)
  • aspect=1 (number) - Aspect ratio. typically viewport width/height
  • near=0.1 (number) - Near bound of the frustum
  • far=500 (number|Infinity) - Far bound of the frustum
determinant(): number

Returns the determinant of the matrix (does not modify the matrix).

const determinant = matrix4.determinant()

Returns (number) - the determinant

  • If the determinant is zero, the matrix is not invertible.
  • Determinant calculation is somewhat expensive.
transpose(): this

Sets this matrix to its transpose matrix.

matrix4.transpose()

  • The transpose matrix mirrors the original matrix elements in the diagonal.
invert(): this

Sets this matrix to its inverse matrix.

matrix4.invert()

  • The inverse matrix mirrors the original matrix elements in the diagonal.
multiplyLeft(matrix: number[16]): this

Multiplies in another matrix from the left

matrix4.multiplyLeft(matrix4)

  • When using Matrix4 to transform vectors, the vectors are multiplied in from the right. This means that the multiplying in a matrix from the left will cause it to be applied last during transformation (unless additional matrices are multiplied in from the left of course).
multiplyRight(matrix: number[16]): this

matrix4.multiplyRight(matrix4)

  • When using Matrix4 to transform vectors, the vectors are multiplied in from the right. This means that the multiplying in a matrix from the left will cause it to be applied last during transformation (unless additional matrices are multiplied in from the left of course).
rotateX(radians: number): this

Adds a rotation by the given angle around the X axis. Equivalent to right multiplying the new transform into the matrix but more performant.

matrix4.rotateX(radians)

rotateY(radians: number): this

Adds a rotation by the given angle around the Y axis.

rotateY(radians)

  • Equivalent to right multiplying the new transform into the matrix but more performant.
rotateZ(radians: number): this

Adds a rotation by the given angle around the Z axis.

matrix4.rotateZ(radians)

  • Equivalent to right multiplying the new transform into the matrix but more performant.
rotateXYZ(angles: [rx: number, ry: number, rz: number]): this

Adds successive rotations by the given angles around the X, Y and Z axis.

rotateXYZ([rx, ry, rz])

  • Equivalent to right multiplying the new transform into the matrix but more performant.
rotateAxis(radians: number, axis: number[3]): this

Adds successive rotations by the given angles around the X, Y and Z axis.

rotateAxis(radians, axis)

Equivalent to right multiplying the new transform into the matrix but more performant.

scale(factor: number | number[3]): this

Adds a scaling transform, each axis can be scaled independently.

matrix4.scale(factor)

  • factor (number) - scale factor to be applied to each axis.

matrix4.scale([x, y, z])

  • x (number) - scale factor to be multiplied into x component
  • y (number) - scale factor to be multiplied into y component
  • z (number) - scale factor to be multiplied into z component

Equivalent to right multiplying the new transform into the matrix but more performant.

  • During vector transformation all coordinates will be multiplied with the given factors.
  • Scale with -1 will flip the coordinate system in that axis.
  • Scale with 0 will drop that component.
translate(scale: number[3]): this

Adds a translation to the matrix.

matrix4.translate([x, y, z])

  • x (number) - translation to be added to the x component
  • y (number) - translation to be added to the y component
  • z (number) - translation to be added to the z component

Equivalent to right multiplying the new transform into the matrix but more performant.

During vector transformation the given translation values are added to each component of the vector being transformed.

Decomposition

getRotation(result?: number[16]) : number[16]

Returns a 4x4 rotation matrix.

getRotationMatrix3(result?: number[9]) : number[9]

Returns a 3x3 rotation matrix.

getTranslation(result?: number[3]) : number[3]

Returns the 3-element translation vector component of the affine transform described by the matrix.

For performance, an existing vector can be provided, if not a new vector will be returned.

getScale(result?: number[3]) : number[3]

Returns the 3-element scale vector component of the affine transform described by the matrix.

For performance, an existing vector can be provided, if not a new vector will be returned.

Point Transformations

transformAsPoint(vector : number[4]) : number[4]

Transforms any 2, 3 or 4 element vector as a "point" by multiplying it (from the right) with this matrix. Point here means that the returned vector will include any translations in this matrix.

const vector = matrix4.transformPoint(vector, out=)

  • vector (Array|Vector2|Vector3|Vector4)

  • out - unless supplied, will be a Vector2, Vector3 or Vector4, matching the length of input vector. Returns out, or a newly minted Vector2, Vector3 or Vector4

  • If vector is specified in homogeneous coordinates, w coordinate must NOT be 0.

  • If vector is specified in homogeneous coordinates the returned vector will be w adjusted, (i.e. w coordinate will be 1, even if the supplied vector was not normalized).

transformAsVector(vector : number[4]) : number[4]

Transforms any 2, 3 or 4 element vector interpreted as a direction (i.e. all vectors are based in the origin so the transformation not pick up any translations from the matrix).

const vector = matrix4.transformDirection(vector, out)

  • If vector is specified in homogeneous coordinates, w coordinate must be 0.

Remarks

  • All transforms are effectively "right multiplied" onto the matrix (meaning that during transform they will be applied in opposite order).
  • Matrix4 is stored internally in column major format (per WebGL conventions). This only matters when you read out the matrix to use it with other software.
- + \ No newline at end of file diff --git a/docs/modules/core/api-reference/pose.html b/docs/modules/core/api-reference/pose.html index fccca6f8..061ab47a 100644 --- a/docs/modules/core/api-reference/pose.html +++ b/docs/modules/core/api-reference/pose.html @@ -4,7 +4,7 @@ Pose | math.gl - + @@ -18,7 +18,7 @@ second coordinate system into the coordinate system of this pose.

Returns Matrix4.

getTransformationMatrixToPose

pose.getTransformationMatrixToPose(otherPose)

Given a second pose that represent the same object in a second coordinate system, this method returns a 4x4 matrix that transforms coordinates in the coordinate system of this pose into the coordinate system of the second pose.

Returns Matrix4.

- + \ No newline at end of file diff --git a/docs/modules/core/api-reference/quaternion.html b/docs/modules/core/api-reference/quaternion.html index 89e850bd..f61244db 100644 --- a/docs/modules/core/api-reference/quaternion.html +++ b/docs/modules/core/api-reference/quaternion.html @@ -4,13 +4,13 @@ Quaternion | math.gl - +

Quaternion

class Quaternion extends MathArray extends Array

A class to handle Quaternions. More information on quternions can be found here. The quaternion will be represented by an instance with x, y, z, w components that make a quaternion like: xi + yj + zk + w.

Usage

import {Quaternion} from '@math.gl/core';

Members

x, y, z, w

Gets or sets element 0, 1, 2 or 3 respectively

Methods

Many of the most commonly used methods are inherited from MathArray:

  • quaternion.clone()
  • quaternion.copy(array)
  • quaternion.set(...args)
  • quaternion.fromArray(array, offset = 0)
  • quaternion.toString()
  • quaternion.toArray(array = [], offset = 0)
  • quaternion.equals(array)
  • quaternion.exactEquals(array)
  • quaternion.validate(array = this)
  • quaternion.check(array = this)
  • quaternion.normalize()

Note that Quaternion is a subclass of the built in JavaScript Array and can thus technically be supplied as a parameter to any function expecting an Array.

constructor

constructor(x = 0, y = 0, z = 0, w = 1)

fromMatrix3(m: number[9]): this

Creates a quaternion from the given 3x3 rotation matrix. NOTE: The resultant quaternion is not normalized, so you should be sure to renormalize the quaternion yourself where necessary.

fromMatrix3(m)

fromValues(x: number, y: number, z: number, w): number: this

Creates a new quat initialized with the given values

fromValues(x, y, z, w)

identity(): this

Set a quat to the identity quaternion

identity()

length(): number

Calculates the length of a quaternion

length()

squaredLength(): number

Calculates the squared length of a quaternion

squaredLength(a)

@returnNumber}

dot(): number

Calculates the dot product of two quat's

quaternion.dot(a, b)

getAxisAngle

Gets the rotation axis and angle for a given quaternion.

quaternion.getAxisAngle()

If a quaternion is created with setAxisAngle, this method will return the same values as providied in the original parameter list OR functionally equivalent values.

Example: The quaternion formed by axis [0, 0, 1] and angle -90 is the same as the quaternion formed by [0, 0, 1] and 270. This method favors the latter.

rotationTo

Sets a quaternion to represent the shortest rotation from one vector to another. Both vectors are assumed to be unit length.

quaternion.rotationTo(vectorA, vectorB)

add

Adds two quaternions

quaternion.add(a, b)

calculateW

Calculates the W component of a quat from the X, Y, and Z components. Any existing W component will be ignored.

quaternion.calculateW()

conjugate

Calculates the conjugate of a quat If the quaternion is normalized, this function is faster than quat_inverse and produces the same result.

quaternion.conjugate()

invert(): this

Calculates the inverse of a quat

quaternion.invert()

lerp

Performs a linear interpolation between two quat's

quaternion.lerp(a, b, t)

multiply

Multiplies two quat's

multiply(a, b)

normalize

Normalize a quat

rotateX

Rotates a quaternion by the given angle about the X axis

rotateX(rad)

rotateY

Rotates a quaternion by the given angle about the Y axis

rotateY(rad)

rotateZ

Rotates a quaternion by the given angle about the Z axis

rotateZ(rad)

scale

Scales a quat by a scalar number

scale(b)

set

Set the components of a quat to the given values

set(i, j, k, l)

setAxisAngle

Sets a quat from the given angle and rotation axis, then returns it.

setAxisAngle(axis, rad)

slerp

Performs a spherical linear interpolation between two quaternions

slerp({start = [0, 0, 0, 1], target, ratio})

s

- + \ No newline at end of file diff --git a/docs/modules/core/api-reference/spherical-coordinates.html b/docs/modules/core/api-reference/spherical-coordinates.html index c4083728..f07070ec 100644 --- a/docs/modules/core/api-reference/spherical-coordinates.html +++ b/docs/modules/core/api-reference/spherical-coordinates.html @@ -4,13 +4,13 @@ SphericalCoordinates | math.gl - +

SphericalCoordinates

This documentation is incomplete and may be incorrect

class SphericalCoordinates

See also Wikipedia, Wolfram MathWorld.

  • The poles (phi) are at the positive and negative y axis.
  • The equator starts at positive z.

Conversion from spherical to Cartesian (rectilinear) coordinates:

<math xmlns="http://www.w3.org/1998/Math/MathML">
<mfenced open="{" close="">
<mtable columnalign="left">
<mtr><mrow><mi>x</mi><mo>=</mo><mn>ρ</mn><mi>cos</mi><mn>θφ</mn></mrow></mtr>
<mtr><mrow><mi>y</mi><mo>=</mo><mn>ρ</mn><mi>cos</mi><mn>θφ</mn></mrow></mtr>
<mtr><mrow><mi>z</mi><mo>=</mo><mn>ρ</mn><mi>cos</mi><mn>θφ</mn></mrow></mtr>
</mtable>
</mfenced>
</math>

Conversion from Cartesian (rectilinear) to spherical coordinates:

<math xmlns="http://www.w3.org/1998/Math/MathML">
<mfenced open="{" close="">
<mtable columnalign="left">
<mtr><mrow><mi>r</mi><mo>=</mo><msqrt>
<msup><mi>x</mi><mn>2</mn></msup><mo>+</mo>
<msup><mi>y</mi><mn>2</mn></msup><mo>+</mo>
<msup><mi>z</mi><mn>2</mn></msup>
</msqrt></mrow></mtr>
<mtr><mrow><mi>θ</mi><mo>=</mo><mo>arccos</mo><mfrac><mi>z</mi><mi>r</mi></mfrac></mrow></mtr>
<mtr><mrow><mi>φ</mi><mo>=</mo><mo>arctan</mo><mfrac><mi>y</mi><mi>x</mi></mfrac></mrow></mtr>
</mtable>
</mfenced>
</math>

Ranges

<math xmlns="http://www.w3.org/1998/Math/MathML">
<mfenced open="{" close="">
<mtable columnalign="left">
<mtr><mrow><mi>r</mi><mo>≥<mn>0</mn></mtr>
<mtr><mrow><mi>θ</mi><mo>≥<mn>0</mn></mtr>
<mtr><mrow><mi>φ</mi><mo>≥<mn>0</mn></mtr>
</mtable>
</mfenced>
</math>

Usage

import {SphericalCoordinates} from '@math.gl/core';

Creating a SphericalCoordinates object

const spherical = new SphericalCoordinates({phi: 0, theta: 0});
const spherical = new SphericalCoordinates({pitch: 0, bearing: 0});
const spherical = new SphericalCoordinates({longitude: 0, latitude: 0});

Converting to a direction Vector3

const direction = new SphericalCoordinates().toVector3();

Manipulating spherical coordinates;

spherical.bearing += 3; // Add three degrees to bearing
spherical.theta -= Math.PI / 4; // Subtract PI/4 radians from theta.

Members

// Standard spherical coordinates

phi

theta

radius

altitude

// lnglatZ coordinates

lng

lat

z

Methods

constructor

SphericalCoordinates({phi = 0, theta = 0, radius = 1.0})
SphericalCoordinates({bearing = 0, pitch = 0, altitude = 1.0})
SphericalCoordinates({longitude = 0, latitude = 0, z = 1.0})
  • phi=0 - rotation around X (latitude)
  • theta=0 - rotation around Y (longitude)
  • radius=1 - Distance from center

set

set(radius, phi, theta)

clone

clone()

copy

copy(other)

fromLngLatZ

fromLngLatZ([lng, lat, z])

fromVector3

fromVector3(v)

makeSafe

makeSafe()

// restrict phi to be betwee EPS and PI-EPS

toVector3

toVector3(center = [0, 0, 0])

// TODO - add parameter for orientation of sphere? up vector etc?

check

Remarks

  • Inspired by THREE.js THREE.Spherical class
- + \ No newline at end of file diff --git a/docs/modules/core/api-reference/utilities.html b/docs/modules/core/api-reference/utilities.html index 4beb240b..5540ced2 100644 --- a/docs/modules/core/api-reference/utilities.html +++ b/docs/modules/core/api-reference/utilities.html @@ -4,13 +4,13 @@ Math Utility Functions | math.gl - +

Math Utility Functions

GLSL math function equivalents. Work on both single values and vectors.

Usage

import {config, equals} from '@math.gl/core';

Setting configuration

import {config} from '@math.gl/core';
config.EPSILON = 1e-12;
config.debug = true;
config.printRowMajor = true;
config.precision = 4;

Functions

configure

configure(options)

checkNumber

checkNumber(value)

formatValue

formatValue(value, precision = config.precision || 4)

isArray

Returns true if value is either an array or a typed array

isArray(value)

Note: does not return true for ArrayBuffers and DataViews

clone

clone(array)If the array has a clone function, calls it, otherwise returns a copy

toRadians

toRadians(degrees)

Works on single values and vectors

toDegrees

toDegrees(radians)

Works on single values and vectors

equals

equals(a, b, epsilon)

  • Works on single values and vectors
  • Numeric values need to be closer than config.EPSILON
  • Objects will be compared with their .equals() method if present.

exactEquals

exactEquals(a, b)

  • Works on single values and vectors.
  • Numeric values need to be exactly identical
  • Objects will be compared with their .exactEquals() method if present.

GLSL equivalents

radians

radians(degrees)

GLSL equivalent: Works on single values and vectors

degrees

degrees(radians)

GLSL equivalent: Works on single values and vectors

sin

sin(radians)

GLSL equivalent: Works on single values and vectors

cos

cos(radians)

GLSL equivalent: Works on single values and vectors

tan

tan(radians)

GLSL equivalent: Works on single values and vectors

asin

asin(radians)

GLSL equivalent: Works on single values and vectors

acos

acos(radians)

GLSL equivalent: Works on single values and vectors

atan

atan(radians)

clamp

clamp(value, min, max)

Remarks

  • When setting global configs, you may need to consider the order of code loadint when using imports and requires
- + \ No newline at end of file diff --git a/docs/modules/core/api-reference/vector.html b/docs/modules/core/api-reference/vector.html index 6811b905..e0361999 100644 --- a/docs/modules/core/api-reference/vector.html +++ b/docs/modules/core/api-reference/vector.html @@ -4,13 +4,13 @@ Vector | math.gl - +

Vector

Vector is a base class for Vector2, Vector3 and Vector4, providing common methods to those classes.

Inheritance

class Vector extends [MathArray](./docs/api-reference/math-array) extends [Array](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array)

Methods

Vector.clone()

Vector.copy(array)

Vector.set(...args)

Vector.fromArray(array, offset = 0)

Vector.toString()

Vector.toArray(array = [], offset = 0)

Vector.equals(array)

Vector.exactEquals(array)

Vector.validate(array = this)

Vector.check(array = this)

Vector.normalize()

- + \ No newline at end of file diff --git a/docs/modules/core/api-reference/vector2.html b/docs/modules/core/api-reference/vector2.html index 5388876c..7cb4914b 100644 --- a/docs/modules/core/api-reference/vector2.html +++ b/docs/modules/core/api-reference/vector2.html @@ -4,13 +4,13 @@ Vector2 | math.gl - +

Vector2

A two dimensional vector

Usage

import {Vector2} from '@math.gl/core';
const vector = new Vector2(1, 1);

Inheritance

Vector2 extends Vector extends MathArray extends Array

Many commonly used Vector2 methods are inherited from Vector and MathArray:

  • Vector2.clone()
  • Vector2.copy(array)
  • Vector2.set(...args)
  • Vector2.fromArray(array, offset = 0)
  • Vector2.toString()
  • Vector2.toArray(array = [], offset = 0)
  • Vector2.equals(array)
  • Vector2.exactEquals(array)
  • Vector2.validate(array = this)
  • Vector2.check(array = this)
  • Vector2.normalize()

Also note that Vector2 is a subclass of the built in JavaScript Array and can thus be used wherever an Array is expected. It can e.g. supplied as a parameter to any function expecting an Array.

Members

x, y

Gets or sets element 0 or 1 respectively

constructor

Creates a new, empty Vector2, or copies an existing Vector2

constructor((x = 0), (y = 0));
constructor([x, y]);

set

set(x, y)

add

Add zero or more vectors to current vector.

add(...vectors)

subtract

Subtract zero or more vectors from current vector

subtract(...vectors)

multiply

Multiply zero or more vectors with current vector

multiply(...vectors)

divide

Divide zero or more vectors with current vector

divide(...vectors)

scale

scale(scale)

scaleAndAdd

scaleAndAdd(vector, scale)

negate

negate()

normalize

normalize()

dot

dot(vector)

lerp

lerp(vector, coeff)

horizontalAngle

Calculates counterclockwise angle in radians starting from positive x axis

horizontalAngle()

Note: returns Math.atan2(this.y, this.x)

verticalAngle

Calculates clockwise angle in radians starting from positive y axis

verticalAngle()

Note: returns Math.atan2(this.x, this.y)

transform(matrix4 : Number[16]) : Vector4

Equivalent to transformAsPoint.

transformAsPoint(matrix4 : Number[16]) : Vector4

Transforms this vector by the provided 4x4 matrix as a point (i.e includes translations).

Note: Implicitly extends the vector to [x, y, 0, 1] before applying the 4x4 transformation.

transformAsVector(matrix4 : Number[16]) : Vector4

Transforms this vector by the provided 4x4 matrix as a vector (i.e does not include translations).

Note: Implicitly extends the vector to [x, y, 0, 0] before applying the 4x4 transformation.

transformByMatrix3(matrix3 : Number[9]) : Vector4

Transforms this vector by the provided 3x3 matrix.

transformByMatrix2x3(matrix2 : Number[6]) : Vector4

Transforms this vector by the provided 2x3 matrix (A pure 2D transform that can incorporate translations).

transformByMatrix2(matrix2 : Number[4]) : Vector4

Transforms this vector by the provided 2x2 matrix.

- + \ No newline at end of file diff --git a/docs/modules/core/api-reference/vector3.html b/docs/modules/core/api-reference/vector3.html index e260b4d1..81d89517 100644 --- a/docs/modules/core/api-reference/vector3.html +++ b/docs/modules/core/api-reference/vector3.html @@ -4,13 +4,13 @@ Vector3 | math.gl - +

Vector3

class Vector3 extends MathArray extends Array

Usage

import {Vector3} from '@math.gl/core';
const vector = new Vector3(1, 1, 1);

Accessors

v.x = 2;
assert(v[0] === v.x);

Simple rotations

const v = new Vector3([1, 0, 0]);
v.rotateX({radians: Math.PI / 4}); // Rotate around the origin
v.rotateX({radians: Math.PI / 4, origin: [1, 1, 0]}); // Rotate around the specified point

Scaling with constants

const u = v.scale(-1); // Reverse direction vector

Scaling with vectors is very flexible, you can e.g. set a component to zero, or flip a component's sign.

const u = v.scale([1, 1, 0]); // Set z component to zero
const w = v.scale([1, -1, 1]); // Flip y component

Inheritance

Vector3 extends Vector extends MathArray extends Array

Members

x, y, z

Gets or sets element 0, 1 or 2 respectively

Methods

Many of the most commonly used Vector3 methods are inherited from MathArray:

  • Vector3.clone()
  • Vector3.copy(array)
  • Vector3.set(...args)
  • Vector3.fromArray(array, offset = 0)
  • Vector3.toString()
  • Vector3.toArray(array = [], offset = 0)
  • Vector3.equals(array)
  • Vector3.exactEquals(array)
  • Vector3.validate(array = this)
  • Vector3.check(array = this)
  • Vector3.normalize()

Note that Vector3 is a subclass of the built in JavaScript Array and can thus e.g. be supplied as a parameter to any function expecting an Array.

constructor(x = 0, y = 0, z = 0)

set(x, y, z)

length()

distance(vector)

angle(vector)

dot(vector)

// MODIFIERS

add(...vectors)

subtract(...vectors)

multiply(...vectors)

divide(...vectors)

scale(scale)

Scale component wise with a scalar or another Vector3.

  • scale (Number|Vector3) - scale component wise with a scalar or another Vector3.

negate

negate()

inverse

inverse()

normalize

normalize()

cross

cross(vector)

lerp

lerp(vector, coeff)

rotateX

Rotate a 3D vector around the x-axis

rotateX({radians, origin})

  • radians (Number) - angle to rotate.
  • origin=[0, 0, 0] (Vector3) - the origin of the rotation (optional)

rotateY

Rotate a 3D vector around the y-axis

rotateY({radians, origin})

  • radians (Number) - angle to rotate.
  • origin=[0, 0, 0] (Vector3) - the origin of the rotation (optional)

rotateZ(radians)

Rotate a 3D vector around the z-axis

rotateZ({radians, origin})

  • radians (Number) - angle to rotate.
  • origin=[0, 0, 0] (Vector3) - the origin of the rotation (optional)

transform(matrix4 : Number[16]) : Vector4

Transforms the vector by the provided 4x4 matrix.

Note: Scales the resulting vector to ensure that w, if non-zero, is set to 1.

transformByMatrix3(matrix3 : Number[9]) : Vector4

Transforms the vector by the provided 3x3 matrix.

transformByMatrix2(matrix2 : Number[4]) : Vector4

Transform the vector's x and y values by the provided 2x2 matrix.

transformByQuaternion(quaternion : Number[4]) : Vector4

Transform the vector by the provided quaternion.

- + \ No newline at end of file diff --git a/docs/modules/core/api-reference/vector4.html b/docs/modules/core/api-reference/vector4.html index 180bc9a1..d27de0df 100644 --- a/docs/modules/core/api-reference/vector4.html +++ b/docs/modules/core/api-reference/vector4.html @@ -4,13 +4,13 @@ Vector4 | math.gl - +

Vector4

Vector4 is designed to hold three dimensional coordinates in projective space. Using the projective representation allows JavaScript applications to perform the same calculations that the GPU does.

A main feature of vectors is that they can be transformed by matrices and quaternions. And Vector4s are particular general when transformed with 4x4 matrices (Matrix4 or just arrays of 16 numbers), as those can include translations, projections and other transformations that cannot be expressed by e.g. 3x3 matrices or quaternions alone.

Note that the fourth element w is not a coordinate but a scaling factor. The fourth component (w) is usually set to either

  • 0 to represent a vector
  • 1 to represent a point

Vector4 methods will keep the vector scaled so that w (if non-zero) is 1.

The math behind Vector4 comes from projective geometry, which significantly generalizes calculations and removes a number of special cases compared to affine geometry. It is not necessary to understand the details to use Vector4, but see the developer guide for some additional xbackground.

Usage

import {Vector4} from '@math.gl/core';
const vector = new Vector4(1, 1, 1, 0);
const point = new Vector4(0, 0, 0, 1);

Inheritance

Vector4 extends Vector extends MathArray extends Array

Members

x, y, z, w

Gets or sets element 0, 1, 2 or 3 respectively

Methods

Many of the most commonly used Vector2 methods are inherited from MathArray:

  • Vector4.clone()
  • Vector4.copy(array)
  • Vector4.set(...args)
  • Vector4.fromArray(array, offset = 0)
  • Vector4.toString()
  • Vector4.toArray(array = [], offset = 0)
  • Vector4.equals(array)
  • Vector4.exactEquals(array)
  • Vector4.validate(array = this)
  • Vector4.check(array = this)
  • Vector4.normalize()

Note that Vector2 is a subclass of the built in JavaScript Array and can thus e.g. be supplied as a parameter to any function expecting an Array.

constructor(x?: number, y?: number, z?: number, w?: number)

new Vector4(x = 0, y = 0, z = 0, w = 0)

Creates a new, empty Vector4

set(x?: number, y?: number, z?: number, w?: number): thos

Updates a Vector4

distance(vector: number[4]): number

Returns the distance to the specifed Vector.

distanceSquared(vector: number[4]): number

Returns the squared distance to the specifed Vector. Fast to calculate than distance and often sufficient for e.g. sorting etc.

dot(vector: number[4]): number

Calculates the dot product with the supplied vector.

add(vector: number[4]): Vector4

add(...vectors)

subtract(vector: number[4]): Vector4

subtract(...vectors)

multiply(vector: number[4]): Vector4

multiply(...vectors)

divide(vector: number[4]): Vector4

divide(...vectors)

scale(vector: number[4]): Vector4

scale(scale)

negate(): this

Negates each element in the vector.

inverse(): this

Inverses (x = 1/x) each element in the vector.

normalize(): this

Normalizes the vector. Same direction but len() will now return 1.

lerp(vector: number[4], coefficient: number): this

Linearly interpolates between the vectors current value and the supplied vector.

transform(matrix4: number[16]): Vector4

Equivalent to transformByMatrix4.

transformByMatrix4(matrix4: number[16]): Vector4

Transforms a vector by the provided 4x4 matrix.

Note: Scales the resulting vector to ensure that w, if non-zero, is set to 1.

transformByMatrix3(matrix3: number[9]): Vector4

Transforms the vector's x, y and z values by the provided 3x3 matrix.

transformByMatrix2(matrix2: number[4]): Vector4

Transform the vector's x and y values by the provided 2x2 matrix.

transformByQuaternion(quaternion: number[4]): Vector4

Transform the vector by the provided quaternion.

- + \ No newline at end of file diff --git a/docs/modules/culling.html b/docs/modules/culling.html index 28aabd32..3ab41301 100644 --- a/docs/modules/culling.html +++ b/docs/modules/culling.html @@ -4,13 +4,13 @@ Overview | math.gl - +

Overview

The @math.gl/culling module provides primitives for implementing frustum culling:

  • Bounding boxes and intersection logic
  • Fully "transformable" primitives (i.e. oriented bounding boxes as opposed to just axis-aligned bounding boxes).

The culling module does not attempt to be a general "physics-based" collision detection library (e.g. it does not handle time-interpolated intersections like a physics library would).

Classes

ClassDescription
CullingVolume
BoundingSphere
OrientedBoundingBox
Plane

Example Usage

  • Create bounding volumes for your objects/geometries, and create BoundingSphere or OrientedBoundingBox instances.
  • Extract your camera view frustum parameters and create a PerspectiveFrustum instance.
  • You can now test your bounding volumes to see if the intersect the view frustum.

Framework Independence

Like all non-core math.gl modules, this library can be used without the math.gl core classes.

  • Any input vectors can be supplied as length 3 JavaScript Array instances.
  • Any result vectors can be treated as length 3 JavaScript Array instances (they may be math.gl Vector3).
  • The core math.gl classes inherit from JavaScript Array and can be used directly as input.

History

This library was initially developed as a fork of the Cesium math library as part of a collaboration between Cesium and Uber to provide framework-independent, portable support for the 3D tiles specification.

Attribution

This code in was initially forked from Cesium under the Apache 2 License.

- + \ No newline at end of file diff --git a/docs/modules/culling/api-reference/axis-aligned-bounding-box.html b/docs/modules/culling/api-reference/axis-aligned-bounding-box.html index bb18cab0..efd34932 100644 --- a/docs/modules/culling/api-reference/axis-aligned-bounding-box.html +++ b/docs/modules/culling/api-reference/axis-aligned-bounding-box.html @@ -4,13 +4,13 @@ AxisAlignedBoundingBox | math.gl - +

AxisAlignedBoundingBox

An AxisAlignedBoundingBox is a closed and convex cuboid that is aligned with the orthogonal axes.

Usage

AxisAlignedBoundingBox can be created using two corners of the box:

import {AxisAlignedBoundingBox} from '@math.gl/culling';

const box = new AxisAlignedBoundingBox([-1, -1, -1], [1, 1, 1]);

Or from a collection of points:

import {makeAxisAlignedBoundingBoxFromPoints} from '@math.gl/culling';

const box = makeAxisAlignedBoundingBoxFromPoints([
[2, 0, 0],
[-2, 0, 0]
]);

Inheritance

class AxisAlignedBoundingBox implements BoundingVolume.

Global Functions

makeAxisAlignedBoundingBoxFromPoints(positions : Array[3][], result? : AxisAlignedBoundingBox) : AxisAlignedBoundingBox

Computes an instance of an AxisAlignedBoundingBox of the given positions.

  • positions List of Vector3 points that the bounding box will enclose.
  • result Optional object onto which to store the result.

Fields

center: Vector3 = [0, 0, 0]

The center position of the box.

halfDiagonal: Vector3

The positive diagonal vector.

minimum: Vector3

The minimum corner of the bounding box.

maximum: Vector3

The maximum corner of the bounding box.

Methods

constructor(minimum = [0, 0, 0], maximum = [0, 0, 0]) {

constructor

  • {Vector3} [minimum=Vector3.ZERO] The minimum corner of the box, i.e. [xMin, yMin, zMin].
  • {Vector3} [maximum=Vector3.ZERO] The maximum corner of the box, i.e. [xMax, yMax, zMax].

clone() : AxisAlignedBoundingBox

Duplicates a AxisAlignedBoundingBox instance.

Returns

  • A new AxisAlignedBoundingBox instance.

equals(right : AxisAlignedBoundingBox) : Boolean

Compares the provided AxisAlignedBoundingBox componentwise and returns true if they are equal, false otherwise.

  • right The second AxisAlignedBoundingBox

Returns

  • true if left and right are equal, false otherwise.

intersectPlane(plane : Plane) : INTERSECTION

Determines which side of a plane the axis-aligned bounding box is located.

  • plane The plane to test against.

Returns

  • INTERSECTION.INSIDE if the entire box is on the side of the plane the normal is pointing
  • INTERSECTION.OUTSIDE if the entire box is on the opposite side, and
  • INTERSECTION.INTERSECTING if the box intersects the plane.

distanceTo(point : Number[3]) : Number

Computes the estimated distance from the closest point on a bounding box to a point.

  • point The point

Returns

  • The estimated distance from the bounding sphere to the point.

distanceSquaredTo(point : Number[3]) : Number

Computes the estimated distance squared from the closest point on a bounding box to a point.

  • point The point

Returns

  • The estimated distance squared from the bounding sphere to the point.
- + \ No newline at end of file diff --git a/docs/modules/culling/api-reference/bounding-sphere.html b/docs/modules/culling/api-reference/bounding-sphere.html index 85d9888e..081318e1 100644 --- a/docs/modules/culling/api-reference/bounding-sphere.html +++ b/docs/modules/culling/api-reference/bounding-sphere.html @@ -4,7 +4,7 @@ BoundingSphere | math.gl - + @@ -22,7 +22,7 @@ @param {Interval} [result] A Interval to store the nearest and farthest distances. @returns {Interval} The nearest and farthest distances on the bounding sphere from position in direction.

projectTo2D(sphere, projection, result)

Creates a bounding sphere in 2D from a bounding sphere in 3D world coordinates.

@param {BoundingSphere} sphere The bounding sphere to transform to 2D. @param {Object} [projection=GeographicProjection] The projection to 2D.

  • result Optional object onto which to store the result.

Returns

  • The modified result parameter or a new BoundingSphere instance if none was provided.

Attribution

This class was ported from Cesium under the Apache 2 License.

- + \ No newline at end of file diff --git a/docs/modules/culling/api-reference/bounding-volume.html b/docs/modules/culling/api-reference/bounding-volume.html index 2035b40e..879f957d 100644 --- a/docs/modules/culling/api-reference/bounding-volume.html +++ b/docs/modules/culling/api-reference/bounding-volume.html @@ -4,14 +4,14 @@ BoundingVolume (Interface) | math.gl - +

BoundingVolume (Interface)

An interface defining common operations for bounding volumes (i.e. BoundingSphere, AxisAlignedBoundingBox, OrientedBoundingBox).

Global Functions

Members

intersectPlane(plane : Plane) : INTERSECTION

Determines which side of a plane a sphere is located.

  • plane The plane to test against. Returns
  • INTERSECTION.INSIDE if the entire sphere is on the side of the plane the normal is pointing
  • INTERSECTION.OUTSIDE if the entire sphere is on the opposite side
  • INTERSECTION.INTERSECTING if the sphere intersects the plane.

transform(transform : Number[16]) : BoundingSphere

Applies a 4x4 affine transformation matrix to a bounding sphere.

  • transform The transformation matrix to apply to the bounding sphere.

distanceSquaredTo(point) : Number

Computes the estimated distance squared from the closest point on a bounding sphere to a point.

  • point The point

Returns

  • The estimated distance squared from the bounding sphere to the point.

Attribution

This class was ported from Cesium under the Apache 2 License.

- + \ No newline at end of file diff --git a/docs/modules/culling/api-reference/culling-volume.html b/docs/modules/culling/api-reference/culling-volume.html index 46a74987..4ba0b448 100644 --- a/docs/modules/culling/api-reference/culling-volume.html +++ b/docs/modules/culling/api-reference/culling-volume.html @@ -4,13 +4,13 @@ CullingVolume | math.gl - +

CullingVolume

A culling volume defined by planes.

Static Members

CullingVolume.MASK_OUTSIDE

For plane masks (as used in CullingVolume#computeVisibilityWithPlaneMask), this special value represents the case where the object bounding volume is entirely outside the culling volume.

CullingVolume.MASK_INSIDE

For plane masks (as used in CullingVolume.computeVisibilityWithPlaneMask), this value represents the case where the object bounding volume is entirely inside the culling volume.

CullingVolume.MASK_INDETERMINATE

For plane masks (as used inCullingVolume.computeVisibilityWithPlaneMask), this value represents the case where the object bounding volume (may) intersect all planes of the culling volume.

Methods

constructor([planes : Plane[]])

  • planes=[] An array of clipping planes.

Each plane is represented by a Cartesian4 object, where the x, y, and z components define the unit vector normal to the plane, and the w component is the distance of the plane from the origin.

fromBoundingSphere(boundingSphere : BoundingSphere)

Constructs a culling volume from a bounding sphere. Creates six planes that create a box containing the sphere. The planes are aligned to the x, y, and z axes in world coordinates.

  • boundingSphere The bounding sphere used to create the culling volume.

computeVisibility(boundingVolume : Object) : Interset

Determines whether a bounding volume intersects the culling volume.

  • boundingVolume The bounding volume whose intersection with the culling volume is to be tested.

Returns

  • INTERSECTION.OUTSIDE, INTERSECTION.INTERSECTING, or INTERSECTION.INSIDE.

computeVisibilityWithPlaneMask(boundingVolume : Object, parentPlaneMask : Number) : Number

Determines whether a bounding volume intersects the culling volume.

  • boundingVolume The bounding volume whose intersection with the culling volume is to be tested.
  • parentPlaneMask A bit mask from the boundingVolume's parent's check against the same culling volume, such that if planeMask & (1 << planeIndex) === 0, for k < 31, then the parent (and therefore this) volume is completely inside plane[planeIndex] and that plane check can be skipped.

Returns

  • A plane mask as described above (which can be applied to this boundingVolume's children).

Attribution

This class was ported from Cesium under the Apache 2 License.

- + \ No newline at end of file diff --git a/docs/modules/culling/api-reference/oriented-bounding-box.html b/docs/modules/culling/api-reference/oriented-bounding-box.html index cd45f7d1..63ee750a 100644 --- a/docs/modules/culling/api-reference/oriented-bounding-box.html +++ b/docs/modules/culling/api-reference/oriented-bounding-box.html @@ -4,14 +4,14 @@ OrientedBoundingBox | math.gl - +

OrientedBoundingBox

An OrientedBoundingBox is a closed and convex cuboid. It can provide a tighter bounding volume than a bounding sphere or an axis aligned bounding box in many cases.

The class support two representations of an oriented bounding box:

Usage

Create an OrientedBoundingBox using a transformation matrix, a position where the box will be translated, and a scale.

import {Vector3} from '@math.gl/core';
import {OrientedBoundingBox} from '@math.gl/culling';

const center = new Vector3(1.0, 0.0, 0.0);
const halfAxes = new Matrix3().fromScale([1.0, 3.0, 2.0]);
const box = new OrientedBoundingBox(center, halfAxes);

Sort bounding boxes from back to front

boxes.sort(
(boxA, boxB) =>
boxB.distanceSquaredTo(camera.positionWC) - boxA.distanceSquaredTo(camera.positionWC)
);

Compute an oriented bounding box enclosing two points.

import {makeOrientedBoundingBoxFromPoints} from '@math.gl/culling';

const box = makeOrientedBoundingBoxFromPoints([
[2, 0, 0],
[-2, 0, 0]
]);

Inheritance

class OrientedBoundingBox implements BoundingVolume.

Global Functions

makeOrientedBoundingBoxFromPoints(positions : Array[3][], result? : OrientedBoundingBox) : OrientedBoundingBox

Computes an instance of an OrientedBoundingBox of the given positions. This is an implementation of Stefan Gottschalk's Collision Queries using Oriented Bounding Boxes (PHD thesis).

  • positions List of Vector3 points that the bounding box will enclose.
  • result Optional object onto which to store the result.

Fields

center: Vector3

The center position of the box.

halfAxes: Matrix3

The transformation matrix, to rotate the box to the right position.

readonly halfSize: number[]

The array with three half-sizes for the bounding box

readonly quaternion: Quaternion

The quaternion describing the orientation of the bounding box

Methods

constructor(center = [0, 0, 0], halfAxes = [0, 0, 0, 0, 0, 0, 0, 0, 0]) {

constructor

  • center=Vector3.ZERO The center of the box.
  • halfAxes=Matrix3.ZERO The three orthogonal half-axes of the bounding box. Equivalently, the transformation matrix, to rotate and scale a cube centered at the origin.

fromCenterHalfSizeQuaternion(center : number[], halfSize : number[], quaternion : number[]) : OrientedBoundingBox

Create an OrientedBoundingBox from a half-size-quaternion based OBB

clone() : OrientedBoundingBox

Duplicates a OrientedBoundingBox instance.

Returns

  • A new OrientedBoundingBox instance.

equals(right: OrientedBoundingBox) : Boolean

Compares the provided OrientedBoundingBox componentwise and returns true if they are equal, false otherwise.

  • right The second OrientedBoundingBox

Returns

  • true if left and right are equal, false otherwise.

intersectPlane(plane : Plane) : INTERSECTION

Determines which side of a plane the oriented bounding box is located.

  • plane The plane to test against.

Returns

  • INTERSECTION.INSIDE if the entire box is on the side of the plane the normal is pointing
  • INTERSECTION.OUTSIDE if the entire box is on the opposite side, and
  • INTERSECTION.INTERSECTING if the box intersects the plane.

distanceTo(point : Number[3]) : Number

Computes the estimated distance from the closest point on a bounding box to a point.

  • point The point

Returns

  • The estimated distance from the bounding sphere to the point.

distanceSquaredTo(point : Number[3]) : Number

Computes the estimated distance squared from the closest point on a bounding box to a point.

  • point The point

Returns

  • The estimated distance squared from the bounding sphere to the point.

computePlaneDistances(position : Number[3], direction : Number[3], result : Number[2]]) : Number[2]

The distances calculated by the vector from the center of the bounding box to position projected onto direction.

If you imagine the infinite number of planes with normal direction, this computes the smallest distance to the closest and farthest planes from position that intersect the bounding box.

  • position The position to calculate the distance from.
  • direction The direction from position.
  • result An optional Interval to store the nearest and farthest distances.

Returns

  • The nearest and farthest distances on the bounding box from position in direction.

Attribution

This class was ported from Cesium under the Apache 2 License.

- + \ No newline at end of file diff --git a/docs/modules/culling/api-reference/plane.html b/docs/modules/culling/api-reference/plane.html index 89cfd5e0..61fb6062 100644 --- a/docs/modules/culling/api-reference/plane.html +++ b/docs/modules/culling/api-reference/plane.html @@ -4,13 +4,13 @@ Plane | math.gl - +

Plane

A plane in Hessian Normal Form defined by ax + by + cz + d = 0 where [a, b, c] is the plane's normal, d is the signed distance to the plane (from the origin along the normal), and [x, y, z] is any point on the plane.

Usage

Create the plane x=0

import {Plane} from '@math.gl/culling';
const plane = new Plane([1, 0, 0], 0.0);

Create a tangent plane for a cartographic coordinate

import {Plane} from '@math.gl/culling';
import {Ellipsoid} from '@math.gl/geospatial';
const point = [-72.0, 40.0, 0];
const normal = Ellipsoid.WGS84.geodeticSurfaceNormal([-72.0, 40.0]);
const tangentPlane = new Plane().fromPointNormal(point, normal);

Fields

normal : Vector3

The plane's normal.

distance : Number

The shortest distance from the origin to the plane. The sign of distance determines which side of the plane the origin is on. If distance is positive, the origin is in the half-space in the direction of the normal; if negative, the origin is in the half-space opposite to the normal; if zero, the plane passes through the origin.

Methods

constructor(normal : Number[3], distance : Number)

  • Vector3 normal The plane's normal (normalized).
  • Number distance The shortest distance from the origin to the plane. The sign of distance determines which side of the plane the origin is on. If distance is positive, the origin is in the half-space in the direction of the normal; if negative, the origin is in the half-space opposite to the normal; if zero, the plane passes through the origin.

Throws

  • Normal must be normalized

fromPointNormal(point : Number[3], normal : Number[3]) : Plane

Creates a plane from a normal and a point on the plane.

  • Vector3 point The point on the plane.
  • Vector3 normal The plane's normal (normalized).
  • Plane [result] The object onto which to store the result.

Throws

  • Normal must be normalized

Plane.fromCoefficients(coefficients : Number[4]) : Plane

Creates a plane from the general equation

  • coefficients The plane coefficients (normalized).

Throws

  • Normal must be normalized

clone() : Plane

Duplicates a Plane instance.

Returns

  • A new Plane instance with the same values

equals(right : Plane) : Boolean

Compares the provided Planes by normal and distance and returns true if they are equal, false otherwise.

  • right The second plane.

Returns

  • true if left and right are equal, false otherwise.

getPointDistance(point : Number[3]) : Number

Computes the signed shortest distance of a point to a plane. The sign of the distance determines which side of the plane the point is on. If the distance is positive, the point is in the half-space in the direction of the normal; if negative, the point is in the half-space opposite to the normal; if zero, the plane passes through the point.

  • point The point.

Returns

  • Number The signed shortest distance of the point to the plane.

projectPointOntoPlane(point : Number[3], result : Number[3]]) : Number[3]

Projects a point onto the plane.

  • point The point to project onto the plane
  • result The result point. If undefined, a new Array will be created.

Returns

  • The modified result parameter or a new Vector3 instance if one was not provided.

transform(transform : Number[16]) : Plane

Transforms the plane by the given transformation matrix.

  • Matrix4 transform The transformation matrix.
  • Plane [result] The object into which to store the result.

Returns

  • Plane The plane transformed by the given transformation matrix.

Attribution

This class was ported from Cesium under the Apache 2 License.

- + \ No newline at end of file diff --git a/docs/modules/dggs-geohash.html b/docs/modules/dggs-geohash.html index f1246d49..a33c2642 100644 --- a/docs/modules/dggs-geohash.html +++ b/docs/modules/dggs-geohash.html @@ -4,13 +4,13 @@ Overview | math.gl - +

Overview

From-v4.0

caution

This module is still experimental. It may have issues and functionality may change in minor releases.

@math.gl/dggs-geohash is a JavaScript library which provides lightweight support for working with Geohash indices.

Installation

npm install @math.gl/dggs-geohash

Usage

import {getGeohashPolygon} from '@math.gl/dggs-geohash';
const polygon = getGeohashPolygon(geohash);

Attribution

- + \ No newline at end of file diff --git a/docs/modules/dggs-geohash/api-reference/geohash.html b/docs/modules/dggs-geohash/api-reference/geohash.html index 2b238ae1..131e01ea 100644 --- a/docs/modules/dggs-geohash/api-reference/geohash.html +++ b/docs/modules/dggs-geohash/api-reference/geohash.html @@ -4,13 +4,13 @@ GeoHash API | math.gl - +

GeoHash API

From-v4.0

caution

This module is still experimental. It may have issues and functionality may change in minor releases.

The GeoHash functions in math.gl are currently focused on decoding Geohash encoded data, not encoding it.

Functions

getGeohashLngLat(geohash: string): number[]

Returns the center lng, lat of a GeoHash cell.

getGeohashBoundary(geohash: string): number[][]

Returns the boundary of a GeoHash cell as a polygon of [lng, lat], [lng, lat], ... .

getGeohashBoundaryFlat(geohash: string): number[]

Returns the boundary of a GeoHash cell as a flat polygon of lng, lat, lng, lat, ... .

- + \ No newline at end of file diff --git a/docs/modules/dggs-quadkey.html b/docs/modules/dggs-quadkey.html index 2f84f0ad..4b93f313 100644 --- a/docs/modules/dggs-quadkey.html +++ b/docs/modules/dggs-quadkey.html @@ -4,13 +4,13 @@ Overview | math.gl - +

Overview

From-v4.0

caution

This module is still experimental. It may have issues and functionality may change in minor releases.

@math.gl/dggs-quadkey is a JavaScript library providing math for the Quadkey DGGS (Discrete Global Grid System).

Installation

npm install @math.gl/dggs-quadkey

Usage

Get a polygon representing the outline of a specific

import {getQuadkeyLngLat} from '@math.gl/dggs-quadkey';
const center = getQuadkeyLngLat(quadkey);

Attribution

- + \ No newline at end of file diff --git a/docs/modules/dggs-quadkey/api-reference/quadkey.html b/docs/modules/dggs-quadkey/api-reference/quadkey.html index 7035e582..d06d51f4 100644 --- a/docs/modules/dggs-quadkey/api-reference/quadkey.html +++ b/docs/modules/dggs-quadkey/api-reference/quadkey.html @@ -4,13 +4,13 @@ QuadKey API | math.gl - +

QuadKey API

From-v4.0

caution

This module is still experimental. It may have issues and functionality may change in minor releases.

The quadkey library is currently focused on decoding quadkeys.

The quadkey functions in math.gl are currently focused on decoding S2 encoded data, not encoding it.

Functions

getQuadkeyLngLat(quadkey: string): number[]

Returns the center lng, lat of a quadkey cell.

getQuadkeyBoundary(quadkey: string): number[][]

Returns the center lng, lat of a quadkey cell.

getQuadkeyBoundaryFlat(quadkey: string): number[]

Returns the center lng, lat of a quadkey cell.

- + \ No newline at end of file diff --git a/docs/modules/dggs-s2.html b/docs/modules/dggs-s2.html index 10f546f6..72c4dc05 100644 --- a/docs/modules/dggs-s2.html +++ b/docs/modules/dggs-s2.html @@ -4,7 +4,7 @@ Overview | math.gl - + @@ -12,7 +12,7 @@

Overview

From-v4.0

caution

This module is still experimental. It may have issues and functionality may change in minor releases.

@math.gl/dggs-s2 is a small JavaScript library for working with the S2 DGGS (Discrete Global Grid System).

Installation

npm install @math.gl/dggs-s2

Usage

import {} from '@math.gl/dggs-s2';

Attribution

This module is a fork of a subset of the s2-geometry module under ISC License (ISC) Copyright (c) 2012-2016, Jon Atkins github@jonatkins.com Copyright (c) 2016, AJ ONeal aj@daplie.com

- + \ No newline at end of file diff --git a/docs/modules/dggs-s2/api-reference/s2.html b/docs/modules/dggs-s2/api-reference/s2.html index aabbab6a..4fe22fe4 100644 --- a/docs/modules/dggs-s2/api-reference/s2.html +++ b/docs/modules/dggs-s2/api-reference/s2.html @@ -4,7 +4,7 @@ S2 API | math.gl - + @@ -12,7 +12,7 @@

S2 API

From-v4.0

caution

This module is still experimental. It may have issues and functionality may change in minor releases.

Overview

S2 is a discrete global grid system built on the Hilbert curve. See s2geometry.io for more information.

The S2 functions in math.gl are currently focused on decoding S2 encoded data, not encoding it.

API Notes

The API provided by this module mainly works with S2 token strings, as those are typically found in data files.

But note that S2 cells have multiple representations. They can be represented as:

  • S2 token strings (stringified versions of the indexes)
  • S2 indexes which are 64 bit numbers represented by the Long type.
  • Hilbert QuadKey strings.
  • S2 Cells which are tuples of numbers.

Information on the the Long data type can be found here: TBA

Core Functions

getIndexFromS2Token(s2Token: string): Long

Decodes a string into the 64 bit token.

getS2TokenFromIndex(s2Index: Long): string

Encodes the 64 bit token into a string.

getS2ChildIndex(s2Index: Long, index: number): Long

Returns the specific index of a child cell.

getS2Center(s2Token: string): number[]

Returns the center lng, lat of the S2 cell

getS2Boundary(s2Token: string): Float64Array

Returns the boundary as a list of lng, lat of the S2 cell

- + \ No newline at end of file diff --git a/docs/modules/geoid.html b/docs/modules/geoid.html index c0427c05..0d4d6662 100644 --- a/docs/modules/geoid.html +++ b/docs/modules/geoid.html @@ -4,13 +4,13 @@ Overview | math.gl - +

Overview

From-v3.4

The @math.gl/geoid module provides support for irregular Earth models defined by earth gravity model files.

Earth Gravitational Model 1996

A view of the Earth's geoid, as provided by EGM96 (Earth Gravitational Model 1996).
Attribution: From wikipedia, Public Domain.

Background

While spherical and ellipsoidal models of the earth can be very useful, the Earth is ultimately an irregular object, with lumps of higher density etc. This irregular model of the earth is usually referred to as a "geoid" (essentially, an irregular "ellipsoid").

Earth gravity models can be used to describe this geoid. The models implemented by @math.gl/geoid use a superposition of spherical harmonics to approximate measured gravity.

Calculates difference between mean see level height and WGS84 ellipsoid height

Earth Gravity Model Data Files

Gravity Height Model data files tend to be stored in PGM format.

Attribution

This implementation is a JavaScript port of selected code from [GeographicLib-1.50.1(https://geographiclib.sourceforge.io/html/index.html), listed as Copyright Charles Karney charles@karney.com, under the MIT license.

- + \ No newline at end of file diff --git a/docs/modules/geoid/api-reference/geoid.html b/docs/modules/geoid/api-reference/geoid.html index 9acdc70e..e2e58342 100644 --- a/docs/modules/geoid/api-reference/geoid.html +++ b/docs/modules/geoid/api-reference/geoid.html @@ -4,7 +4,7 @@ Geoid | math.gl - + @@ -13,7 +13,7 @@ options.data - binary buffer of .pgm file

Calculates difference between mean see level height and WGS84 ellipsoid height

@param lat - latitude @param lon - longitude @returns height in meters

getHeight(lat: number, lon: number): number;
- + \ No newline at end of file diff --git a/docs/modules/geoid/api-reference/parse-pgm.html b/docs/modules/geoid/api-reference/parse-pgm.html index e28500c8..a40a5e54 100644 --- a/docs/modules/geoid/api-reference/parse-pgm.html +++ b/docs/modules/geoid/api-reference/parse-pgm.html @@ -4,7 +4,7 @@ parsePGM | math.gl - + @@ -12,7 +12,7 @@

parsePGM

From-v3.4

Parse header of "Earth Gravity Model" *.pgm file.

Functions

parsePGM(data, options)

Parse "Earth Gravity Model" loaded from a *.pgm file, e.g. https://geographiclib.sourceforge.io/html/geoid.html

@param {Uint8Array} data - binary buffer of pgm file @param {Object} options - loader options @returns {GeoidHeightModel} - instance of GeoidHeightModel class

- + \ No newline at end of file diff --git a/docs/modules/geospatial.html b/docs/modules/geospatial.html index 39ffa7a3..53b35ec8 100644 --- a/docs/modules/geospatial.html +++ b/docs/modules/geospatial.html @@ -4,13 +4,13 @@ Overview | math.gl - +

Overview

From-v3.0

The @math.gl/geospatial module provides support for ellipsoidal math, focusing on geospatial use cases.

It provides classes and utilities to facilitate working with ellipsoidal geospatial coordinate systems and projections used with computer maps, primarily WGS84 (World Geodetic System) coordinates.

WGS84: The 1984 World Geodetic System Ellipsoid

WGS84: The 1984 World Geodetic System Ellipsoid.
Attribution: From wikipedia, Creative Commons 4.0.

Classes

ClassDescription
EllipsoidImplements ellipsoid
Ellipsoid.WSG84An Ellipsoid instance initialized with Earth radii per WGS84.

Usage Examples

A major use of this library is to convert between "cartesian" (x, y, z) and "cartographic" (longitude, latitude, height) representations of WSG84 coordinates. The Ellipsoid class implements these calculations.

Usage

Determine the Cartesian representation of a Cartographic position on a WGS84 ellipsoid.

import {toRadians} from '@math.gl/core';
import {Ellipsoid} from '@math.gl/geospatial';
const cartographicPosition = [toRadians(21), toRadians(78), 5000];
const cartesianPosition = Ellipsoid.WGS84.cartographicToCartesian(cartographicPosition);

Determine the Cartographic representation of a Cartesian position on a WGS84 ellipsoid.

import {Ellipsoid} from '@math.gl/geospatial';
const cartesianPosition = [17832.12, 83234.52, 952313.73];
const cartographicPosition = Ellipsoid.WGS84.cartesianToCartographic(cartesianPosition);

Get the transform from local east-north-up at cartographic (0.0, 0.0) to Earth's fixed frame.

import {Ellipsoid} from '@math.gl/geospatial';
const transformMatrix = Ellipsoid.WGS84.eastNorthUpToFixedFrame([0, 0, 0]);

Framework Independence

Like all non-core math.gl modules, this module can be used independently of core math.gl classes.

  • Any input or result vectors can be supplied as JavaScript Array instances of length 3, or objects with x, y, z elements.

History

This library was initially created as part of a bigger collaboration between the vis.gl and Cesium teams to provide framework-independent, portable support for the 3D Tiles specification, however it has been designed to provide generic support for WGS84 and ellipsoidal math.

Attribution

This code is a fork of selected classes in the Cesium code base, under the Apache 2 License.

- + \ No newline at end of file diff --git a/docs/modules/geospatial/api-reference/ellipsoid.html b/docs/modules/geospatial/api-reference/ellipsoid.html index 733e571d..7438a462 100644 --- a/docs/modules/geospatial/api-reference/ellipsoid.html +++ b/docs/modules/geospatial/api-reference/ellipsoid.html @@ -4,14 +4,14 @@ Ellipsoid | math.gl - +

Ellipsoid

From-v3.0

A quadratic surface defined in Cartesian coordinates by the equation (x / a)^2 + (y / b)^2 + (z / c)^2 = 1. Primarily used to represent the shape of planetary bodies.

The main use of this class is to convert between the "cartesian" and "cartographic" coordinate systems.

Rather than constructing this object directly, one of the provided constants is used.

Usage

Determine the Cartesian representation of a Cartographic position on a WGS84 ellipsoid.

import {toRadians} from '@math.gl/core';
import {Ellipsoid} from '@math.gl/geospatial';
const cartographicPosition = [toRadians(21), toRadians(78), 5000];
const cartesianPosition = Ellipsoid.WGS84.cartographicToCartesian(cartographicPosition);

Determine the Cartographic representation of a Cartesian position on a WGS84 ellipsoid.

import {Ellipsoid} from '@math.gl/geospatial';
const cartesianPosition = [17832.12, 83234.52, 952313.73];
const cartographicPosition = Ellipsoid.WGS84.cartesianToCartographic(cartesianPosition);

Get the transform from local east-north-up at cartographic (0.0, 0.0) to Earth's fixed frame.

import {Ellipsoid} from '@math.gl/geospatial';
const transformMatrix = Ellipsoid.WGS84.eastNorthUpToFixedFrame([0, 0, 0]);

Static Fields

Ellipsoid.WGS84 : Ellipsoid (readonly)

An Ellipsoid instance initialized to the WGS84 standard.

Members

radii : Vector3 (readonly)

Gets the radii of the ellipsoid.

radiiSquared : Vector3 (readonly)

Gets the squared radii of the ellipsoid.

radiiToTheFourth : Vector3 (readonly)

Gets the radii of the ellipsoid raise to the fourth power.

oneOverRadii : Vector3 (readonly)

Gets one over the radii of the ellipsoid.

oneOverRadiiSquared : Vector3 (readonly)

Gets one over the squared radii of the ellipsoid.

minimumRadius : Number (readonly)

Gets the minimum radius of the ellipsoid.

maximumRadius : Number

Gets the maximum radius of the ellipsoid.

Methods

constructor(x : Number, y : Number, z : Number)

  • x=0 The radius in the x direction.
  • y=0 The radius in the y direction.
  • z=0 The radius in the z direction.

Throws

  • All radii components must be greater than or equal to zero.

clone() : Ellipsoid

Duplicates an Ellipsoid instance.

  • {Ellipsoid} [result] Optional object onto which to store the result, or undefined if a new instance should be created.

Returns

  • The cloned Ellipsoid.

equals(right : Ellipsoid) : Boolean

Compares this Ellipsoid against the provided Ellipsoid componentwise.

  • right The other Ellipsoid. used.

Returns

  • true if they are equal, false otherwise.

toString() : String

Creates a string representing this Ellipsoid in the format used '[radii.x, radii.y, radii.z].

Returns

  • A string representing this ellipsoid in the format '(radii.x, radii.y, radii.z)'.

cartographicToCartesian(cartographic : Number[3], result : Number[3]]) : Vector3 | Number[3]

Converts the provided cartographic to Cartesian representation.

  • cartographic The cartographic position.
  • result Optional object onto which to store the result.

Returns

  • The modified result parameter or a new Vector3 instance if none was provided.

cartesianToCartographic(cartesian : Number[3], result : Number[3]]) : Vector3 | Number[3] | undefined

Converts the provided cartesian to cartographic representation. The cartesian is undefined at the center of the ellipsoid.

  • cartesian The Cartesian position to convert to cartographic representation.
  • result Optional object onto which to store the result.

Returns

  • The modified result parameter, new Vector3 instance if none was provided, or undefined if the cartesian is at the center of the ellipsoid.

eastNorthUpToFixedFrame(origin : Number[3], ellpsoid : Ellipsoid, result : Number[16]) : Matrix4 | Number[16]

Computes a 4x4 transformation matrix from a reference frame with an east-north-up axes centered at the provided origin to the provided ellipsoid's fixed reference frame.

The local axes are defined as:

  • The x axis points in the local east direction.

  • The y axis points in the local north direction.

  • The z axis points in the direction of the ellipsoid surface normal which passes through the position.

  • origin The center point of the local reference frame.

  • ellipsoid=Ellipsoid.WGS84 The ellipsoid whose fixed frame is used in the transformation.

  • result Optional object onto which to store the result.

Returns

  • The modified result parameter or a new Matrix4 instance if none was provided.

Notes

  • Calls localFrameToFixedFrame with east, north, up axis.

localFrameToFixedFrame(String firstAxis, secondAxis : String, thirdAxis : String | null, origin : Number[3] [, result : Number[16]]) : Matrix4 | Number[16]

Computes a 4x4 transformation matrix from a reference frame centered at the provided origin to the ellipsoid's fixed reference frame.

  • firstAxis name of the first axis of the local reference frame. Must be 'east', 'north', 'up', 'west', 'south' or 'down'.
  • secondAxis name of the second axis of the local reference frame.
  • thirdAxis name of the third axis of the local reference frame. Can be omitted as it is implied by the cross product of the first two axis.
  • origin The center point of the local reference frame.
  • result Optional object onto which to store the result.

Returns

  • A 4x4 transformation matrix from a reference frame, with first axis and second axis compliant with the parameters, in the modified result parameter or a new Matrix4 instance if none was provided.

geocentricSurfaceNormal(cartesian : Number[3], result : Number[3]]) : Vector3 | Number[3]

Computes the unit vector directed from the center of this ellipsoid toward the provided Cartesian position.

  • cartesian - The WSG84 cartesian coordinate for which to to determine the geocentric normal.
  • result - Optional object onto which to store the result.

Returns

  • The modified result parameter or a new Vector3 instance if none was provided.

geodeticSurfaceNormalCartographic(cartographic : Number[3], result : Number[3]]) : Vector3 | Number[3]

Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position.

  • cartographic The cartographic position for which to to determine the geodetic normal.
  • result Optional object onto which to store the result.

Returns

The modified result parameter or a new Vector3 instance if none was provided.

geodeticSurfaceNormal(cartesian : Number[3], result : Number[3]]) : Vector3 | Number[3]

Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position.

  • cartesian The Cartesian position for which to to determine the surface normal.
  • result Optional object onto which to store the result.

Returns

  • The modified result parameter or a new Vector3 instance if none was provided.

scaleToGeodeticSurface(cartesian : Number[3], result : Number[3]]) : Vector3 | Number[3] | undefined

Scales the provided Cartesian position along the geodetic surface normal so that it is on the surface of this ellipsoid. If the position is at the center of the ellipsoid, this function returns undefined.

  • cartesian The Cartesian position to scale.
  • result Optional object onto which to store the result.

Returns

  • The modified result parameter, a new Vector3 instance if none was provided, or undefined if the position is at the center.

scaleToGeocentricSurface(cartesian : Number[3], result : Number[3]]) : Vector3 | Number[3]

Scales the provided Cartesian position along the geocentric surface normal so that it is on the surface of this ellipsoid.

  • cartesian The Cartesian position to scale.
  • result Optional object onto which to store the result.

Returns

  • The modified result parameter or a new Vector3 instance if none was provided.

transformPositionToScaledSpace(position : Number[3], result : Number[3]]) : Vector3 | Number[3]

Transforms a Cartesian X, Y, Z position to the ellipsoid-scaled space by multiplying its components by the result of Ellipsoid.oneOverRadii.

  • position The position to transform.
  • result Optional array into which to copy the result.

Returns

  • The position expressed in the scaled space. The returned instance is the one passed as the result parameter if it is not undefined, or a new instance of it is.

transformPositionFromScaledSpace(position : Number[3], result : Number[3]]) : Vector3 | Number[3]

Transforms a Cartesian X, Y, Z position from the ellipsoid-scaled space by multiplying its components by the result of Ellipsoid.radii.

  • position The position to transform.
  • result Optional array to which to copy the result.

Returns

  • The position expressed in the unscaled space. The returned array is the one passed as the result parameter, or a new Vector3 instance.

getSurfaceNormalIntersectionWithZAxis(position, buffer, result) : | undefined

Computes a point which is the intersection of the surface normal with the z-axis.

  • position the position. must be on the surface of the ellipsoid.
  • buffer=0.0 A buffer to subtract from the ellipsoid size when checking if the point is inside the ellipsoid.
  • result Optional array into which to copy the result.

Returns

  • The intersection point if it's inside the ellipsoid, undefined otherwise.

Throws

  • position is required.
  • Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y).
  • Ellipsoid.radii.z must be greater than 0.

Notes:

  • In earth case, with common earth datums, there is no need for this buffer since the intersection point is always (relatively) very close to the center.
  • In WGS84 datum, intersection point is at max z = +-42841.31151331382 (0.673% of z-axis).
  • Intersection point could be outside the ellipsoid if the ratio of MajorAxis / AxisOfRotation is bigger than the square root of 2

Attribution

This class was ported from Cesium under the Apache 2 License.

- + \ No newline at end of file diff --git a/docs/modules/geospatial/api-reference/helpers.html b/docs/modules/geospatial/api-reference/helpers.html index 53badcf2..415eb669 100644 --- a/docs/modules/geospatial/api-reference/helpers.html +++ b/docs/modules/geospatial/api-reference/helpers.html @@ -4,13 +4,13 @@ Helpers | math.gl - +

Helpers

From-v3.0

Helper functions for geospatial.

Usage

Check if a given coordinate is close to the surface of the earth on the earth ellipsoid.

import {isWGS84} from '@math.gl/geospatial';
isWGS84([17832.12, 83234.52, 952313.73]);
- + \ No newline at end of file diff --git a/docs/modules/polygon.html b/docs/modules/polygon.html index 15ace867..d8031e4f 100644 --- a/docs/modules/polygon.html +++ b/docs/modules/polygon.html @@ -4,13 +4,13 @@ Overview | math.gl - +

Overview

Installation

npm install @math.gl/polygon

Usage

import {Vector2} from '@math.gl/polygon';

Attribution

The earcut function is a modified version of the earcut library, which has a permissive ISC License.

- + \ No newline at end of file diff --git a/docs/modules/polygon/api-reference/clip-polygon.html b/docs/modules/polygon/api-reference/clip-polygon.html index 1498ba09..0d394839 100644 --- a/docs/modules/polygon/api-reference/clip-polygon.html +++ b/docs/modules/polygon/api-reference/clip-polygon.html @@ -4,13 +4,13 @@ clipPolygon | math.gl - +

clipPolygon

From-v3.2

Clips a polygon with a bounding box.

import {clipPolygon} from '@math.gl/polygon';

clipPolyline([-10, -10, 10, 10, 30, -10, -10, -10], [0, 0, 20, 20], {size: 2});
// returns [0, 0, 10, 10, 20, 0, 0, 0]

The clipping bounds are defined as an orthoganal rectangle on the XY plane. If a 3D polygon is supplied, it is clipped by the extuded volume from the bounding box.

Usage

clipPolygon(positions, bbox, [options]);

Arguments:

  • positions (Array|TypedArray) - a flat array of the vertex positions that define the polygon.
  • bbox (Array) - the bounding box, in [minX, minY, maxX, maxY]
  • options (Object, optional)
    • size (Number) - the number of elements in each vertex. Size 2 will interpret positions as [x0, y0, x1, y1, ...] and size 3 will interpret positions as [x0, y0, z0, x1, y1, z1, ...]. Default 2.
    • startIndex (Number, optional) - the index in positions to start reading vertices. Default 0.
    • endIndex (Number, optional) - the index in positions to stop reading vertices. Default positions.length.

Returns:

A positions array that describes the intersection of the original polygon and the bounding box. Uses the same vertex size as the input.

If the input polygon does not overlap with the bounding box, an empty array will be returned.

- + \ No newline at end of file diff --git a/docs/modules/polygon/api-reference/clip-polyline.html b/docs/modules/polygon/api-reference/clip-polyline.html index 17686df9..153cec4d 100644 --- a/docs/modules/polygon/api-reference/clip-polyline.html +++ b/docs/modules/polygon/api-reference/clip-polyline.html @@ -4,13 +4,13 @@ clipPolyline | math.gl - +

clipPolyline

From-v3.2

Clips a polyline with a bounding box.

import {clipPolyline} from '@math.gl/polygon';

clipPolyline([-10, -10, 10, 10, 30, -10], [0, 0, 20, 20], {size: 2});
// returns [[0, 0, 10, 10, 20, 0]]

The clipping bounds are defined as an orthoganal rectangle on the XY plane. If a 3D polyline is supplied, it is clipped by the extuded volume from the bounding box.

Usage

clipPolyline(positions, bbox, [options]);

Arguments:

  • positions (Array|TypedArray) - a flat array of the vertex positions that define the polyline.
  • bbox (Array) - the bounding box, in [minX, minY, maxX, maxY]
  • options (Object, optional)
    • size (Number) - the number of elements in each vertex. Size 2 will interpret positions as [x0, y0, x1, y1, ...] and size 3 will interpret positions as [x0, y0, z0, x1, y1, z1, ...]. Default 2.
    • startIndex (Number, optional) - the index in positions to start reading vertices. Default 0.
    • endIndex (Number, optional) - the index in positions to stop reading vertices. Default positions.length.

Returns:

An array of polylines that are parts of the original polyline and contained by the given bounding box. Each polyline is represented by a positions array that uses the same vertex size as the input.

If the input polyline is entirely outside of the bounding box, an empty array will be returned.

- + \ No newline at end of file diff --git a/docs/modules/polygon/api-reference/cut-polygon-by-grid.html b/docs/modules/polygon/api-reference/cut-polygon-by-grid.html index c5dfdb91..60283d01 100644 --- a/docs/modules/polygon/api-reference/cut-polygon-by-grid.html +++ b/docs/modules/polygon/api-reference/cut-polygon-by-grid.html @@ -4,13 +4,13 @@ cutPolygonByGrid | math.gl - +

cutPolygonByGrid

From-v3.2

Subdivides a polygon by intersecting with a uniform grid.

import {cutPolygonByGrid} from '@math.gl/polygon';

cutPolygonByGrid([0, 15, 15, 0, 0, -15, 0, 15], {size: 2, gridResolution: 20});
// returns [
// [15, 0, 0, -15, 0, 0, 15, 0],
// [15, 0, 0, 0, 0, 15, 15, 0]
// ]
]

Usage

cutPolygonByGrid(positions, holeIndices, [options]);

Arguments:

  • positions (Array|TypedArray) - a flat array of the vertex positions that define the polygon's rings.
  • holeIndices (Array|TypedArray|null) - the indices in positions where each hole starts. If null, the polygon has no holes.
  • options (Object, optional)
    • size (Number) - the number of elements in each vertex. Size 2 will interpret positions as [x0, y0, x1, y1, ...] and size 3 will interpret positions as [x0, y0, z0, x1, y1, z1, ...]. Default 2.
    • gridResolution (Number, optional) - the grid size. Default 10.
    • gridOffset (Array, optional) - the grid offset in [x, y]. Default [0, 0] i.e. the grid starts from the coordinate origin.
    • edgeTypes (Boolean) - if true, returns an additional array for each polygon that describes the nature of each vertex. See "returns" below.

Returns:

An array of polygons. Each polygons is represented by an object with the following fields:

  • positions (Array|TypedArray) - a flat array of the vertex positions that define the polygon's rings.

  • holeIndices (Array|TypedArray) - the indices in positions where each hole starts. Not present if the polygon has no holes.

  • edgeTypes (Array) - describes the nature of each vertex in positions:

    • 0 - the segment connecting this vertex to the next is inside the original polygon
    • 1 - the segment connecting this vertex to the next is on the border of the original polygon
- + \ No newline at end of file diff --git a/docs/modules/polygon/api-reference/cut-polygon-by-mercator-bounds.html b/docs/modules/polygon/api-reference/cut-polygon-by-mercator-bounds.html index 154386ec..d1d04dd0 100644 --- a/docs/modules/polygon/api-reference/cut-polygon-by-mercator-bounds.html +++ b/docs/modules/polygon/api-reference/cut-polygon-by-mercator-bounds.html @@ -4,13 +4,13 @@ cutPolygonByMercatorBounds | math.gl - +

cutPolygonByMercatorBounds

From-v3.2

Splits a geospatial polygon at the 180th meridian and the top (latitude=90) and bottom (latitude=-90) edges of the Web Mercator map.

import {cutPolygonByMercatorBounds} from '@math.gl/polygon';

cutPolygonByMercatorBounds([-170, 0, 170, 0, 170, 20, -170, 20], {size: 2});
// returns [
// [170, 20, 180, 20, 180, 0, 170, 0],
// [-180, 20, -170, 20, -170, 0, -180, 0]
// ]
]

Usage

cutPolygonByMercatorBounds(positions, holeIndices, [options]);

Arguments:

  • positions (Array|TypedArray) - a flat array of the vertex positions that define the polygon's rings. x is longitude in degrees, and y is latitude in degrees.
  • holeIndices (Array|TypedArray|null) - the indices in positions where each hole starts. If null, the polygon has no holes.
  • options (Object, optional)
    • size (Number) - the number of elements in each vertex. Size 2 will interpret positions as [x0, y0, x1, y1, ...] and size 3 will interpret positions as [x0, y0, z0, x1, y1, z1, ...]. Default 2.
    • normalize (Boolean) - make sure the output longitudes are within [-180, 180]. Default true.
    • maxLatitude (Number) - since latitude=90 projects to infinity in Web Mercator projection, maxLatitude will be used to represent the pole. Default 85.051129 which makes the map square.
    • edgeTypes (Boolean) - if true, returns an additional array for each polygon that describes the nature of each vertex. See "returns" below.

Returns:

An array of polygons. Each polygons is represented by an object with the following fields:

  • positions (Array|TypedArray) - a flat array of the vertex positions that define the polygon's rings.
  • holeIndices (Array|TypedArray) - the indices in positions where each hole starts. Not present if the polygon has no holes.
  • edgeTypes (Array) - describes the nature of each vertex in positions:
    • 0 - the segment connecting this vertex to the next is inside the original polygon
    • 1 - the segment connecting this vertex to the next is on the border of the original polygon
- + \ No newline at end of file diff --git a/docs/modules/polygon/api-reference/cut-polyline-by-grid.html b/docs/modules/polygon/api-reference/cut-polyline-by-grid.html index 561abb75..c4d790ed 100644 --- a/docs/modules/polygon/api-reference/cut-polyline-by-grid.html +++ b/docs/modules/polygon/api-reference/cut-polyline-by-grid.html @@ -4,13 +4,13 @@ cutPolylineByGrid | math.gl - +

cutPolylineByGrid

From-v3.2

Subdivides a polyline by intersecting with a uniform grid.

import {cutPolylineByGrid} from '@math.gl/polygon';

cutPolylineByGrid([-10, -10, 10, 10, 30, -10], {size: 2, gridResolution: 10});
// returns [-10, -10, 0, 0, 10, 10, 20, 0, 30, -10]

Usage

cutPolylineByGrid(positions, [options]);

Arguments:

  • positions (Array|TypedArray) - a flat array of the vertex positions that define the polyline.
  • options (Object, optional)
    • size (Number) - the number of elements in each vertex. Size 2 will interpret positions as [x0, y0, x1, y1, ...] and size 3 will interpret positions as [x0, y0, z0, x1, y1, z1, ...]. Default 2.
    • startIndex (Number, optional) - the index in positions to start reading vertices. Default 0.
    • endIndex (Number, optional) - the index in positions to stop reading vertices. Default positions.length.
    • gridResolution (Number, optional) - the grid size. Default 10.
    • gridOffset (Array, optional) - the grid offset in [x, y]. Default [0, 0] i.e. the grid starts from the coordinate origin.
    • broken (Boolean, optional) - if true, the polyline is broken into multiple polylines at the subdivision points. If false, subdivision points are inserted into the original polyline. Default false.

Returns:

A polyline or an array of polylines, depending on the broken option. Each polyline is represented by a positions array that uses the same vertex size as the input.

- + \ No newline at end of file diff --git a/docs/modules/polygon/api-reference/cut-polyline-by-mercator-bounds.html b/docs/modules/polygon/api-reference/cut-polyline-by-mercator-bounds.html index 1893fbca..89b2351c 100644 --- a/docs/modules/polygon/api-reference/cut-polyline-by-mercator-bounds.html +++ b/docs/modules/polygon/api-reference/cut-polyline-by-mercator-bounds.html @@ -4,13 +4,13 @@ cutPolylineByMercatorBounds | math.gl - +

cutPolylineByMercatorBounds

From-v3.2

Splits a geospatial polyline at the 180th meridian.

import {cutPolylineByMercatorBounds} from '@math.gl/polygon';

cutPolylineByMercatorBounds([-10, -10, 10, 10, 30, -10], {size: 2, gridResolution: 10});
// returns [-10, -10, 0, 0, 10, 10, 20, 0, 30, -10]

Usage

cutPolylineByMercatorBounds(positions, [options]);

Arguments:

  • positions (Array|TypedArray) - a flat array of the vertex positions that define the polyline. x is longitude in degrees, and y is latitude in degrees.
  • options (Object, optional)
    • size (Number) - the number of elements in each vertex. Size 2 will interpret positions as [x0, y0, x1, y1, ...] and size 3 will interpret positions as [x0, y0, z0, x1, y1, z1, ...]. Default 2.
    • startIndex (Number, optional) - the index in positions to start reading vertices. Default 0.
    • endIndex (Number, optional) - the index in positions to stop reading vertices. Default positions.length.
    • normalize (Boolean) - make sure the output longitudes are within [-180, 180]. Default true.

Returns:

An array of polylines. Each polyline is represented by a positions array that uses the same vertex size as the input.

- + \ No newline at end of file diff --git a/docs/modules/polygon/api-reference/earcut.html b/docs/modules/polygon/api-reference/earcut.html index 9a89f1be..6a89351c 100644 --- a/docs/modules/polygon/api-reference/earcut.html +++ b/docs/modules/polygon/api-reference/earcut.html @@ -4,13 +4,13 @@ earcut | math.gl - +

earcut

From-v3.5

Computes a triangulation of a polygon using the earcut library.

import {earcut} from '@math.gl/polygon';

earcut([10, 0, 0, 50, 60, 60, 70, 10]);
// returns [1, 0, 3, 3, 2, 1]

// Polygon with a hole starting at vertex 4
earcut([0, 0, 100, 0, 100, 100, 0, 100, 20, 20, 80, 20, 80, 80, 20, 80], [4]);
// returns [3, 0, 4, 5, 4, 0, 3, 4, 7, 5, 0, 1, 2, 3, 7, 6, 5, 1, 2, 7, 6, 6, 1, 2]

Usage

earcut(positions[, holeIndices, size = 2, areas, plane]);

Arguments:

  • positions (Array|TypedArray) - a flat array of the vertex positions that define the polygon.
  • holeIndices (Array, optional) - is an array of hole indices if any (e.g. [5, 8] for a 12-vertex input would mean one hole with vertices 5–7 and another with 8–11).
  • size (Number, optional) - the number of elements in each vertex. Size 2 will interpret positions as [x0, y0, x1, y1, ...] and size 3 will interpret positions as [x0, y0, z0, x1, y1, z1, ...]. Default 2.
  • areas (Array, optional) - areas of outer polygon and holes as computed by getPolygonSignedArea(). Can be optionally supplied to speed up triangulation
  • plane (String, optional) - the 2D projection plane on which to tesselate a 3D polygon on. One of xy, yz, xz. Default to xy

Returns:

An array of indices into the positions array that describes the triangulation of the polygon

- + \ No newline at end of file diff --git a/docs/modules/polygon/api-reference/polygon-utils.html b/docs/modules/polygon/api-reference/polygon-utils.html index 27565563..c7ba27ff 100644 --- a/docs/modules/polygon/api-reference/polygon-utils.html +++ b/docs/modules/polygon/api-reference/polygon-utils.html @@ -4,13 +4,13 @@ polygon-utils | math.gl - +

polygon-utils

A set of polygon-related utility functions. Utility functions are available for flat arrays and for arrays of points. Note: the *Points set of functions is used for arrays of points, and is separated for performance and backwards compatibility reasons.

Usage

import {getPolygonWindingDirection} from '@math.gl/polygon';

Types

PolygonParams

PolygonParams

Fields:

  • start (number) - Start index of the polygon in the array of positions. Defaults to 0.
  • end (number) - End index of the polygon in the array of positions. Defaults to number of positions.
  • size (Number) - Size of a point, 2 (XZ) or 3 (XYZ). Defaults to 2. Affects only polygons stored in flat arrays.
  • isClosed (Boolean) - Indicates that the first point of the polygon is equal to the last point, and additional checks should be ommited.
  • plane ('xy' | 'yz' | 'xz') - The 2D projection plane on which to calculate the area of a 3D polygon. Default 'xy'.

Functions

modifyPolygonWindingDirection

Checks winding direction of the polygon and reverses the polygon in case if opposite winding direction. Note: points are modified in-place.

modifyPolygonWindingDirection(points, direction, params)

Arguments:

  • points (Array|TypedArray) - a flat array of the points that define the polygon.
  • direction (Number) - Requested winding direction. A positive 1 for clockwise, -1 for counter clockwise.
  • options (PolygonParams) - Polygon parameters.

Returns:

Returns true if the winding direction was changed.

getPolygonSignedArea

Returns signed area of the polygon.

getPolygonSignedArea(points, options, plane)

Arguments:

  • points (Array|TypedArray) - a flat array of the points that define the polygon.
  • options (PolygonParams, optional) - Polygon parameters.

Returns:

Signed area of the polygon.

getPolygonWindingDirection

Returns winding direction of the polygon.

getPolygonWindingDirection(points, options)

Arguments:

  • points (Array|TypedArray) - a flat array of the points that define the polygon.
  • options (PolygonParams) - Polygon parameters.

Returns:

  • A positive number is clockwise.
  • A negative number is counter clockwise.

forEachSegmentInPolygon

Calls visitor callback for each segment in the polygon.

forEachSegmentInPolygon(points, (p1x, p1y, p2x, p2y, ind1, ind2) => ...), options

Arguments:

  • points (Array[]|TypedArray[]) - a flat array of the points that define the polygon.
  • visitor (SegmentVisitorFlat) - a callback to call for each segment of the polygon.
  • options (PolygonParams) - Polygon parameters.

modifyPolygonWindingDirectionPoints

Checks winding direction of the polygon and reverses the polygon in case if opposite winding direction. Note: points are modified in-place.

modifyPolygonWindingDirectionPoints(points, direction, options)

Arguments:

  • points (Array[]|TypedArray[]) - an array of the points that define the polygon.
  • direction (Number) - Requested winding direction. A positive 1 for clockwise, -1 for counter clockwise.
  • options (PolygonParams) - Polygon parameters.

Returns:

Returns true if the winding direction was changed.

getPolygonSignedAreaPoints

Returns signed area of the polygon.

getPolygonSignedAreaPoints(points, options)

Arguments:

  • points (Array[]|TypedArray[]) - an array of the points that define the polygon.
  • options (PolygonParams) - Polygon parameters.

Returns:

Signed area of the polygon.

getPolygonWindingDirectionPoints

Returns winding direction of the polygon.

getPolygonWindingDirectionPoints(points, options)

Arguments:

  • points (Array[]|TypedArray[]) - an array of the points that define the polygon.
  • options (PolygonParams) - Polygon parameters.

Returns:

  • A positive number is clockwise.
  • A negative number is counter clockwise.

forEachSegmentInPolygonPoints

Calls visitor callback for each segment in the polygon.

forEachSegmentInPolygonPoints(points, (p1, p2, ind1, ind2) => ..., options)

Arguments:

  • points (Array[]|TypedArray[]) - an array of the points that define the polygon.
  • visitor (SegmentVisitor) - a callback to call for each segment of the polygon.
  • options (PolygonParams) - Polygon parameters.
- + \ No newline at end of file diff --git a/docs/modules/polygon/api-reference/polygon.html b/docs/modules/polygon/api-reference/polygon.html index 6af75a31..24442abf 100644 --- a/docs/modules/polygon/api-reference/polygon.html +++ b/docs/modules/polygon/api-reference/polygon.html @@ -4,14 +4,14 @@ Polygon | math.gl - +

Polygon

Allows an array of points (whether closed or non-closed) to be treated as a Polygon.

Implements the Shoelace formula for determining the area and winding direction of an arbitrary polygon.

Usage

import {Polygon} from '@math.gl/polygon';

Methods

constructor

Creates a new Polygon object.

The polygon object will reference the provided points, assuming them to not be modified for the lifetime of the Polygon object.

getSignedArea

Returns the area with a sign indicating the winding direction.

polygon.getSignedArea()

getArea

polygon.getArea()

Note:

  • A convenience method that returns Math.abs(polygon.getSignedArea()).

getWindingDirection

Returns the direction of the polygon path.

polygon.getWindingDirection()

  • A positive number is clockwise.
  • A negative number is counter clockwise.

Note:

  • A convenience method that returns Math.sign(polygon.getSignedArea())

forEachSegment

Lets the application iterate over each segment.

polygon.forEachSegment((p1, p2) => ...);

modifyWindingDirection

Checks winding direction of the polygon and reverses the polygon in case if opposite winding direction. Note: points of the polygon are modified in-place.

  • A positive number is clockwise.
  • A negative number is counter clockwise.

polygon.modifyWindingDirection(direction);

Returns:

Returns true if the winding direction was changed.

Remarks

  • To avoid having to copy a non-closed path to be able to treat it as a polygon (by adding a copy of the first vertex to then end of the path), instead we define a forEachSegment iteration method that makes sure the last segment is iterated over.
- + \ No newline at end of file diff --git a/docs/modules/proj4.html b/docs/modules/proj4.html index ae3c5db5..a6d31f42 100644 --- a/docs/modules/proj4.html +++ b/docs/modules/proj4.html @@ -4,13 +4,13 @@ Overview | math.gl - +

Overview

From-v3.3

The @math.gl/proj4 module provides support for conversion between major geospatial coordinate reference systems (CRS) and projections used with computer maps, such as:

Classes

ClassDescription
Proj4ProjectionA projection class

Usage

Reproject WGS84 coordinates to another CRS

import {Proj4Projection} from '@math.gl/proj4';

const nad83Proj =
'+title=NAD83 (long/lat) +proj=longlat +a=6378137.0 +b=6356752.31414036 +ellps=GRS80 +datum=NAD83 +units=degrees';
const projection = new Proj4Projection({from: 'WGS84', to: nad83Proj});

const wgs84Position = [21, 78, 5000];
const reprojectedPosition = projection.project(wgs84Position);

Geospatial Coordinate Systems

There are an infinite number of possible coordinate systems; therefore strict syntax is required to describe the parameters of any given CRS. Two main systems are supported in this module: Proj4 strings and WKT strings. Within WKT there exists both OGC WKT and ESRI WKT syntax; both are generally supported though some more-obscure projection keywords may not be used. Note that Proj4 strings can be slightly more accurate in some circumstances than WKT strings.

There are thousands of named "EPSG" projections. This module only includes aliases for those in the section below by default. To use a different EPSG projection, you can use https://epsg.io. For example, https://epsg.io/4326 defines standard longitude-latitude coordinates and lists multiple projection strings. Choose one of the OGC WKT, ESRI WKT, or PROJ.4 strings listed.

The epsg.io website also has a public API, e.g., for WGS 84: https://epsg.io/?q=4326&format=json

{
"status": "ok",
"number_result": 1,
"results": [
{
"code": "4326",
"kind": "CRS-GEOGCRS",
"bbox": [90.0, -180.0, -90.0, 180.0],
"wkt": "GEOGCS[\"WGS 84\",DATUM[\"WGS_1984\",SPHEROID[\"WGS 84\",6378137,298.257223563,AUTHORITY[\"EPSG\",\"7030\"]],AUTHORITY[\"EPSG\",\"6326\"]],PRIMEM[\"Greenwich\",0,AUTHORITY[\"EPSG\",\"8901\"]],UNIT[\"degree\",0.0174532925199433,AUTHORITY[\"EPSG\",\"9122\"]],AUTHORITY[\"EPSG\",\"4326\"]]",
"unit": "degree (supplier to define representation)",
"proj4": "+proj=longlat +datum=WGS84 +no_defs",
"name": "WGS 84",
"area": "World.",
"default_trans": 0,
"trans": [],
"accuracy": ""
}
]
}

If you already know the EPSG identifier, you can make the API request even simpler by adding the desired extension to your url:

// https://epsg.io/4326.wkt
GEOGCS["WGS 84",DATUM["WGS_1984",SPHEROID["WGS 84",6378137,298.257223563,AUTHORITY["EPSG","7030"]],AUTHORITY["EPSG","6326"]],PRIMEM["Greenwich",0,AUTHORITY["EPSG","8901"]],UNIT["degree",0.0174532925199433,AUTHORITY["EPSG","9122"]],AUTHORITY["EPSG","4326"]]
// https://epsg.io/4326.proj4
+proj=longlat +datum=WGS84 +no_defs

Aliases

Note that Proj4Projection allows aliases to be defined and comes with the following pre-installed aliases.

Coordinate systemAliases
Lat/lon, WGS84 datumEPSG:4326, WGS84
Lat/lon, NAD83 datumEPSG:4269
Web mercatorEPSG:3857, EPSG:3785, GOOGLE, EPSG:900913, EPSG:102113

References

E.g. https://epsg.io/4326 provides the definition of WGS84 in WKT-CRS format:

GEOGCS["WGS 84",
DATUM["WGS_1984",
SPHEROID["WGS 84",6378137,298.257223563,
AUTHORITY["EPSG","7030"]],
AUTHORITY["EPSG","6326"]],
PRIMEM["Greenwich",0,
AUTHORITY["EPSG","8901"]],
UNIT["degree",0.0174532925199433,
AUTHORITY["EPSG","9122"]],
AUTHORITY["EPSG","4326"]]

Attribution

This module is a wrapper around proj4js, which has a permissive license. A part of the MetaCRS libraries.

- + \ No newline at end of file diff --git a/docs/modules/proj4/api-reference/proj4-projection.html b/docs/modules/proj4/api-reference/proj4-projection.html index 818469a1..99faa4e7 100644 --- a/docs/modules/proj4/api-reference/proj4-projection.html +++ b/docs/modules/proj4/api-reference/proj4-projection.html @@ -4,13 +4,13 @@ Proj4Projection | math.gl - +

Proj4Projection

From-v3.3

Usage

Reproject WGS84 coordinates to another CRS

import {Proj4Projection} from '@math.gl/proj4';

const nad83Proj =
'+title=NAD83 (long/lat) +proj=longlat +a=6378137.0 +b=6356752.31414036 +ellps=GRS80 +datum=NAD83 +units=degrees';
const projection = new Proj4Projection({from: 'WGS84', to: nad83Proj});

const wgs84Position = [21, 78, 5000];
const reprojectedPosition = projection.project(wgs84Position);

Define Projection Aliases

import {Proj4Projection} from '@math.gl/proj4';

Proj4Projection.defineProjectionAliases({
'EPSG:4326': '+title=WGS 84 (long/lat) +proj=longlat +ellps=WGS84 +datum=WGS84 +units=degrees',
'EPSG:4269':
'+title=NAD83 (long/lat) +proj=longlat +a=6378137.0 +b=6356752.31414036 +ellps=GRS80 +datum=NAD83 +units=degrees'
});
const projection = new Proj4Projection({from: 'EPSG:4326', to: 'EPSG:4269'});

Static Fields

Proj4Projection.defineProjectionAliases(projections: {[alias: string]: string});

Defines projection aliases

Methods

constructor(options: {from?: string, to?: string})

Create a new Proj4Projection instance that can convert between the specified coordinate systems.

project(coord: number[]): number[]

Project a coordinate project from first to second coordinate system

unproject(coord: number[]): number[]

Project a coordinate project from second to first coordinate system

- + \ No newline at end of file diff --git a/docs/modules/sun.html b/docs/modules/sun.html index 2e1274bc..376b1229 100644 --- a/docs/modules/sun.html +++ b/docs/modules/sun.html @@ -4,13 +4,13 @@ Overview | math.gl - +

Overview

@math.gl/sun is a tiny JavaScript library for calculating sun position for the given location and time.

Installation

npm install @math.gl/sun

Usage

import {getSunDirection} from '@math.gl/sun';
const latitude = 37.7749;
const longitude = -122.4194;
const sunDir = getSunDirection(Date.now(), latitude, longitude);

Attribution

This module is a fork of @mourner's SunCalc under BSD 2-clause license.

- + \ No newline at end of file diff --git a/docs/modules/sun/api-reference/get-sun-direction.html b/docs/modules/sun/api-reference/get-sun-direction.html index 6b20d782..8ab636d0 100644 --- a/docs/modules/sun/api-reference/get-sun-direction.html +++ b/docs/modules/sun/api-reference/get-sun-direction.html @@ -4,13 +4,13 @@ getSunDirection | math.gl - + - + \ No newline at end of file diff --git a/docs/modules/sun/api-reference/get-sun.html b/docs/modules/sun/api-reference/get-sun.html index 3493e727..70df13b4 100644 --- a/docs/modules/sun/api-reference/get-sun.html +++ b/docs/modules/sun/api-reference/get-sun.html @@ -4,13 +4,13 @@ getSun | math.gl - + - + \ No newline at end of file diff --git a/docs/modules/types.html b/docs/modules/types.html index 007e633d..41b46bd1 100644 --- a/docs/modules/types.html +++ b/docs/modules/types.html @@ -4,14 +4,14 @@ Overview | math.gl - + - + \ No newline at end of file diff --git a/docs/modules/types/api-reference/array-types.html b/docs/modules/types/api-reference/array-types.html index 9ab9a3b6..1861a351 100644 --- a/docs/modules/types/api-reference/array-types.html +++ b/docs/modules/types/api-reference/array-types.html @@ -4,13 +4,13 @@ Array Types | math.gl - +

Array Types

Types

TypedArray

Any javascript typed array

NumericArray

Any javascript typed array, or any javascript array containing numbers

Utilities

isTypedArray(value: unknown): TypedArray | null

Avoids type problems with the ArrayBuffer.isView() check.

isNumericArray(value: unknown): TypedArray | null

Avoids type problems with the ArrayBuffer.isView() check.

Note: only the type of the first element in a standard array is checked to be a number.

- + \ No newline at end of file diff --git a/docs/modules/web-mercator.html b/docs/modules/web-mercator.html index cec22ece..5cb7bc6d 100644 --- a/docs/modules/web-mercator.html +++ b/docs/modules/web-mercator.html @@ -4,13 +4,13 @@ Overview | math.gl - +

Overview

From-v3.1

The @math.gl/web-mercator module is the new home for the now archivedviewport-mercator-project repository, as of Oct 1, 2019.

The @math.gl/web-mercator module offers projection and camera utilities supporting the spherical Web Mercator Projection. At its core, this is a utility for converting to and from map coordinates (i.e. latitude, longitude) to screen coordinates and back.

Who is this for?

Specifically built for use with deck.gl and react-map-gl, but potentially useful for any web mapping application that wants to support perspective enabled Web Mercator Projections with floating point zoom levels.

Example Usage

The WebMercatorViewport class offers the equivalent of a 3D matrix "camera" class of the type you would find in any 3D/WebGL/OpenGL library.

npm install @math.gl/web-mercator --save
import WebMercatorViewport from '@math.gl/web-mercator';

// A viewport looking at San Francisco city area
const viewport = new WebMercatorViewport({
width: 800,
height: 600,
longitude: -122.45,
latitude: 37.78,
zoom: 12,
pitch: 60,
bearing: 30
});

viewport.project([-122.45, 37.78]);
// returns pixel coordinates [400, 300]
viewport.unproject([400, 300]);
// returns map coordinates [-122.45, 37.78]
- + \ No newline at end of file diff --git a/docs/modules/web-mercator/api-reference/web-mercator-utils.html b/docs/modules/web-mercator/api-reference/web-mercator-utils.html index 12504f0c..352ae9d1 100644 --- a/docs/modules/web-mercator/api-reference/web-mercator-utils.html +++ b/docs/modules/web-mercator/api-reference/web-mercator-utils.html @@ -4,13 +4,13 @@ Web Mercator Utility Functions | math.gl - +

Web Mercator Utility Functions

From-v3.1

lngLatToWorld(lngLat)

Project a coordinate on sphere onto the 512x512 Web Mercator plane.

Parameters:

  • lngLat (Array, required) - Specifies a point on the sphere to project. [lng,lat] in degrees.

Returns:

  • [x, y]

worldToLngLat(xy, scale)

Unproject a coordinate from the 512x512 Web Mercator plane back to the sphere.

Parameters:

  • xy (Array, required) - Specifies a point on the Web Mercator tile to unproject. [x, y] in pixels.

Returns:

  • [lng, lat]

worldToPixels(xyz, projectionMatrix)

Project a coordinate from the Web Mercator coordinate system to screen.

Parameters:

  • xyz (Array, required) - Specifies a point in the Web Mercator tile. z is the elevation and optional.
  • projectionMatrix (Matrix4, required) - The projection matrix.

Returns:

  • [x, y, z] - coordinates on screen, z is the pixel depth.

pixelsToWorld(xyz, unprojectionMatrix, targetZ)

Project a coordinate from screen to the Web Mercator coordinate system.

Parameters:

  • xyz (Array, required) - Specifies a point on screen. z is the pixel depth and optional.
  • unprojectionMatrix (Matrix4, required) - The unprojection matrix.
  • targetZ (Number, optional) - If pixel depth is not specified, targetZ is used as the elevation plane to unproject onto. Default 0.

Returns:

  • [x, y, z] - coordinates on the Web Mercator tile, z is the elevation.

getMeterZoom(viewport)

Returns the zoom level that gives a 1 meter pixel at a certain latitude.

Parameters:

  • viewport (Object) - viewport props
  • viewport.latitude (Number, required)

getDistanceScales(viewport)

Calculate linear scales for quick conversion between meters/degrees/pixels distances around the given lat/lon.

In mercator projection mode, the distance scales vary significantly with latitude. The scale is only reasonably accurate locally.

Parameters:

  • viewport (Object) - viewport props
  • viewport.longitude (Number, required)
  • viewport.latitude (Number, required)
  • viewport.highPrecision (bool, optional) - default false

Returns:

  • distanceScales (Object)
  • distanceScales.unitsPerMeter (Array) - world units per meter in [x, y, z].
  • distanceScales.metersPerUnit (Array) - meters per world unit in [x, y, z]
  • distanceScales.unitsPerDegree (Array) - world units per degree in [x, y, z]
  • distanceScales.degreesPerUnit (Array) - degree per world unit in [x, y, z]
  • distanceScales.unitsPerMeter2 (Array) - if highPrecision is true, returns world units per meter adjustment in [x2, y2, z2]. It offers a cheap way to compensate for the precision loss with latitude. Amends unitsPerMeter by y offset (in meters): [x + x2 * dy, y + y2 * dy, z + z2 * dy].
  • distanceScales.unitsPerDegree2 (Array) - if highPrecision is true, returns world units per degree adjustment in [x2, y2, z2]. It offers a cheap way to compensate for the precision loss with latitude. Amends unitsPerDegree by y offset (in degrees): [x + x2 * dy, y + y2 * dy, z + z2 * dy].

addMetersToLngLat(lngLatZ, xyz)

Offset a spherical position by meters.

Parameters:

  • lngLatZ (Array) - origin in [lng, lat, alt]. Altitude is optional.
  • xyz (Array) - offset from the origin [x, y, z] in meters. x is easting and y is northing. z is optional.

Returns:

  • [lng, lat] if the third component in neither argument is specified, or
  • [lng, lat, alt] otherwise.

getViewMatrix(viewport)

Get a transform matrix that projects from the mercator (pixel) space into the camera (view) space. Centers the map at the given coordinates.

Parameters:

  • viewport (Object) - viewport props
  • viewport.height (Number, required)
  • viewport.pitch (Number, required)
  • viewport.bearing (Number, required)
  • viewport.scale (Number, required)
  • viewport.altitude (Number, required)
  • viewport.center (Array, optional) - pre-calculated world position of map center using getWorldPosition. Default [0, 0].

Returns:

  • viewMatrix (Array) 4x4 matrix.

getProjectionMatrix(viewport)

Get a transform matrix that projects from camera (view) space to clipspace.

Parameters:

  • viewport (Object) - viewport props
  • viewport.width (Number, required)
  • viewport.height (Number, required)
  • viewport.pitch (Number, required)
  • viewport.scale (Number, optional) - required if center is specified
  • viewport.center (Number[], optional) - offset of the target, vec3 in world space
  • viewport.offset (Number[], optional) - offset of the focal point, vec2 in screen space
  • viewport.fovy (Number, optional) - field of view in degrees
  • viewport.altitude (Number, optional) - if provided, field of view is calculated using altitudeToFovy()
  • viewport.nearZMultiplier (Number, optional) - near plane multiplier. Default 1.
  • viewport.farZMultiplier (Number, optional) - far plane multiplier. Default 1

Notes:

To match Mapbox's z-buffer, use these parameters:

  • Before 0.29:

    • nearZMultiplier: 0.1
    • farZMultiplier: 1
  • Starting 0.29:

    • nearZMultiplier: 1 / viewport.height
    • farZMultiplier: 1.01
  • fovy: altitudeToFovy(1.5)

getProjectionParameters({width, height, altitude, fovy, pitch, farZMultiplier}})

Parameters:

  • width (Number, required)
  • height (Number, required)
  • viewport.pitch (Number, optional) - default 0.
  • viewport.scale (Number, optional) - required if center is specified
  • viewport.center (Number[], optional) - offset of the target, vec3 in world space
  • viewport.offset (Number[], optional) - offset of the focal point, vec2 in screen space
  • viewport.fovy (Number, optional) - field of view in degrees
  • altitude (Number, optional) - if provided, field of view is calculated using altitudeToFovy()
  • farZMultiplier (Number, optional) - near plane multiplier. Default 1.
  • farZMultiplier (Number, optional) - far plane multiplier. Default 1.

Returns

  • Object with {fov, aspect, focalDistance, near, far} fields. Note that returned fov is in radians

altitudeToFovy(altitude)

Convert an altitude to field of view such that the focal distance is equal to the altitude.

Parameters:

  • altitude (Number, required) - altitude of camera in screen units

Returns:

  • fovy field of view in degrees

fovyToAltitude(fovy)

Convert a field of view to an altitude equal to the focal distance

Parameters:

  • fovy (Number, required) field of view in degrees

Returns:

  • altitude altitude of camera in screen units

fitBounds(opts)

Returns map settings (longitude, latitude and zoom) that will contain the provided corners within the provided dimensions. Only supports non-perspective mode.

Parameters:

  • opts (Object) - options
  • opts.width (Number, required)
  • opts.height (Number, required)
  • opts.bounds (Array, required) - opposite corners specified as [[lon, lat], [lon, lat]]
  • opts.minExtent (Number, optional) - If supplied, the bounds used to calculate the new map settings will be expanded if the delta width or height of the supplied bounds is smaller than this value.
  • opts.maxZoom=24 (Number, optional) - The returned zoom value will be capped to this value. Avoids returning infinite zoom when the supplied bounds have zero width or height deltas.
  • opts.padding=0 (Number, optional) - the amount of padding in pixels to add to the given bounds.
  • opts.offset=[0,0] (Array, optional) - the center of the given bounds relative to the map's center, [x, y] measured in pixels.

Returns:

  • {longitude, latitude, zoom}

Notes:

  • minExtent - Note that this value represents delta latitude/longitudes and value of 0.01 would roughly represent 1km.

normalizeViewportProps(viewport)

This will adjust the map center and zoom so that the projected map fits into the target viewport size without white gaps.

Parameters:

  • viewport (Object)
  • viewport.width (Number, required)
  • viewport.height (Number, required)
  • viewport.longitude (Number, required)
  • viewport.latitude (Number, required)
  • viewport.zoom (Number, required)
  • viewport.pitch (Number, optional)

Returns:

  • viewport - normalized {width, height, longitude, latitude, zoom, pitch, bearing}

flyToViewport(startProps, endProps, t, opts)

While flying from one viewport to another, returns in-transition viewport props at a given time. This util function implements the algorithm described in “Smooth and efficient zooming and panning.” by Jarke J. van Wijk and Wim A.A. Nuij.

Parameters:

  • startProps (Object) - viewport to fly from
  • startProps.width (Number, required)
  • startProps.height (Number, required)
  • startProps.longitude (Number, required)
  • startProps.latitude (Number, required)
  • startProps.zoom (Number, required)
  • endProps (Object) - viewport to fly from
  • endProps.longitude (Number, required)
  • endProps.latitude (Number, required)
  • endProps.zoom (Number, required)
  • t (Number) - a time factor between 0 and 1. 0 indicates the start of the transition, 1 indicates the end of the transition.
  • opts (Object, optional)
  • opts.curve (Number, optional, default: 1.414) - The zooming "curve" that will occur along the flight path, .

Returns:

  • {longitude, latitude, zoom}

getFlyToDuration(startProps, endProps, opts)

Returns time in milliseconds, that is required perform transition from one viewport to another. Time returned is proportional to the distance we are transitioning to. This util function implements mapbox-gl-js (https://docs.mapbox.com/mapbox-gl-js/api/#map#flyto) duration calculation.

Parameters:

  • startProps (Object) - viewport to fly from
  • startProps.width (Number, required)
  • startProps.height (Number, required)
  • startProps.longitude (Number, required)
  • startProps.latitude (Number, required)
  • startProps.zoom (Number, required)
  • endProps (Object) - viewport to fly from
  • endProps.longitude (Number, required)
  • endProps.latitude (Number, required)
  • endProps.zoom (Number, required)
  • opts (Object, optional) - optional parameters that effect duration calculation.
  • opts.curve (Number, optional, default: 1.414) - The zooming "curve" that will occur along the flight path.
  • opts.speed (Number, optional, default: 1.2) - The average speed of the animation defined in relation to options.curve, it linearly affects the duration, higher speed returns smaller durations and vice versa.
  • opts.screenSpeed (Number, optional) - The average speed of the animation measured in screenfuls per second. Similar to opts.speed it linearly affects the duration, when specified opts.speed is ignored.
  • opts.maxDuration (Number, optional) - Maximum duration in milliseconds, if calculated duration exceeds this value, 0 is returned.

Returns:

  • duration Number, in milliseconds.
- + \ No newline at end of file diff --git a/docs/modules/web-mercator/api-reference/web-mercator-viewport.html b/docs/modules/web-mercator/api-reference/web-mercator-viewport.html index dccda27e..3f6b19b5 100644 --- a/docs/modules/web-mercator/api-reference/web-mercator-viewport.html +++ b/docs/modules/web-mercator/api-reference/web-mercator-viewport.html @@ -4,7 +4,7 @@ WebMercatorViewport | math.gl - + @@ -18,7 +18,7 @@ the bounding box. Each corner is specified in [lon, lat].
  • options.padding (number|{top:number, bottom: number, left: number, right: number}, optional) - The amount of padding in pixels to add to the given bounds from the edge of the viewport. If padding is set as object, all parameters are required.
  • options.offset ([number,number], optional) - The center of the given bounds relative to the viewport's center, [x, y] measured in pixels.
  • opts.minExtent (number, optional) - If supplied, the bounds used to calculate the new map settings will be expanded if the delta width or height of the supplied bounds is smaller than this value.
  • opts.maxZoom=24 (number, optional) - The returned zoom value will be capped to this value. Avoids returning infinite zoom when the supplied bounds have zero width or height deltas.
  • Returns:

    • A new WebMercatorViewport instance
    getMapCenterByLngLatPosition(options: object): [number, number]

    Get the map center that place a given [lng, lat] coordinate at screen point [x, y].

    Parameters:

    • options.lngLat (Array, required) - [lng,lat] coordinates of a location on the sphere.
    • options.pos (Array, required) - [x,y] coordinates of a pixel on screen.

    Returns:

    • [longitude, latitude] as the new map center
    - + \ No newline at end of file diff --git a/docs/roadmap.html b/docs/roadmap.html index c999d366..44bbb51d 100644 --- a/docs/roadmap.html +++ b/docs/roadmap.html @@ -4,13 +4,13 @@ Roadmap | math.gl - +

    Roadmap

    Some of the high-level goals for future and past versions

    v.Next

    • Geometry primitives (spheres, cubes etc)
    • ...

    v4.0

    • Support ES modules
    • Fork gl-matrix (because they are moving to 32 bit precision which is too low for geospatial use cases, and also gl-matrix is not merging the ES module exports we need for wide compatibility).

    v3.6

    • Full typescript support
    - + \ No newline at end of file diff --git a/docs/upgrade-guide.html b/docs/upgrade-guide.html index a21f984b..367e0dbf 100644 --- a/docs/upgrade-guide.html +++ b/docs/upgrade-guide.html @@ -4,7 +4,7 @@ Upgrade Guide | math.gl - + @@ -13,7 +13,7 @@ While the API itself has not changed, in some cases, the introduction of types made it harder to keep supporting some type signatures and overloads.

    Known changes

    • Matrix4.lookAt() - Now only accepts named parameters.
    • SphericalCoordinates() - Constructor is now more restrictive in terms of what parameters it accepts.

    Note that some omissions may be unintentional, feel free to report upgrade issues in the math.gl github repo.

    Upgrading to v3.0

    Matrix API changes

    Matrix setter functions no longer support ommitted parameters. (Motivation: Increased API rigor, improved debugging and library compactness).

    Matrix transforms now return Arrays by default

    The Matrix4 and Matrix3 classes no longer by default create new Vector2, Vector3 and Vector4 instances. Instead they create standard JavaScript arrays.

    Previously a new Vector4 would be allocated if no result parameter was provided.

    import {Matrix4, Vector4} from '@math.gl/core';
    const vector = new Matrix4().transform([0, 0, 0, 1]);
    assert(vector instanceof Vector4);

    Now a plain JavaScript Array is allocated

    import {Matrix4} from '@math.gl/core';
    const vector = new Matrix4().transform([0, 0, 0, 1]);
    assert(vector instanceof Array);

    The old behavior can be restored by providing the result parameter

    import {Matrix4, Vector4} from '@math.gl/core';
    const vector = new Matrix4().transform([0, 0, 0, 1], new Vector4());
    assert(vector instanceof Vector4);

    Motivation: This change reduces dependencies between math.gl core classes which improves tree-shaking and bundle sizes.

    Matrix setter functions no longer support ommitted parameters

    Motivation: This change increases rigor, facilitates debugging, and improves library compactness, and the use case for default parameters was questionable.

    The following functions have been deprecated:

    MethodReplacementReason
    Matrix*.setColumnMajorMatrix*.setAPI simplification
    Matrix4.transformPointMatrix4.transformName alignment
    Matrix4.transformVectorMatrix4.transformName alignment
    Matrix4.transformDirectionMatrix4.transformAsVectorName alignment
    Matrix3.transformVectorMatrix3.transformName alignment
    Matrix3.transformVector2Matrix3.transformGeneralize
    Matrix3.transformVector3Matrix3.transformGeneralize

    The following functions have been removed:

    MethodReplacementReason
    Vector2.crossVector3.crossCross products by definition work on 3 dimensional vectors.

    Upgrading to v2.0

    Experimental exports are now exported with a leading underscore (_), instead of as members of the experimental namespace:

    NOW: math.gl v2

    import {_Euler as Euler} from '@math.gl/core';

    BEFORE: math.gl v1.x

    import {experimental} from '@math.gl/core';
    const {Euler} = experimental;

    The experimental name space export has been removed.

    Upgrading to v1.1

    Removed Functionality

    The Euler class is no longer included as an experimental export. It would need to be imported from the dist folder.

    - + \ No newline at end of file diff --git a/docs/whats-new.html b/docs/whats-new.html index 1c3ada29..9ad00a6b 100644 --- a/docs/whats-new.html +++ b/docs/whats-new.html @@ -4,7 +4,7 @@ What's New | math.gl - + @@ -12,7 +12,7 @@

    What's New

    v4.0 S2 (DGGS)

    v4.0 GeoHash (DGGS)

    v4.0 Quadkey (DGGS)

    v3.4 Geoid (Earth Gravity Model)

    v3.2 TypeScript

    v3.0 WGS84 & Ellipsoid

    v4.0

    Release Date: Oct 14, 2023.

    • ESM (ECMAScript modules).
    • Node.js v16, v18, v20.
    • Typescript v5
    • gl-matrix dependency removed.
    • New modules for working with DGGS (Discrete Global Grid System) math.

    @math.gl/dggs-geohash (NEW MODULE)

    • New module with lightweight math for the GeoHash DGGS (Discrete Global Grid System).

    @math.gl/dggs-quadkey (NEW MODULE)

    • New module with lightweight math for the quadkey DGGS (Discrete Global Grid System).

    @math.gl/dggs-s2 (NEW MODULE)

    • New module that contains a lightweight implementation of the S2 DGGS (Discrete Global Grid System).

    @math.gl/core

    • config is now truly global (stored on globalThis).
    • gl-matrix dependency removed.

    @math.gl/types

    • New isTypedArray() and isNumericArray() utilities that check values and return properly restricted types to help write clean TypeScript code (e.g. avoids the DataView case when using ArrayBuffer.isView()).

    v3.6

    Release Date: June 10, 2022

    Codebase has been fully converted to typescript. In general this means that users can expect the types exported from math.gl to be considerably improved, however in some function signatures are no longer supported. For details, consult the upgrade guide.

    @math.gl/types (NEW)

    • New module that exports a few typescript types that e.g. generalize handling of numeric arrays.

    @math.gl/polygon (NEW)

    • Includes earcut 2.2 (various bug fixes for edge cases)
    • The earcut utility supports a new argument plane to calculate tesselation on alternative projection planes.

    v3.5

    Release Date: July 14, 2021

    @math.gl/web-mercator

    • getBounds() now supports an optional fovy parameter on the WebMercatorViewport object
    • getProjectionMatrix() and getProjectionParameters() now accept a fovy parameter

    @math.gl/polygon

    • Improve performance of getPolygonSignedArea() by 3x
    • Addition of earcut() method for triangulating polygons

    math.gl/culling

    • New TypeScript interface BoundingVolume with common operations for bounding volumes (BoundingSphere, AxisAlignedBoundingBox, OrientedBoundingBox).
    • BoundingVolume.transform() supported on all bounding volumes.

    v3.4

    Release Date: Jan 7, 2021

    @math.gl/geoid - New module

    • Support for geoid-based earth gravity models.
    • New Geoid class calculates the height offset (aka "undulation") from the pure ellipsoid for a given lng/lat (using spherical harmonics).
    • Geoid instances can be initialized with PGM-encoded earth gravity model coefficient files from standard sources.

    @math.gl/polygon

    • Support for flat arrays (e.g. polygons stored in typed arrays)
    • Support for calling polygon utilities directly on arrays, without a Polygon instance.
    • New function modifyPolygonWindingDirection() to modify polygon array winding direction in-place.

    v3.3

    Release Date: Oct 9, 2020

    @math.gl/proj4 - New module

    • A new module supporting conversion between a wide range of geospatial coordinate reference systems specified e.g. using the OGC WKT-CRS specification.

    v3.2

    Release Date: July 18, 2020

    Typescript

    • Typescript type definitions (.d.ts files) are now exported for all math.gl modules.

    @math.gl/polygon - New module

    • A new module offering geospatial polygon clipping functions.

    v3.1

    Release date: Dec 16, 2019

    @math.gl/web-mercator

    • WebMercator projection support is now available through the new @math.gl/web-mercator npm sub-module.
    • The @math.gl/web-mercator module is an evolution of the now archived viewport-mercator-project repository.

    v3.0

    Release date: Aug 8, 2019

    The 3.0 release brings support for geospatial math, culling, performance improvements, and some API consolidation.

    @math.gl/geospatial

    A new module (developed in collaboration with the Cesium engineering team) providing WebGL-framework-independent geospatial math classes and algorithms:

    • New class Ellipsoid and constant Ellipsoid.WGS84 for working with WSG84 coordinates

    @math.gl/culling

    A new module (developed in collaboration with the Cesium engineering team) providing WebGL-framework-independent classesthat support geometric intersection calculations (primarily intended to support frustum culling operations):

    • New class AxisAlignedBoundingBox
    • New class OrientedBoundingBox
    • New class BoundingSphere
    • New class CullingVolume

    @math.gl/core

    Transform API Consolidation

    The API for transformations (i.e. multiplying vectors with matrices or quaternions) has been extended and made more orthogonal:

    • The transform* methods are now available on all Vector classes, in addition to on the Matrix classes. Among other things, this enables transformations without using Matrix classes.
    • Naming consistency of transform methods across classes (transform, transformAsPoint, transformAsVector).
    • Alternative transform methods added to the Vector classes (transformByMatrix3, transformByMatrix2, transformByMatrix2x3 and transformByQuaternion). Simplifies using the most efficient transformation for the job.

    Matrix classes

    • New methods Matrix*.setColumn() and Matrix*.getColumn()
    • New method Matrix*.toString()
    • Improved method: Matrix4.frustum() now supports infinite far plane (parity with Matrix4.perspective, which already supported this).

    Utility Functions

    • New: global functions toRadians and toDegrees
    • New: global function exactEqual

    Performance Improvements (and Website Benchmarks)

    A benchmarking example has been added to the website that makes it easy to assess the performance of the math.gl library on your own browser. The math.gl library has been carefully tuned based on these benchmarks and performance of the library has been significantly improved over version 2.x.

    v2.3

    Release date: Jan 29, 2019

    • New class: Matrix3
    • New: Add scale factor support to Matrix3 and Matrix4
    • Support quaternion to euler conversion
    • Now uses the official gl-matrix@3.0.0 package as dependency instead of forked gl-matrix packages.

    v2.2

    Release date: Sep 20, 2018

    • Use @babel/runtime to reduce bundle size
    • equals function fix on arrays

    v2.0

    Release date: June 25, 2018

    New Naming Convention for Experimental Exports

    Experimental exports are now exported with a leading underscore (_), instead of as members of the experimental namespace.

    The change was made to make it possible for tree-shaking bundlers to remove unused experimental exports from applications.

    v1.2

    Release date: May 4, 2018

    • New lerp utility
    • Experimental Pose class

    v1.1

    Release date: April 16, 2018

    Matrix4 Improvements

    Matrix4.orthographic() - To simplify switching between perspective and orthographic views, math.gl now offers an additional method for creating orthographic projection matrix, that takes the same parameters as Matrix4.perspective(), with the addition of one additional parameter, focalDistance. See Matrix4.orthographic({fovy, aspect, focalDistance, near, far})

    Bundle Size Reduction

    math.gl has been tuned to have approximately 20% smaller footprint when bundled in applications.

    THREE.js Compatibility

    math.gl classes now pass large parts of the THREE.js test suite, which should make it easier to reuse code written for the THREE.js math library.

    v1.0

    Release date: Jan 9, 2018

    Initial release.

    - + \ No newline at end of file diff --git a/examples.html b/examples.html index 1e088d28..f677c65a 100644 --- a/examples.html +++ b/examples.html @@ -4,13 +4,13 @@ math.gl - + - + \ No newline at end of file diff --git a/examples/benchmarks.html b/examples/benchmarks.html index 1208785d..ecfa6e0d 100644 --- a/examples/benchmarks.html +++ b/examples/benchmarks.html @@ -4,13 +4,13 @@ math.gl - + - + \ No newline at end of file diff --git a/index.html b/index.html index 0e0a0735..ad0266dd 100644 --- a/index.html +++ b/index.html @@ -4,13 +4,13 @@ Home | math.gl - +

    math.gl

    A collection of math modules for Geospatial and 3D visualization use cases

    GET STARTED

    A collection of math modules for Geospatial and 3D use cases.


    Toolbox of 3D math modules

    Matrices and vectors, bounding boxes, frustum culling etc

    Geospatial reprojection, gravity models, solar position, etc

    Strict TypeScript and run-time checks that detect bad data

    - + \ No newline at end of file diff --git a/search-index-docs-default-current.json b/search-index-docs-default-current.json index 55396e71..6324a43d 100644 --- a/search-index-docs-default-current.json +++ b/search-index-docs-default-current.json @@ -1 +1 @@ -{"documents":[{"id":1,"pageTitle":"Introduction","sectionTitle":"Introduction","sectionRoute":"/math.gl/docs","type":"docs"},{"id":2,"pageTitle":"Introduction","sectionTitle":"Features","sectionRoute":"/math.gl/docs#features","type":"docs"},{"id":3,"pageTitle":"Introduction","sectionTitle":"Modules","sectionRoute":"/math.gl/docs#modules","type":"docs"},{"id":4,"pageTitle":"Introduction","sectionTitle":"Supported Browsers and Node 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