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Vector2DOps Trait - Proposal #1025

Merged
merged 13 commits into from
Jul 31, 2023
2 changes: 2 additions & 0 deletions geo/CHANGES.md
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- Add `TriangulateEarcut` algorithm trait to triangulate polygons with the earcut algorithm.
- <https://github.com/georust/geo/pull/1007>
- Add `Vector2DOps` trait to algorithims module and implemented it for `Coord<T::CoordFloat>`
- <https://github.com/georust/geo/pull/1025>

## 0.25.0

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4 changes: 4 additions & 0 deletions geo/src/algorithm/mod.rs
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Expand Up @@ -236,6 +236,10 @@ pub mod triangulate_earcut;
#[cfg(feature = "earcutr")]
pub use triangulate_earcut::TriangulateEarcut;

/// Vector Operations for 2D coordinates
mod vector_ops;
pub use vector_ops::Vector2DOps;

/// Calculate the Vincenty distance between two `Point`s.
pub mod vincenty_distance;
pub use vincenty_distance::VincentyDistance;
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366 changes: 366 additions & 0 deletions geo/src/algorithm/vector_ops.rs
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//! This module defines the [Vector2DOps] trait and implements it for the
//! [Coord] struct.

use crate::{Coord, CoordFloat, CoordNum};

/// Defines vector operations for 2D coordinate types which implement CoordFloat
///
/// This trait is intended for internal use within the geo crate as a way to
/// bring together the various hand-crafted linear algebra operations used
/// throughout other algorithms and attached to various structs.
pub trait Vector2DOps<Rhs = Self>
where
Self: Sized,
{
type Scalar: CoordNum + Send + Sync;

/// The euclidean distance between this coordinate and the origin
///
/// `sqrt(x² + y²)`
///
fn magnitude(self) -> Self::Scalar;

/// The squared distance between this coordinate and the origin.
/// (Avoids the square root calculation when it is not needed)
///
/// `x² + y²`
///
fn magnitude_squared(self) -> Self::Scalar;

/// Rotate this coordinate around the origin by 90 degrees clockwise.
///
/// `a.left() => (-a.y, a.x)`
///
/// Assumes a coordinate system where positive `y` is up and positive `x` is
/// to the right. The described rotation direction is consistent with the
/// documentation for [crate::algorithm::rotate::Rotate].
fn left(self) -> Self;

/// Rotate this coordinate around the origin by 90 degrees anti-clockwise.
///
/// `a.right() => (a.y, -a.x)`
///
/// Assumes a coordinate system where positive `y` is up and positive `x` is
/// to the right. The described rotation direction is consistent with the
/// documentation for [crate::algorithm::rotate::Rotate].
fn right(self) -> Self;

/// The inner product of the coordinate components
///
/// `a · b = a.x * b.x + a.y * b.y`
///
fn dot_product(self, other: Rhs) -> Self::Scalar;

/// The calculates the `wedge product` between two vectors.
///
/// `a ∧ b = a.x * b.y - a.y * b.x`
///
/// Also known as:
///
/// - `exterior product`
/// - because the wedge product comes from 'Exterior Algebra'
/// - `perpendicular product`
/// - because it is equivalent to `a.dot(b.right())`
/// - `2D cross product`
/// - because it is equivalent to the signed magnitude of the
/// conventional 3D cross product assuming `z` ordinates are zero
/// - `determinant`
/// - because it is equivalent to the `determinant` of the 2x2 matrix
/// formed by the column-vector inputs.
///
/// ## Examples
///
/// The following list highlights some examples in geo which might be
/// brought together to use this function:
///
/// 1. [geo_types::Point::cross_prod()] is already defined on
/// [geo_types::Point]... but that it seems to be some other
/// operation on 3 points??
/// 2. [geo_types::Line] struct also has a [geo_types::Line::determinant()]
/// function which is the same as `line.start.wedge_product(line.end)`
/// 3. The [crate::algorithm::Kernel::orient2d()] trait default
/// implementation uses cross product to compute orientation. It returns
/// an enum, not the numeric value which is needed for line segment
/// intersection.
///
/// ## Properties
///
/// - The absolute value of the cross product is the area of the
/// parallelogram formed by the operands
/// - Anti-commutative: The sign of the output is reversed if the operands
/// are reversed
/// - If the operands are colinear with the origin, the value is zero
/// - The sign can be used to check if the operands are clockwise with
/// respect to the origin, or phrased differently:
/// "is a to the left of the line between the origin and b"?
/// - If this is what you are using it for, then please use
/// [crate::algorithm::Kernel::orient2d()] instead as this is more
/// explicit and has a `RobustKernel` option for extra precision.
fn wedge_product(self, other: Rhs) -> Self::Scalar;

/// Try to find a vector of unit length in the same direction as this
/// vector.
///
/// Returns `None` if the result is not finite. This can happen when
///
/// - the vector is really small (or zero length) and the `.magnitude()`
/// calculation has rounded-down to `0.0`
/// - the vector is really large and the `.magnitude()` has rounded-up
/// or 'overflowed' to `f64::INFINITY`
/// - Either x or y are `f64::NAN` or `f64::INFINITY`
fn try_normalize(self) -> Option<Self>;

/// Returns true if both the x and y components are finite
// Annotation to disable bad clippy lint; It is not good to use
// `&self` as clippy suggests since Coord is Copy
#[allow(clippy::wrong_self_convention)]
fn is_finite(self) -> bool;
}

impl<T> Vector2DOps for Coord<T>
where
T: CoordFloat + Send + Sync,
{
type Scalar = T;

fn wedge_product(self, right: Coord<T>) -> Self::Scalar {
self.x * right.y - self.y * right.x
}

fn dot_product(self, other: Self) -> Self::Scalar {
self.x * other.x + self.y * other.y
}

fn magnitude(self) -> Self::Scalar {
(self.x * self.x + self.y * self.y).sqrt()
}

fn magnitude_squared(self) -> Self::Scalar {
self.x * self.x + self.y * self.y
}

fn left(self) -> Self {
Self {
x: -self.y,
y: self.x,
}
}

fn right(self) -> Self {
Self {
x: self.y,
y: -self.x,
}
}

fn try_normalize(self) -> Option<Self> {
let magnitude = self.magnitude();
let result = self / magnitude;
// Both the result AND the magnitude must be finite they are finite
// Otherwise very large vectors overflow magnitude to Infinity,
// and the after the division the result would be coord!{x:0.0,y:0.0}
// Note we don't need to check if magnitude is zero, because after the division
// that would have made result non-finite or NaN anyway.
if result.is_finite() && magnitude.is_finite() {
Some(result)
} else {
None
}
}

fn is_finite(self) -> bool {
self.x.is_finite() && self.y.is_finite()
}
}

#[cfg(test)]
mod test {
use super::Vector2DOps;
use crate::coord;

#[test]
fn test_cross_product() {
// perpendicular unit length
let a = coord! { x: 1f64, y: 0f64 };
let b = coord! { x: 0f64, y: 1f64 };

// expect the area of parallelogram
assert_eq!(a.wedge_product(b), 1f64);
// expect swapping will result in negative
assert_eq!(b.wedge_product(a), -1f64);

// Add skew; expect results should be the same
let a = coord! { x: 1f64, y: 0f64 };
let b = coord! { x: 1f64, y: 1f64 };

// expect the area of parallelogram
assert_eq!(a.wedge_product(b), 1f64);
// expect swapping will result in negative
assert_eq!(b.wedge_product(a), -1f64);

// Make Colinear; expect zero
let a = coord! { x: 2f64, y: 2f64 };
let b = coord! { x: 1f64, y: 1f64 };
assert_eq!(a.wedge_product(b), 0f64);
}

#[test]
fn test_dot_product() {
// perpendicular unit length
let a = coord! { x: 1f64, y: 0f64 };
let b = coord! { x: 0f64, y: 1f64 };
// expect zero for perpendicular
assert_eq!(a.dot_product(b), 0f64);

// Parallel, same direction
let a = coord! { x: 1f64, y: 0f64 };
let b = coord! { x: 2f64, y: 0f64 };
// expect +ive product of magnitudes
assert_eq!(a.dot_product(b), 2f64);
// expect swapping will have same result
assert_eq!(b.dot_product(a), 2f64);

// Parallel, opposite direction
let a = coord! { x: 3f64, y: 4f64 };
let b = coord! { x: -3f64, y: -4f64 };
// expect -ive product of magnitudes
assert_eq!(a.dot_product(b), -25f64);
// expect swapping will have same result
assert_eq!(b.dot_product(a), -25f64);
}

#[test]
fn test_magnitude() {
let a = coord! { x: 1f64, y: 0f64 };
assert_eq!(a.magnitude(), 1f64);

let a = coord! { x: 0f64, y: 0f64 };
assert_eq!(a.magnitude(), 0f64);

let a = coord! { x: -3f64, y: 4f64 };
assert_eq!(a.magnitude(), 5f64);
}

#[test]
fn test_magnitude_squared() {
let a = coord! { x: 1f64, y: 0f64 };
assert_eq!(a.magnitude_squared(), 1f64);

let a = coord! { x: 0f64, y: 0f64 };
assert_eq!(a.magnitude_squared(), 0f64);

let a = coord! { x: -3f64, y: 4f64 };
assert_eq!(a.magnitude_squared(), 25f64);
}

#[test]
fn test_left_right() {
let a = coord! { x: 1f64, y: 0f64 };
let a_left = coord! { x: 0f64, y: 1f64 };
let a_right = coord! { x: 0f64, y: -1f64 };

assert_eq!(a.left(), a_left);
assert_eq!(a.right(), a_right);
assert_eq!(a.left(), -a.right());
}

#[test]
fn test_left_right_match_rotate() {
use crate::algorithm::rotate::Rotate;
use crate::Point;
// The aim of this test is to confirm that wording in documentation is
// consistent.

// when the user is in a coordinate system where the y axis is flipped
// (eg screen coordinates in a HTML canvas), then rotation directions
// will be different to those described in the documentation.

// The documentation for the Rotate trait says: 'Positive angles are
// counter-clockwise, and negative angles are clockwise rotations'

let counter_clockwise_rotation_degrees = 90.0;
let clockwise_rotation_degrees = -counter_clockwise_rotation_degrees;

let a: Point = coord! { x: 1.0, y: 0.0 }.into();
let origin: Point = coord! { x: 0.0, y: 0.0 }.into();

// left is anti-clockwise
assert_relative_eq!(
Point::from(a.0.left()),
a.rotate_around_point(counter_clockwise_rotation_degrees, origin),
);
// right is clockwise
assert_relative_eq!(
Point::from(a.0.right()),
a.rotate_around_point(clockwise_rotation_degrees, origin),
);
}

#[test]
fn test_try_normalize() {
// Already Normalized
let a = coord! {
x: 1.0,
y: 0.0
};
assert_relative_eq!(a.try_normalize().unwrap(), a);

// Already Normalized
let a = coord! {
x: 1.0 / f64::sqrt(2.0),
y: -1.0 / f64::sqrt(2.0)
};
assert_relative_eq!(a.try_normalize().unwrap(), a);

// Non trivial example
let a = coord! { x: -10.0, y: 8.0 };
assert_relative_eq!(
a.try_normalize().unwrap(),
coord! { x: -10.0, y: 8.0 } / f64::sqrt(10.0 * 10.0 + 8.0 * 8.0)
);
}

#[test]
fn test_try_normalize_edge_cases() {
use float_next_after::NextAfter;

// The following tests demonstrate some of the floating point
// edge cases that can cause try_normalize to return None.

// Zero vector - Normalize returns None
let a = coord! { x: 0.0, y: 0.0 };
assert_eq!(a.try_normalize(), None);

// Very Small Input - Normalize returns None because of
// rounding-down to zero in the .magnitude() calculation
let a = coord! {
x: 0.0,
y: 1e-301_f64
};
assert_eq!(a.try_normalize(), None);

// A large vector where try_normalize returns Some
// Because the magnitude is f64::MAX (Just before overflow to f64::INFINITY)
let a = coord! {
x: f64::sqrt(f64::MAX/2.0),
y: f64::sqrt(f64::MAX/2.0)
};
assert!(a.try_normalize().is_some());

// A large vector where try_normalize returns None
// because the magnitude is just above f64::MAX
let a = coord! {
x: f64::sqrt(f64::MAX / 2.0),
y: f64::sqrt(f64::MAX / 2.0).next_after(f64::INFINITY)
};
assert_eq!(a.try_normalize(), None);

// Where one of the components is NaN try_normalize returns None
let a = coord! { x: f64::NAN, y: 0.0 };
assert_eq!(a.try_normalize(), None);

// Where one of the components is Infinite try_normalize returns None
let a = coord! { x: f64::INFINITY, y: 0.0 };
assert_eq!(a.try_normalize(), None);
}
}