3D Geometry Project

This project involves creating a series of classes to represent 3D geometries in Cartesian space. The project includes creating points, vectors, triangles, faces, and constructing a 3D cube using a mesh of triangles and faces. Below are details of the classes, their functionality, and the objectives of the project.

Table of Contents

• Classes
  • Point.java
  • UnitVector.java
  • Triangle.java
  • Face.java
  • Cube.java
• Instructions
• Grading
• Additional Notes

Classes

Point.java

This class represents a point in 3D Cartesian space.

• Fields:

  • x, y, z (all double, private): Represents the coordinates of the point.

• Constructors:

  • Point(double x, double y, double z): Initializes the point with given coordinates.
  • Point(): Initializes the point at (0.0, 0.0, 0.0).

• Methods:

  • getX(), getY(), getZ(): Returns the respective coordinate values.
  • setX(double x), setY(double y), setZ(double z): Sets the respective coordinate values.
  • compareWith(Point point): Compares this point with another within a precision of ±0.0001.
  • toString(): Returns the formatted string of the point (xX.xxx, yY.xxx, zZ.xxx).

UnitVector.java

Represents a 3D unit vector with a magnitude of 1.

• Fields:

  • i, j, k (all double, private): The vector components.

• Constructors:

  • UnitVector(double i, double j, double k): Creates a vector and scales it to ensure its magnitude is 1.
  • UnitVector(Point start, Point end): Creates a vector from two points and scales it if necessary.
  • UnitVector(): Creates an invalid vector (0.0, 0.0, 0.0).

• Methods:

  • getI(), getJ(), getK(): Returns the respective vector components.
  • compareWith(UnitVector vector): Compares two vectors for equality within ±0.0001.
  • crossProduct(UnitVector b): Returns the cross product of two unit vectors.
  • toString(): Returns the formatted string representation <iI.xxx, jJ.xxx, kK.xxx>.

Triangle.java

Represents a triangle in 3D space defined by three vertices and a surface normal.

• Fields:

  • vertexA, vertexB, vertexC (all Point, private): The three vertices.
  • surfaceNormal (UnitVector, private): The surface normal vector.

• Constructors:

  • Triangle(Point vertA, Point vertB, Point vertC): Initializes a triangle with the cross product of vectors from A to B and A to C.
  • Triangle(): Creates a default triangle with vertices at (0.0, 0.0, 0.0) and an invalid surface normal.

• Methods:

  • getVertexA(), getVertexB(), getVertexC(): Returns the respective vertex points.
  • getSurfaceNormal(): Returns the surface normal vector.
  • getVertices(): Returns an array of the triangle's vertices.
  • compareWith(Triangle triangle): Compares this triangle with another for equality.
  • toString(): Returns the formatted string representation of the triangle.

Face.java

Represents a face of a cube made up of two triangles sharing two vertices.

• Fields:

  • mesh (Triangle[], private): Array of two triangles forming a face.
  • surfaceNormal (UnitVector, private): The surface normal vector.

• Constructors:

  • Face(Triangle one, Triangle two): Initializes the face if the triangles share two vertices and have equal surface normals.
  • Face(): Initializes an invalid face.

• Methods:

  • getMesh(): Returns the array of triangles forming the face.
  • getSurfaceNormal(): Returns the surface normal vector.
  • compareWith(Face face): Compares this face with another for equality.
  • toString(): Returns the formatted string representation of the face.

Cube.java

Represents a cube comprised of six faces, each of which is made up of two triangles.

• Fields:

  • mesh (Face[], private): Array of six faces making up the cube.

• Constructors:

  • Cube(Face one, Face two, Face three, Face four, Face five, Face six): Initializes a cube if each face shares an edge with four others and opposed faces have opposite normals.
  • Cube(): Initializes an invalid cube.

• Methods:

  • getMesh(): Returns the array of faces forming the cube.
  • toString(): Returns the formatted string representation of the cube.

Instructions

1. Implement the classes as specified above.
2. Ensure that all constructors and methods work as per the assignment description.
3. Test your classes using the provided GeoFactory.java.
4. Adhere to the coding style guidelines.

Grading

This project is worth 2.5% of your final grade. Your code will be graded on the following:

• Correctness of implementation
• Adherence to coding standards
• Handling of edge cases and precision requirements

Additional Notes

• Double Precision: For this assignment, comparisons of double values should be within ±0.0001.
• Equality Checks: Use precision checks for comparing Point, UnitVector, Triangle, and Face objects.
• Cube Geometry: No need to differentiate between squares and parallelograms or cubes and parallelepipeds.
• Invalid Objects: Handle invalid triangles, faces, and cubes as described.

Good luck, and remember to test thoroughly!