Crate lowdim

Affine geometry for discrete 2d, 3d and 4d worlds.

Provides vectors, matrices, points and more to simplify programming for 2d to 4d worlds. Features include:

• Vector and point arithmetic
• Bounding boxes and iterators over the points inside them
• Arrays indexed by points in bounding boxes
• Taxicab (L1) and maximum (L∞) metrics
• Iterators over orthogonal and king’s move neighbourhoods
• Rotations and reflections (currently only implemented for 2d)

This was originally motivated by Advent of Code (yes, Santa’s elves use the 4th dimension, for example for time travel).

Crate Status

Experimental

Limitations

• Rotations and reflections are only implemented for the 2d case.

Crate Feature Flags

• random
  • Off by default.
  • Adds a dependency to the rand crate.
  • Adds the method random_point to generate random points in a bounding box.

Modules

• affine_transformation
  Affine transformations for n-dimensional discrete spaces.
• array
  n-dimensional arrays indexed by points in a bounding box.
• bbox
  n-dimensional bounding boxes.
• integer
  Contains traits defining required properties of the underlying integer types.
• matrix
  Traits for matrices.
• matrix2d
  2d matrices.
• matrix3d
  3d matrices.
• matrix4d
  4d matrices.
• point
  Points in the affine space.
• sym2d
  Symmetries of 2d vectors.
• vec2d
  2d vectors.
• vec3d
  3d vectors.
• vec4d
  4d vectors.
• vector
  Traits for vectors.

Structs

• AffineTransformation
  An affine transformation.
• Array
  An array indexed by points in a bounding box.
• BBox
  A bounding box.
• Matrix2d
  A 2d discrete matrix.
• Matrix3d
  A 3d discrete matrix.
• Matrix4d
  A 4d discrete matrix.
• Point
  A point in a discrete space.
• Vec2d
  A 2d discrete vector.
• Vec3d
  A 3d discrete vector.
• Vec4d
  A 4d discrete vector.

Enums

• Sym2d
  The symmetries of discrete 2d vectors.

Traits

• Integer
  Required traits and operations for integers.
• Matrix
  Required traits and operations for matrices.
• MatrixOps
  Required arithmetic operations for matrices.
• Vector
  Required traits and operations for vectors.
• VectorOps
  Required arithmetic operations for vectors.

Functions

• bb2d
  Creates a 2d bounding box from ranges of x and y coordinates.
• bb3d
  Creates a 3d bounding box from ranges of x, y and z coordinates.
• bb4d
  Creates a 4d bounding box from ranges of x, y, z and w coordinates.
• p2d
  Creates a 2d point.
• p3d
  Creates a 3d point.
• p4d
  Creates a 4d point.
• v2d
  Creates a 2d vector.
• v3d
  Creates a 3d vector.
• v4d
  Creates a 4d vector.

Type Aliases

• AffineTransformation2d
  A 2d affine transformation.
• AffineTransformation3d
  A 3d affine transformation.
• AffineTransformation4d
  A 4d affine transformation.
• Array2d
  A 2d array indexed by points in a bounding box.
• Array3d
  A 3d array indexed by points in a bounding box.
• Array4d
  A 4d array indexed by points in a bounding box.
• BBox2d
  A 2d bounding box.
• BBox3d
  A 3d bounding box.
• BBox4d
  A 4d bounding box.
• Point2d
  A 2d point.
• Point3d
  A 3d point.
• Point4d
  A 4d point.