#projection #4d #sphere #graphics

hypersphere

Simple 4D primitives for rotation and projection

2 releases

0.1.1 Aug 26, 2023
0.1.0 Aug 26, 2023

#1936 in Math

MIT/Apache

21KB
341 lines

Hypersphere

This crate implements some simple rotation and projection primitives for 4D geometry on top of glam.

Projection

Implements 4D to 3D projection on the surface of a sphere by way of stereographic projection.

It allows you to project both points and vectors tangent to the sphere at a point through a stereographic projection. The latter is useful when embedding 3D geometry on the surface of a hypersphere and ensuring that normal vectors remain normal vectors under projection (recall that stereographic projection is angle-preserving).

4D Rotations

Implements a double-quaternion representation of 4D rotations.

Includes:

  • Rotation through basis planes (XY, XZ, etc.).
  • Rotation through arbitrary pairs of planes specified by orthonormal vectors.
  • Minimal rotations from one point to another.
  • Cayley's decomposition of arbitrary 4D rotation matrices into this crate's representation.
  • Slerp, inherited from quaternions.

Basis Utilities

Includes functions to:

  • Construct an arbitrary orthogonal vector to another vector.
  • Construct an arbitrary orthogonal vector to two vectors.
  • Construct a scaled version of the orthogonal vector to three vectors.
  • Construct an orthonormal basis given two vectors that span a plane.

Sample Data

Implements a simple algorithm to generate the 600-cell's vertices (not indices), as useful sample data.

Dependencies

~3.5MB
~103K SLoC