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.