This crate implements some simple rotation and projection primitives for 4D geometry on top of glam.
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).
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.
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.
Implements a simple algorithm to generate the 600-cell's vertices (not indices), as useful sample data.