https://github.com/optimisticpeach/hypersphere

4D rotation and projection primitives.
https://github.com/optimisticpeach/hypersphere

Last synced: 3 months ago
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4D rotation and projection primitives.

• Host: GitHub
• URL: https://github.com/optimisticpeach/hypersphere
• Owner: OptimisticPeach
• License: apache-2.0
• Created: 2023-08-26T04:09:56.000Z (over 1 year ago)
• Default Branch: main
• Last Pushed: 2023-08-27T05:51:03.000Z (over 1 year ago)
• Last Synced: 2024-10-06T13:17:51.562Z (3 months ago)
• Language: Rust
• Size: 29.3 KB
• Stars: 2
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: readme.md
  • License: LICENSE-APACHE2

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README

        
# 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.