Ray Tracing in 4-dimensional World

This repo extends a simplest 3-dimensional ray tracing engine(CPU implementation) to 4-dimensional world.

.	3D	4D
Parameterization of Rotation	SO3, axis-angle or quaternion	SO4, bi-vector or two quaternions (Rodrigous formula doesn't hold anymore)
Camera Model
Image of a 3D object	by 3D camera, resolution: 640x480	by 4D camera, resolution: 640x480x32

4D Objects

A 4D cube frame and a 4d sphere.

Installation and Run

clone code

git clone https://github.com/XiaoxingChen/ray_tracing_4d
cd ray_tracing_4d
git submodule init
git submodule update

Download assets(wget was used, doesn't work on Windows) and render a 3D scene. If you use Windows, please download the assets in lfs.yaml and put them in build/assets/.

./build.py --sync-lfs

Render 3D, 4D scenes

./build.py --run app/render_3d
./build.py --run app/render_4d

References

1. Miegakure
2. python geometric algebra library
3. scratch a pixel
4. ray tracing in one weekend
5. decomposition of n-d rotations
6. block diagonalize rotation matrix