This a proof-of-concept demo for rendering 3D cross-sections of 4D geometry in real-time using the GPU.
Cross-sections of a 3x3x3x3 arrangement of hypercubes. The texture is a dirt cube with grass growing on top, resembling the iconic block from Minecraft.
For a good analogy of cross-sectional rendering, imagine slicing a 3D cube with a 2D plane. If you slice it parallel to one of its faces, you will get a perfect square as the cross-section. However, if you slice it at an arbitrary angle, you might get a triangle, quadrilateral, or a hexagon. Similarly, in four-dimensions, if you slice a 4D hypercube with a 3D hyperplane, you will get various solid 3D shapes for the cross-sections.
As the above arrangement of hybercubes is rotated in 4D space, different 3D sections of each hypercube become visible. Additionally, the surface of each slice is textured using 2D slices of a 3D volume texture. The texture used in this demo can be seen, in flattened (2D) form, here.
When cloning, there are several submodules in deps/ that must also be cloned. After that, just
mkdir build && cd build
cmake .. && make
and the project should build. The resulting binary must be run from within the build directory, as
the shaders and textures are loaded from file and the paths are currently hard-coded.