Clifftrace

Overview:

This project uses Conformal Geometric Algebra (CGA) to build a ray tracing engine with the clifford library with the following functionality:

• Recursive tracing of reflected rays up to a specified max depth
• A Blinn-Phong lighting model
• Shadows
• Spherical objects and planes only
• A single point light source

Here is the latest rendering from the code in the repo:

Usage:

Run the script with python3 clifftrace.py

Package requirements:

The script requires the following non-standard python packages:

• clifford
• NumPy
• Pillow

Interface with GAOnline:

Note GAOnline is now deprecated and a version is no longer hosted on a web server! Instructions still apply to a local version which can be forked from here.

The output image is saved in the working directory as fig.png but there is also a terminal output which allows the scene composition to be drawn in GAOnline so that it can be viewed interactively. An example terminal output is:

DrawLine((1.0^e245),rgb(255, 0 , 0));
DrawLine((0.70711^e245) - (0.70711^e345),rgb(255, 0 , 0));
DrawEucPoint(-(6.0^e2) + (6.0^e3) + (35.5^e4) + (36.5^e5),rgb(0, 0, 255));
...

Copy and paste the terminal output into the box outlined in red in the GAOnline example image shown below.

The output draws:

1. Camera: The position, optic axis, viewing screen and corner rays.
2. Objects in the scene: Object geometry and colour.
3. Lighting: Position will be drawn as yellow point inside a sphere.

Planned Future Work:

• Move interactive visualisation over to pyganja
• Acceleration with Numba starting with the PointsFromPP function.
• A front-end to interact with the view as in GAOnline. (With Tkinter? PyGame?)
• Ability to draw planes.
• Ability to draw meshes.
• Full parallelisation either with Numba or on the GPU.
• Implement a BSP-Tree to accelerate intersection tests.
• Change the sphere intersection test to imitate that of the plane

Read about Geometric Algebra!

Geometric Algebra is a super exciting field for exploring 3D geometry and beyond. For further reading into GA see:

• Mathoma's tutorials are super cool and provide a good start. Skip to the 9th video if you have some basic understanding of linear algebra in 3D.

• Many of the concepts used in the ray tracer can be found in A Covariant Approach to Geometry using Geometric Algebra which can be found online here. The report really summarises the power of working in the conformal model.

• For a more complete introduction to GA check out Geometric Algebra for Physicists and for a deeper look into GA theory: Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry (companion site here) which includes documentation of another ray tracer implemented in GA!