My favorite project in my mathematical art hobby has been writing a physically based path tracer to render photo-realistic images of mathematical objects. I was honored to be asked to speak on this at the Fall 2024 conference of of CMC3 (California Mathematics Council Community Colleges). This was my first talk on the process of making math art itself (of hopefully many to come!). This talk specifically highlights how to make some wonderful images using just lower division undergraduate mathematics: in particular, it follows the process of building a naive path tracer using only math one might see in a multivariable calculus course.

Accompanying Software

The illustrations for the talk were all made with some custom path tracers, or simulations of the behavior of these path tracers. I’ve uploaded these simulations to my website, and linked them here. (There are also links directly within the slide deck):

Simulated Pathtracers:

• Simulation: Raymarching Step by Step

• Simulation: Raymarching

• Simulation: Lighting

• Simulation: Multiple Lights

• Simulation: Lights + Shadows

• Simulation: Single Ray

• Simulation: Two Nearby Rays

• Simulation: Single Ray: Integration

• Simulation: Multiple Rays

• Simulation: Roughness

• Simulation: Refraction

• Simulation: Surbsurface Ray

• Simulation: Multiple Subsurface Rays

Raytracing Rendering Spheres

• Raytrace Ambient Lighting
• Raytrace Diffuse Lighting
• Raytrace Phong Lighting
• Raytrace Multiple Lights
• Raytrace Shadow
• Raytrace Lights + Shadows

Pathtracing Rendering Spheres

• Pathtracing Single Sample
• Pathtracing Metal and Dielectics
• Pathtracing Clear Glass
• Pathtracing Colored Glass

Drawing a Cocktail

• An Infinite Cylinder
• A Finite Cylinder
• Empty Cocktail Glass
• The Finished Cocktail

Slides

Here are the slides from my talk on November 1 2024: