https://github.com/kmill/lean4-raytracer

A simple raytracer written in Lean 4
https://github.com/kmill/lean4-raytracer

lean4 raytracing

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A simple raytracer written in Lean 4

• Host: GitHub
• URL: https://github.com/kmill/lean4-raytracer
• Owner: kmill
• License: apache-2.0
• Created: 2021-01-31T19:48:50.000Z (over 5 years ago)
• Default Branch: master
• Last Pushed: 2024-05-16T18:10:48.000Z (about 2 years ago)
• Last Synced: 2025-03-26T14:18:48.488Z (over 1 year ago)
• Topics: lean4, raytracing
• Language: Lean
• Homepage:
• Size: 9.84 MB
• Stars: 134
• Watchers: 6
• Forks: 5
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md

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README

          
# Simple raytracer in Lean 4

[Lean 4](https://github.com/leanprover/lean4) is a dependently typed programming language, and 

it can be used both as a proof assistant and for practical programs.

This repository implements the ray tracer described in 

[_Ray Tracing in One Weekend_](https://raytracing.github.io/books/RayTracingInOneWeekend.html).

Code for writing PPM files originally came from

[TOTBWF/lean4-raytrace](https://github.com/TOTBWF/lean4-raytrace).

The raytracer uses `Task`s to render in parallel.  Part of a raytracer is using supersampling

to better estimate the amount of light entering each pixel, so it is trivial to parallelize:

the entire image is rendered multiple times, and the results are averaged together.

![final test image](https://github.com/kmill/lean4-raytracer/blob/master/output/test13.png?raw=true)

(8 minutes 10 seconds with 10 threads on an Apple M2 Max. 500x333 pixels, 80 total samples per pixel, max depth 30.)

![final test image, higher resolution](https://github.com/kmill/lean4-raytracer/blob/master/output/test13.bigger.png?raw=true)

(2 hours with 16 threads on an Intel Xeon E5-2665. 800x533 pixels, 480 total samples per pixel, max depth 50.)

## Running the code

Assuming you already have Lean 4 setup, this builds an executable and runs it:

```

$ lake build && time lake exe render test.ppm

```

The rendering settings are hard-coded in `writeTestImage` in `render.lean`.

## C benchmark

The `c` folder contains an implementation of the raytracer in C, hand translated from Lean using C idioms.

This is not meant to be a fair comparison, and I spent more time thinking about optimizing the C version.

The only purpose here is to get some idea of the relative speed of my Lean code.

The first test image in C took 5.9 seconds with the same configuration,

and the second test image took 1 minute 19 seconds (but with Apple M2 Max).