# Goursat

Steve Trettel

Medium | Custom GPU path tracer for algebraic varieties. |
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The Art | A path traced image of a goursat surface - one of a particular family of algebraic varieties. The path tracer aims to compute physically correct material properties, lighting, and reflections. |

The Math | An algebraic variety is the set of zeroes of a polynomial equation. Sometimes these are smooth manifolds, and other times they have singularities, which look like the vertices of double cones here in dimension 2. The Goursat surfaces are a 2-parameter family of quartic surfaces exhibiting symmetries of the cube. |

Categories | GPU Computing, Path tracing, Algebraic Geometry, Physics Simulation |