An implementation of Boy’s surface, an immersion of the real projective plane in three-dimensional Euclidean space. The parameterization is based on a formula by Robert Bryant and Rob Kusner. This is a WebGPU port of an earlier version.

Given a complex variable parameterizing a disk in the complex plane, the surface coordinates are

The final surface position is then normalized:

The vertex shader receives a surface parameterized by coordinates, where is the radial distance and is the angle in the complex plane. It evaluates Boy’s surface function using complex arithmetic and normalizes the result. Transparency is achieved through depth peeling.