GPU-based visualization of domain-coloured algebraic Riemann surfaces

We examine an algorithm for the visualization of domain-coloured Riemann surfaces of plane algebraic curves. The approach faithfully reproduces the topology of the surface and also preserves some of its geometry. We discuss how the algorithm can be implemented efficiently in OpenGL with geometry shaders, and (less efficiently) even in WebGL with multiple render targets and floating point textures. As examples, we look at the complex square root and the folium of Descartes. For the folium of Descartes, the visualization reveals features of the algebraic curve which are not obvious from its equation.