2015/07/16 by Stefan Kranich, Kranich, Stefan
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Computer Graphics and Visualization Techniques #FOS: Computer and information sciences #FOS: Mathematics #Graphics (cs.GR) #Polynomial and algebraic computation #cs.GR #math.AG #math.CV
paper · pdf · doi:10.48550/arxiv.1507.04571
revised version; 21 pages, 12 figures
openalex publication_date 2015/07/16 · arxiv created 2015/11/10 · arxiv updated 2015/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We examine an algorithm for the visualization of domain-coloured Riemann surfaces of plane algebraic curves. The approach faithfully reproduces the topology and the holomorphic structure of the Riemann surface. 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. While the generation of the surface takes noticeable time in both implementations, the visualization of a cached Riemann surface mesh is possible with interactive performance. This allows us to visually explore otherwise almost unimaginable mathematical objects. 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.