CmcMesh: a python implementation of the DPW method

Abstract

Minimal and constant mean curvature (CMC) surfaces in three-dimensional space forms can be constructed with the Dorfmeister--Pedit--Wu (DPW) method. We introduce CmcMesh, a Python implementation covering the whole pipeline from holomorphic potential to rendered surfaces, using Hoffman and Hoffman's Mesh algorithm. We implement the Weierstrass representation for minimal surfaces in ${\mathbb{R}}^3$, Bryant's representation for CMC-1 surfaces in ${\mathbb{H}}^3$, and the DPW method for CMC surfaces in ${\mathbb{R}}^3$ and for minimal and CMC surfaces in ${\mathbb{S}}^3$. The package is modular, making it easy to add new DPW variants without modifying existing code.

Project repository: https://scm.univ-tours.fr/projetspublics/idp/cmcmesh