CmcMesh: a python implementation of the DPW method

2026/07/23 by Thomas Raujouan, Martin Traizet
Mathematics · #math.DG

paper · pdf

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 ℝ³, Bryant's representation for CMC-1 surfaces in ℍ³, and the DPW method for CMC surfaces in ℝ³ and for minimal and CMC surfaces in \mathbbS³. The package is modular, making it easy to add new DPW variants without modifying existing code.

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