  This paper solves the problem of computing conformal structures of general
2-manifolds represented as triangle meshes. We compute conformal structures in
the following way: first compute homology bases from simplicial complex
structures, then construct dual cohomology bases and diffuse them to harmonic
1-forms. Next, we construct bases of holomorphic differentials. We then obtain
period matrices by integrating holomorphic differentials along homology bases.
We also study the global conformal mapping between genus zero surfaces and
spheres, and between general meshes and planes. Our method of computing
conformal structures can be applied to tackle fundamental problems in computer
aid design and computer graphics, such as geometry classification and
identification, and surface global parametrization.
