Conformal Flattening by Curvature Prescription and Metric Scaling
Triangular meshes are a popular representation for 3D models. They are used in a wide range of applications, many of which require the parameterization of the model to a planar domain. Examples are texture mapping, detail mapping, morphing and remeshing, to mention just a few. Parameterization is also an important preliminary step for many geometry processing algorithms. The main challenge for parameterization algorithms is to bound the distortion of the resulting parameterization. The distortion can be either angular the angles between edges in the parameter domain are very different from those in the input 3D mesh, or area distortion large areas of the 3D mesh are mapped to small areas in the parameterization and vice-versa, or both.