Conformal Parameterization by Minimizing Distortion Energy

Planar parameterization of triangulated surface meshes is used to find an isomorphic mapping between a discrete 3D surface and a planar patch, a crucial problem in computer graphics, computer aided design and digital geometric processing. This paper introduces an algorithm for parameterizing 3D meshes by minimizing the angle and area distortion energy. The parameterization algorithm traverses the mesh in a region growing way and is able to yield results with less global distortion. Various applications are tested to illustrate the effectiveness of the techniques proposed in this paper.