Feature-sensitive parameterization of polygonal meshes

This paper investigates a parameterization method for polygonal meshes which is able to improve map distortion exploiting local curvature of the surface mesh. Parametrization is an important tool in geometric modelling and computer graphics applications such as, for example, texture mapping, shape morphing, and remeshing. The paper presents a feature-sensitive scheme which is based on a stretch-minimizing strategy which iterates the shape-preserving parameterization taking into account the influence of the curvature on the mesh stretch. In particular, the main goal is to provide a distortion in the parametrization driven by the curvature directions, in such a way that strong distortion correspond to area with mean curvature approaching to zero. Computed examples demonstrate the effectiveness of the proposed method using geometric measures on angle, edge and area stretching, and illustrate the high quality of the mesh parameterizations produced.