Energy optimized parameterization of triangular meshes

Parameterization of triangular meshes is a fundamental problem for texture mapping, surface fitting, surface reconstruction, and mesh editing. To minimize the distortion of parameterization of triangular meshes, a new parameterization method based on deformation energy optimization is presented in this paper. The method involves an iterative procedure, which incrementally flattens a 3D triangular mesh by region growing and obtains a parameterization with free boundary. The result is then converted to a parameterization with regular boundary by conformal mapping. Our method accounts for both the angle and area distortion during parameterization, it yields a parameterization with less global distortion and no triangular flipping. Experiments in texture mapping show that the proposed method has better performance than some popular parameterization methods.