Abstract: 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.