Intrinsic Parameterizations of Surface Meshes

Parameterization of discrete surfaces is a fundamental and widely-used operation in graphics, required, for instance, for texture mapping or remeshing. As 3D data becomes more and more detailed, there is an increased need for fast and robust techniques to automatically compute least-distorted parameterizations of large meshes. In this paper, we present new theoretical and practical results on the parameterization of triangulated surface patches. Given a few desirable properties such as rotation and translation invariance, we show that the only admissible parameterizations form a two-dimensional set and each parameterization in this set can be computed using a simple, sparse, linear system. Since these parameterizations minimize the distortion of different intrinsic measures of the original mesh, we call them Intrinsic Parameterizations. In addition to this partial theoretical analysis, we propose robust, efficient and tunable tools to obtain least-distorted parameterizations automatic...

• Type: Journal
• Year: 2002
• Where: CGF
• Authors: Mathieu Desbrun, Mark Meyer, Pierre Alliez
• Keywords: CGF 2002, Intrinsic Parameterization, Natural Intrinsic Parameterization, Widely-used Operation