Discrete laplace operator on meshed surfaces

In recent years a considerable amount of work in graphics and geometric optimization used tools based on the Laplace-Beltrami operator on a surface. The applications of the Laplacian include mesh editing, surface smoothing, and shape interpolations among others. However, it has been shown [12, 23, 25] that the popular cotangent approximation schemes do not provide convergent point-wise (or even L2) estimates, while many applications rely on point-wise estimation. Existence of such schemes has been an open question [12]. In this paper we propose the first algorithm for approximating the Laplace operator of a surface from a mesh with point-wise convergence guarantees applicable to arbitrary meshed surfaces. We show that for a sufficiently fine mesh over an arbitrary surface, our mesh Laplacian is close to the Laplace-Beltrami operator on the surface at every point of the surface. Moreover, the proposed algorithm is simple and easily implementable. Experimental evidence shows that our al...

• Type: Conference
• Year: 2008
• Where: COMPGEOM
• Authors: Mikhail Belkin, Jian Sun, Yusu Wang
• Keywords: COMPGEOM 2008, Computer Science, Discrete Geometry, Laplace Operator, Laplace-Beltrami Operator