Localized discrete Laplace-Beltrami operator over triangular mesh

摘要: The Laplace-Beltrami operator is the foundation of describing geometric partial differential equations, and it also plays an important role in fields computational geometry, computer graphics image processing, such as surface parameterization, shape analysis, matching interpolation. However, constructing discretized with convergent property has been open problem. In this paper we propose a new discretization scheme over triangulated surfaces. We prove that our converges to at every point arbitrary smooth size triangular mesh tends zero. Numerical experiments are conducted, which support theoretical analysis. construct localized discrete mesh.Our algorithm based on heat kernel defined surface.Our point-wise for surfaces.We method estimate parameters involved adaptively.Experimental results shows outperforms other schemes.