Discrete Differential-Geometry Operators for Triangulated 2-Manifolds

Discrete Differential-Geometry Operators for Triangulated 2-Manifolds Mark Meyer1, Mathieu Desbrun1,2, Peter Schroder1, and Alan H. Barr1 1 Caltech 2 USC Summary. This paper proposes a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and cur- vatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Voronoi cells and the mixed Finite-Element/Finite-Volume method, and compare them to existing for- mulations.

• discrete operators
• spatial averages
• triangle mesh
• triangle of the mesh
• meshes
• definition
• gaussian curvature
• vertex
• surface
• area
• average