Mean value coordinates in 3D

Abstract: Barycentric coordinates can be used both to express a point inside a tetrahedron as a convex combination of the four vertices and to linearly interpolate data given at the vertices. In this paper we generalize these coordinates to convex polyhedra and the kernels of star-shaped polyhedra. These coordinates generalize in a natural way a recently constructed set of coordinates for planar polygons, called mean value coordinates. Key words: barycentric coordinates, parameterization, mean value theorem.

• Type: Journal
• Year: 2005
• Where: CAGD
• Authors: Michael S. Floater, Géza Kós, Martin Reimers
• Keywords: Barycentric Coordinates, CAGD 2005, Convex Combination, Mean Value