Mean value coordinates in 3D

Authors:
Michael S. Floater;Géza Kós;Martin Reimers
Affiliations:
CMA/IFI, University of Oslo, Oslo, Norway;Computer and Automation Research Institute, Budapest, Hungary;CMA/IFI, University of Oslo, Oslo, Norway
Venue:
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Year:
2005

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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.