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CAGD
2007

A general geometric construction of coordinates in a convex simplicial polytope

9 years 10 months ago
A general geometric construction of coordinates in a convex simplicial polytope
Barycentric coordinates are a fundamental concept in computer graphics and geometric modeling. We extend the geometric construction of Floater’s mean value coordinates [8,11] to a general form that is capable of constructing a family of coordinates in a convex 2D polygon, 3D triangular polyhedron, or a higher-dimensional simplicial polytope. This family unifies previously known coordinates, including Wachspress coordinates, mean value coordinates and discrete harmonic coordinates, in a simple geometric framework. Using the construction, we are able to create a new set of coordinates in 3D and higher dimensions and study its relation with known coordinates. We show that our general construction is complete, that is, the resulting family includes all possible coordinates in any convex simplicial polytope. Key words: Barycentric coordinates, convex simplicial polytopes
Tao Ju, Peter Liepa, Joe D. Warren
Added 12 Dec 2010
Updated 12 Dec 2010
Type Journal
Year 2007
Where CAGD
Authors Tao Ju, Peter Liepa, Joe D. Warren
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