Spherical Barycentric Coordinates

Langer, Torsten; Belyaev, Alexander; Seidel, Hans-Peter

Spherical Barycentric Coordinates

Files

081-088.pdf (261.63 KB)

Date

2006

Authors

Langer, Torsten
Belyaev, Alexander
Seidel, Hans-Peter

Publisher

The Eurographics Association

Abstract

We develop spherical barycentric coordinates. Analogous to classical, planar barycentric coordinates that describe the positions of points in a plane with respect to the vertices of a given planar polygon, spherical barycentric coordinates describe the positions of points on a sphere with respect to the vertices of a given spherical polygon. In particular, we introduce spherical mean value coordinates that inherit many good properties of their planar counterparts. Furthermore, we present a construction that gives a simple and intuitive geometric interpretation for classical barycentric coordinates, like Wachspress coordinates, mean value coordinates, and discrete harmonic coordinates. One of the most interesting consequences is the possibility to construct mean value coordinates for arbitrary polygonal meshes. So far, this was only possible for triangular meshes. Furthermore, spherical barycentric coordinates can be used for all applications where only planar barycentric coordinates were available up to now. They include Bézier surfaces, parameterization, free-form deformations, and interpolation of rotations.

        @inproceedings{:10.2312/SGP/SGP06/081-088
,
booktitle = {Symposium on Geometry Processing
},
editor = {Alla Sheffer and Konrad Polthier
},
title = {{Spherical Barycentric Coordinates
}},
author = {Langer, Torsten and 
Belyaev, Alexander and 
Seidel, Hans-Peter
},
year = {2006
},
publisher = {The Eurographics Association
},
ISSN = {1727-8384
},
ISBN = {3-905673-24-X
},
DOI = {/10.2312/SGP/SGP06/081-088
}
}