Maximum Entropy Coordinates for Arbitrary Polytopes

dc.contributor.authorHormann, K.en_US
dc.contributor.authorSukumar, N.en_US
dc.date.accessioned2015-02-21T17:32:37Z
dc.date.available2015-02-21T17:32:37Z
dc.date.issued2008en_US
dc.description.abstractBarycentric coordinates can be used to express any point inside a triangle as a unique convex combination of the triangle s vertices, and they provide a convenient way to linearly interpolate data that is given at the vertices of a triangle. In recent years, the ideas of barycentric coordinates and barycentric interpolation have been extended to arbitrary polygons in the plane and general polytopes in higher dimensions, which in turn has led to novel solutions in applications like mesh parameterization, image warping, and mesh deformation. In this paper we introduce a new generalization of barycentric coordinates that stems from the maximum entropy principle. The coordinates are guaranteed to be positive inside any planar polygon, can be evaluated efficiently by solving a convex optimization problem with Newton s method, and experimental evidence indicates that they are smooth inside the domain. Moreover, the construction of these coordinates can be extended to arbitrary polyhedra and higher-dimensional polytopes.en_US
dc.description.number5en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume27en_US
dc.identifier.doi10.1111/j.1467-8659.2008.01292.xen_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages1513-1520en_US
dc.identifier.urihttps://doi.org/10.1111/j.1467-8659.2008.01292.xen_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltden_US
dc.titleMaximum Entropy Coordinates for Arbitrary Polytopesen_US
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