A multisided generalization of Bézier surfaces
ACM Transactions on Graphics (TOG)
Computer Aided Geometric Design
A quadrilateral rendering primitive
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
Mean value coordinates for closed triangular meshes
ACM SIGGRAPH 2005 Papers
Image deformation using moving least squares
ACM SIGGRAPH 2006 Papers
Mean value coordinates for arbitrary planar polygons
ACM Transactions on Graphics (TOG)
Harmonic coordinates for character articulation
ACM SIGGRAPH 2007 papers
On transfinite barycentric coordinates
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
GPU-assisted positive mean value coordinates for mesh deformations
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
A unified, integral construction for coordinates over closed curves
Computer Aided Geometric Design
Coordinates for instant image cloning
ACM SIGGRAPH 2009 papers
Maximum entropy coordinates for arbitrary polytopes
SGP '08 Proceedings of the Symposium on Geometry Processing
Volumetric modeling with diffusion surfaces
ACM SIGGRAPH Asia 2010 papers
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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We introduce a new construction of transfinite barycentric coordinates for arbitrary closed sets in two dimensions. Our method extends weighted Gordon-Wixom interpolation to non-convex shapes and produces coordinates that are positive everywhere in the interior of the domain and that are smooth for shapes with smooth boundaries. We achieve these properties by using the distance to lines tangent to the boundary curve to define a weight function that is positive and smooth. We derive closed-form expressions for arbitrary polygons in two dimensions and compare the basis functions of our coordinates with several other types of barycentric coordinates.