A multisided generalization of Bézier surfaces
ACM Transactions on Graphics (TOG)
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Generalized barycentric coordinates on irregular polygons
Journal of Graphics Tools
Computer Aided Geometric Design
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
Convex Optimization
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
Mean value coordinates for arbitrary planar polygons
ACM Transactions on Graphics (TOG)
A general geometric construction of coordinates in a convex simplicial polytope
Computer Aided Geometric Design
Harmonic coordinates for character articulation
ACM SIGGRAPH 2007 papers
Spherical barycentric coordinates
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
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
Deriving the Continuity of Maximum-Entropy Basis Functions via Variational Analysis
SIAM Journal on Optimization
Transfinite mean value interpolation
Computer Aided Geometric Design
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Delaunay refinement algorithms for triangular mesh generation
Computational Geometry: Theory and Applications
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Interior distance using barycentric coordinates
SGP '09 Proceedings of the Symposium on Geometry Processing
On transfinite interpolations with respect to convex domains
Computer Aided Geometric Design
Bounded biharmonic weights for real-time deformation
ACM SIGGRAPH 2011 papers
Positive Gordon-Wixom coordinates
Computer-Aided Design
The Bernstein polynomial basis: A centennial retrospective
Computer Aided Geometric Design
Computer Graphics Forum
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
Bijective composite mean value mappings
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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Barycentric 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.