Barycentric Coordinates and Transfinite Interpolation
Welcome	to the Barycentric Coordinates homepage! This website follows our minisymposium given at 10th SIAM Conference on Geometric Design & Computing and provides links to online resources.
Contributors	Kai Hormann, Clausthal University of Technology Michael Floater, University of Oslo Solveig Bruvoll, University of Oslo Tao Ju, Washington University Scott Schaefer, Texas A&M University N. Sukumar, UC Davis
Slides	Minisymposium on Barycentric Coordinates and Transfinite Interpolation Lecture 1: Generalized Barycentric Coordinates by Kai Hormann Lecture 2: Barycentric Coordinates for Closed Curves by Scott Schaefer Lecture 3: Hermite Mean Value Interpolation by Michael Floater Lecture 4: A General, Geometric Construction of Coordinates in any Dimensions by Tao Ju Lecture 5: Transfinite Mean Value Interpolation over Volumetric Domains by Solveig Bruvoll Lecture 6: Barycentric Finite Element Methods by N. Sukumar
Papers	before 1900 Der barycentrische Calcul August F. Möbius, 1827 before 2000 A Rational basis for function approximation Eugene L. Wachspress, 1971 A Rational basis for function approximation. II: Curved sides Eugene L. Wachspress, 1973 Pseudo-harmonic interpolation on convex domains William J. Gordon and James A. Wixom, 1974 A Rational Finite Element Basis Eugene L. Wachspress, 1975 Rational basis functions for curved elements Eugene L. Wachspress, 1979 High-order curved finite elements Eugene L. Wachspress, 1981 A pentagonal surface patch for computer aided geometric design Peter Charrot and John A. Gregory, 1984 A multisided generalization of Bézier surfaces Charles T. Loop and Tony D. DeRose, 1989 Computing discrete minimal surfaces and their conjugates Ulrich Pinkall and Konrad Polthier, 1993 Multiresolution analysis of arbitrary meshes Matthias Eck, Tony DeRose, Tom Duchamp, Hugues Hoppe, Michael Lounsbery, and Werner Stuetzle, 1995 Barycentric coordinates for convex polytopes Joe Warren, 1996 Parametrization and smooth approximation of surface triangulations Michael S. Floater, 1997 2002 Generalized barycentric coordinates on irregular polygons Mark Meyer, Haeyoung Lee, Alan Barr, and Mathieu Desbrun 2003 Interpolants within convex polygons: Wachspress' shape functions Gautam Dasgupta Integration within polygonal finite elements Gautam Dasgupta Mean value coordinates Michael S. Floater On the uniqueness of barycentric coordinates Joe Warren 2004 A quadrilateral rendering primitive Kai Hormann and Marco Tarini Interpolations for temperature distributions: A method for all non-concave polygons Elisabeth A. Malsch and Gautam Dasgupta Shape functions for polygonal domains with interior nodes Elisabeth A. Malsch and Gautam Dasgupta Construction of polygonal interpolants: A maximum entropy approach N. Sukumar Conforming polygonal finite elements N. Sukumar and Alireza Tabarraei 2005 Mean value coordinates in 3D Michael S. Floater, Géza Kós, and Martin Reimers Algebraic construction of smooth interpolants on polygonal domains Elisabeth A. Malsch and Gautam Dasgupta Smooth two dimensional interpolants: A recipe for all polygons Elisabeth A. Malsch, John J. Lin, and Gautam Dasgupta Mean value coordinates for closed triangular meshes Tao Ju, Scott Schaefer, and Joe Warren Geometric construction of coordinates for convex polyhedra using polar duals Tao Ju, Scott Schaefer, Joe Warren, and Mathieu Desbrun 2006 Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods. Marino Arroyo and Michael Ortiz On transfinite barycentric coordinates Alexander Belyaev A general construction of barycentric coordinates over convex polygons Michael S. Floater, Kai Hormann, and Géza Kós Mean value coordinates for arbitrary planar polygons Kai Hormann and Michael S. Floater Spherical barycentric coordinates Torsten Langer, Alexander Belyaev, and Hans-Peter Seidel Recent advances in the construction of polygonal finite element interpolants N. Sukumar and Elisabeth A. Malsch 2007 Barycentric rational interpolation with no poles and high rates of approximation Michael S. Floater and Kai Hormann Harmonic coordinates for character articulation Pushkar Joshi, Mark Meyer, Tony DeRose, Brian Green, and Tom Sanocki A general geometric construction of coordinates in a convex simplicial polytope Tao Ju, Peter Liepa, and Joe Warren Mean value coordinates for arbitrary spherical polygons and polyhedra in R³ Torsten Langer, Alexander Belyaev, and Hans-Peter Seidel Mean value Bézier surfaces Torsten Langer and Hans-Peter Seidel GPU-assisted positive mean value coordinates for mesh deformations Yaron Lipman, Johannes Kopf, Daniel Cohen-Or, and David Levin A unified, integral construction for coordinates over closed curves Scott Schaefer, Tao Ju, and Joe Warren Deriving the continuity of maximum-entropy basis functions via variational analysis N. Sukumar and Roger J-B Wets Overview and construction of meshfree basis functions: from moving least squares to entropy approximants N. Sukumar and Roy W. Wright Discrete Laplace operators: No free lunch Max Wardetzky, Saurabh Mathur, Felix Kälberer, and Eitan Grinspun Barycentric coordinates for convex sets Joe Warren, Scott Schaefer, Anil N. Hirani, and Mathieu Desbrun 2008 The adjoint for an algebraic finite element Gautam Dasgupta and Eugene L. Wachspress Basis functions for concave polygons Gautam Dasgupta and Eugene L. Wachspress Pointwise radial minimization: Hermite interpolation on arbitrary domains Michael S. Floater and Christian Schulz Maximum Entropy Coordinates for Arbitrary Polytopes Kai Hormann and N. Sukumar Reusable Skinning Templates Using Cage-based Deformations Tao Ju, Qian-Yi Zhou, Michiel van de Panne, Daniel Cohen-Or, and Ulrich Neumann Higher order barycentric coordinates Torsten Langer and Hans-Peter Seidel Mean Value Bézier Maps Torsten Langer and Hans-Peter Seidel Green Coordinates Yaron Lipman, David Levin and Daniel Cohen-Or Polyhedral Finite Elements Using Harmonic Basis Functions Sebastian Martin, Peter Kaufmann, Mario Botsch, Martin Wicke and Markus Gross Boundary element formulation of harmonic coordinates Raif M. Rustamov Extended Finite Element Method on Polygonal and Quadtree Meshes Alireza Tabarraei and N. Sukumar Voronoi-based interpolants for fracture modelling N. Sukumar and John E. Bolander 2009 Transfinite mean value interpolation in general dimension Solveig Bruvoll and Michael S. Floater Transfinite mean value interpolation Christopher Dyken and Michael S. Floater On the injectivity of Wachspress and mean value mappings between convex polygons Michael S. Floater and Jiří Kosinka Complex barycentric coordinates with applications to planar shape deformation Ofir Weber, Mirela Ben-Chen and Craig Gotsman
Links	basic facts on barycentric coordinates Barycentric coordinates from Wolfram MathWorld Barycentric coordinates from Wikipedia Barycentric coordinates from Cut-the-Knot Barycentric coordinates from Ken Joy's On-Line Computer Graphics Notes other useful online resources Ceva's Theorem Routh's Theorem Van Obel's Theorem