Free-form deformation of solid geometric models
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
A multisided generalization of Bézier surfaces
ACM Transactions on Graphics (TOG)
Bernstein-Be´zier polynomials on spheres and sphere-like surfaces
Computer Aided Geometric Design
Illumination for computer generated pictures
Communications of the ACM
Spherical averages and applications to spherical splines and interpolation
ACM Transactions on Graphics (TOG)
Generalized barycentric coordinates on irregular polygons
Journal of Graphics Tools
Computer Aided Geometric Design
ACM SIGGRAPH 2004 Papers
Mean value coordinates for closed triangular meshes
ACM SIGGRAPH 2005 Papers
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Geometric modeling with conical meshes and developable surfaces
ACM SIGGRAPH 2006 Papers
Mean value coordinates for arbitrary planar polygons
ACM Transactions on Graphics (TOG)
A geometric construction of coordinates for convex polyhedra using polar duals
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
A unified, integral construction for coordinates over closed curves
Computer Aided Geometric Design
Continuous Shading of Curved Surfaces
IEEE Transactions on Computers
A general geometric construction of coordinates in a convex simplicial polytope
Computer Aided Geometric Design
Discrete laplace operators: no free lunch
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Scalable Hybrid Unstructured and Structured Grid Raycasting
IEEE Transactions on Visualization and Computer Graphics
ACM SIGGRAPH 2008 papers
Sparse Key Points Controlled Animation for Individual Face Model
Edutainment '08 Proceedings of the 3rd international conference on Technologies for E-Learning and Digital Entertainment
Transfinite mean value interpolation
Computer Aided Geometric Design
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Transfinite mean value interpolation in general dimension
Journal of Computational and Applied Mathematics
Pointwise radial minimization: Hermite interpolation on arbitrary domains
SGP '08 Proceedings of the Symposium on Geometry Processing
Maximum entropy coordinates for arbitrary polytopes
SGP '08 Proceedings of the Symposium on Geometry Processing
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Barycentric interpolation and mappings on smooth convex domains
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
A User-editable C1-Continuous 2.5D Space Deformation Method For 3D Models
Electronic Notes in Theoretical Computer Science (ENTCS)
High Order Finite Difference and Finite Volume Methods for Advection on the Sphere
Journal of Scientific Computing
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Bijective composite mean value mappings
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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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.