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)
Surfaces over Dirichlet Tessellations
Computer Aided Geometric Design
Generalized B-spline surfaces of arbitrary topology
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Difference formulas for the surface Laplacian on a triangulated surface
Journal of Computational Physics
Generalized barycentric coordinates on irregular polygons
Journal of Graphics Tools
Computer Aided Geometric Design
Multisided arrays of control points for multisided Bézier patches
Computer Aided Geometric Design
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
A geometric construction of coordinates for convex polyhedra using polar duals
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Spherical 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
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
*Cages:: A multilevel, multi-cage-based system for mesh deformation
ACM Transactions on Graphics (TOG)
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Bernstein polynomials are a classical tool in Computer Aided Design to create smooth maps with a high degree of local control. They are used for the construction of Bézier surfaces, free-form deformations, and many other applications. However, classical Bernstein polynomials are only defined for simplices and parallelepipeds. These can in general not directly capture the shape of arbitrary objects. Instead, a tessellation of the desired domain has to be done first. We construct smooth maps on arbitrary sets of polytopes such that the restriction to each of the polytopes is a Bernstein polynomial in mean value coordinates (or any other generalized barycentric coordinates). In particular, we show how smooth transitions between different domain polytopes can be ensured.