Bernstein-Be´zier polynomials on spheres and sphere-like surfaces
Computer Aided Geometric Design
Automatic reconstruction of B-spline surfaces of arbitrary topological type
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Dimension and local bases of homogeneous spline spaces
SIAM Journal on Mathematical Analysis
Fitting scattered data on sphere-like surfaces using spherical splines
Journal of Computational and Applied Mathematics - Special issue on scattered data
Journal of Computational and Applied Mathematics - Special issue on scattered data
On calculating normalized Powell-Sabin B-splines
Computer Aided Geometric Design
Simplifying surfaces with color and texture using quadric error metrics
Proceedings of the conference on Visualization '98
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Piecewise Quadratic Approximations on Triangles
ACM Transactions on Mathematical Software (TOMS)
Fundamentals of spherical parameterization for 3D meshes
ACM SIGGRAPH 2003 Papers
Automatic construction of control triangles for subdivided Powell-Sabin splines
Computer Aided Geometric Design
Robust spherical parameterization of triangular meshes
Computing - Geometric modelling dagstuhl 2002
Practical Spherical Embedding of Manifold Triangle Meshes
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
Quadratic spherical spline quasi-interpolants on Powell--Sabin partitions
Applied Numerical Mathematics
Construction of spherical spline quasi-interpolants based on blossoming
Journal of Computational and Applied Mathematics
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We present an algorithm for computing a B-spline representation for Powell-Sabin splines on the sphere. The B-splines form a partition of unity and we define control points that constitute control triangles that give us a good insight in the shape of the spline. We further consider a number of CAGD applications such as approximation and compression of a given sphere-like triangular mesh, and editing global shape and local detail of a spline using spline subdivision.