Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
On calculating normalized Powell-Sabin B-splines
Computer Aided Geometric Design
Subdivision of uniform Powell—Sabin splines
Computer Aided Geometric Design
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Piecewise Quadratic Approximations on Triangles
ACM Transactions on Mathematical Software (TOMS)
Local subdivision of Powell-Sabin splines
Computer Aided Geometric Design
C1 hierarchical Riesz bases of Lagrange type on Powell-Sabin triangulations
Journal of Computational and Applied Mathematics
Modeling sphere-like manifolds with spherical Powell--Sabin B-splines
Computer Aided Geometric Design
Quasi-hierarchical Powell--Sabin B-splines
Computer Aided Geometric Design
Local subdivision of Powell--Sabin splines
Computer Aided Geometric Design
Powell--Sabin spline based multilevel preconditioners for the biharmonic equation
Applied Numerical Mathematics
A C1 globally interpolatory spline of arbitrary topology
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
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In this paper we present an algorithm for calculating the B-spline representation of a Powell-Sabin spline surface on a refinement of the given triangulation. The resulting subdivision scheme is a √3 scheme; a new vertex is added inside every original triangle. Applying the √3 scheme twice yields a triadic scheme, every original edge is split into three new edges, but special care is needed at the boundaries. The scheme is numerically stable and generally applicable, there are no restrictions on the initial triangulation.