Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
On calculating normalized Powell-Sabin B-splines
Computer Aided Geometric Design
Cubic precision Clough-Tocher interpolation
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
On the stability of normalized Powell-Sabin B-splines
Journal of Computational and Applied Mathematics
Quasi-hierarchical Powell--Sabin B-splines
Computer Aided Geometric Design
Numerical solution of partial differential equations with Powell-Sabin splines
Journal of Computational and Applied Mathematics
Nonnegativity preserving macro-element interpolation of scattered data
Computer Aided Geometric Design
A normalized basis for quintic Powell--Sabin splines
Computer Aided Geometric Design
Multivariate normalized Powell-Sabin B-splines and quasi-interpolants
Computer Aided Geometric Design
Isogeometric analysis on triangulations
Computer-Aided Design
A normalized basis for C1 cubic super spline space on Powell-Sabin triangulation
Mathematics and Computers in Simulation
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We present the construction of a suitable normalized B-spline representation for reduced cubic Clough-Tocher splines. The basis functions have a local support, they are nonnegative, and they form a partition of unity. Geometrically, the problem can be interpreted as the determination of a set of triangles that must contain a specific set of points. This leads to a natural definition of tangent control triangles. We also consider a stable computation of the Bezier control net of the spline surface.