Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Curve and surface fitting with splines
Curve and surface fitting with splines
Surface fitting using convex Powell-Sabin splines
Journal of Computational and Applied Mathematics
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)
Macro-elements and stable local bases for splines on Powell-Sabin triangulations
Mathematics of Computation
Uniform Powell--Sabin spline wavelets
Journal of Computational and Applied Mathematics
Automatic construction of control triangles for subdivided Powell-Sabin splines
Computer Aided Geometric Design
Multiresolution terrain modeling using level curve information
Journal of Computational and Applied Mathematics
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We present an algorithm for local subdivision of Powell-Sabin spline surfaces. The construction of such a spline is based on a particular PS-refinement of a given triangulation. We build the new triangulation on top of this PS-refinement by applying a 3-subdivision scheme on a local part of the domain. To avoid degeneration we introduce a simple heuristic for refinement propagation, driven by a parameter. This parameter manages the trade-off between the mesh quality and the refinement localization.