Local subdivision of Powell–Sabin splines

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 -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.