Point-augmented bi-cubic subdivision surfaces

Point-Augmented Subdivision (PAS) replaces complex geometry-dependent guided subdivision, known to yield high-quality surfaces, by explicit subdivision formulas that yield similarly-good limit surfaces and are easy to implement using any subdivision infrastructure: map the control net d augmented by a fixed central limit point C, to a finer net ((d) over tilde ,C) = M(d,C), where the subdivision matrix M is assembled from the provided stencil Tables. Point-augmented bi-cubic subdivision improves the state of the art so that bi-cubic subdivision surfaces can be used in high-end geometric design: the highlight line distribution for challenging configurations lacks the shape artifacts usually associated with explicit iterative generalized subdivision operators near extraordinary points. Five explicit formulas define Point-augmented bi-cubic subdivision in addition to uniform B-spline knot insertion. Point-augmented bi-cubic subdivision comes in two flavors, either generating a sequence of C-2-joined surface rings (PAS2) or C-1-joined rings (PAS1) that have fewer pieces.

Automated summary

Point-Augmented Subdivision (PAS) is a subdivision method that replaces complex geometry-dependent guided subdivision with explicit subdivision formulas. It can generate high-quality surfaces and is suitable for high-end geometric design, eliminating shape artifacts near extraordinary points.