Point‐augmented bi‐cubic subdivision surfaces

Abstract

AbstractPoint‐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 (d̃,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 C2‐joined surface rings (PAS2) or C1‐joined rings (PAS1) that have fewer pieces.