| Guided subdivision (2005) | |||||||||||||||
Abstract | |||||||||||||||
| Curvature continuous surfaces with subdivision structure are constructed by higher-order sampling of a piecewise polynomial guide surface, at positions defined and derivatives weighted by a special, scalable reparametrization. Two variants are developed. One variant applies to the conventional sprocket subdivision layout, say of Catmull-Clark subdivision, i.e. nested rings consisting of N copies of L-shaped segments with three patches. The curvature continuous surfaces are of degree (6,6). A second variant, called polar guided subdivision, is particularly suitable for high valences N and to cap cylindrical structures. It yields curvature continuous surfaces of degree (4,3). Additionally, we discuss a scheme that samples with increasing density to generate a C 2 surface of piecewise degree (3,3). Curvature continuity is verified by showing convergence of anchored osculation paraboloids. 1 | |||||||||||||||
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