Polynomial C2 Spline Surfaces Guided by Rational Multisided Patches

Abstract

An algorithm is presented for approximating a rational multi-sided M- patch by a O?“ Spline surface. The motivation is that the multi-Sided patch can be assumed to have good shape but is in nonstandard representation or of too high a degree. The algorithm generates a finite approximation of the M-patch, by a sequence of patches of bidegree (5, 5) capped off by patches of bidegree (11, 11) surrounding the extraordinary point. The philosophy of the approach is (i) that intricate reparametrizations are permis- sible if they improve the surface parametrization since they can be precomputed and thereby do not reduce the time efficiency at runtime; and (ii) that high patch degree is acceptable if the shape is controlled by a guiding patch.