Smooth Bi-3 spline surfaces with fewest knots
Computer-Aided Design
SMI 2012: Full Component-aware tensor-product trivariate splines of arbitrary topology
Computers and Graphics
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We exhibit the essentially unique projective linear (rational linear) reparameterization for constructing C^s surfaces of genus g0. Conversely, for quadrilaterals and isolated vertices of valence 8, we show constructively for s=1,2 that this map yields a projective linear spline space for surfaces of genus greater or equal to 1. This establishes the reparametrization to be the simplest possible transition map.