1 February 1992 Modeling with multivariate B-spline surfaces over arbitrary triangulations
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Abstract
This paper describes the first results of a test implementation of the new multivariate B-splines as recently developed for quadratics and cubics. The surface scheme is based on blending functions and control points and allows us to model Ck-1-continuous piecewise polynomial surfaces of degree k over arbitrary triangulations of the parameter plane. The surface scheme exhibits both affine invariance and the convex hull property, and the control points can be used to manipulate the shape of the surface locally. Additional degrees of freedom in the underlying knot net allow for the modeling of discontinuities. Explicit formulas are given for the representation of polynomials and piecewise polynomials as linear combinations of B-splines.
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Phillip Fong, Phillip Fong, Hans-Peter Seidel, Hans-Peter Seidel, } "Modeling with multivariate B-spline surfaces over arbitrary triangulations", Proc. SPIE 1610, Curves and Surfaces in Computer Vision and Graphics II, (1 February 1992); doi: 10.1117/12.135138; https://doi.org/10.1117/12.135138
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