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Control Points for Multivariate B‐Spline Surfaces over Arbitrary Triangulations
Author(s) -
Fong Philip,
Seidel HansPeter
Publication year - 1991
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/1467-8659.1040309
Subject(s) - mathematics , piecewise , spline (mechanical) , classification of discontinuities , knot (papermaking) , convex hull , surface (topology) , b spline , polynomial , affine transformation , regular polygon , invariant (physics) , multivariate statistics , discrete mathematics , geometry , mathematical analysis , statistics , structural engineering , chemical engineering , engineering , mathematical physics
This paper describes first results of a test implementation that implements the new multivariate B‐splines as recently developed by Dahmen et al. 10for quadratics and cubics. The surface scheme is based on blending functions and control points and allows the modelling of C k − 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 modelling of discontinuities. Explicit formulas are given for the representation of polynomials and piecewise polynomials as linear combinations of B‐splines.