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Computer Aided Geometric Design
Free-form deformation of solid geometric models
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Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
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A multisided generalization of Bézier surfaces
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Computer Aided Geometric Design
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Computer Aided Geometric Design
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Computer Aided Geometric Design
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Computer-Aided Design
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s-power series: an alternative to Poisson expansions for representing analytic functions
Computer Aided Geometric Design
Composition of parametrizations, using the paired algebras of forms and sites
Computer Aided Geometric Design
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Computer-Aided Design
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Computer Aided Geometric Design
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This paper describes two algorithms for solving the following general problem: Given two polynomial maps f: Rn ↦ RN and S RN ↦ Rd in Bézier simplex form, find the composition map &Stilde; = S ° f in Bézier simplex form (typically, n ≤ N ≤ d ≤ 3). One algorithm is more appropriate for machine implementation, while the other provides somewhat more geometric intuition. The composition algorithms can be applied to the following problems: evaluation, subdivision, and polynomial reparameterization of Bézier simplexes; joining Bézier curves with geometric continuity of arbitrary order; and the determination of the control nets of Bézier curves and triangular Bézier surface patches after they have undergone free-form deformations.