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Your search keyword '"bézier curves and surfaces"' showing total 2 results
Start Over Descriptor "bézier curves and surfaces" Journal computer-aided design
2 results on '"bézier curves and surfaces"'

1. Construction of Bézier surface patches with Bézier curves as geodesic boundaries

Author

Farouki, R.T., Szafran, N., and Biard, L.

Subjects
*GEODESICS, *SCHEMES (Algebraic geometry), *COMPUTER-aided design, *ALGEBRAIC curves, *POLYNOMIALS, *ALGEBRAIC surfaces, *INTERPOLATION, *TENSOR products, *COMPUTER software
Abstract

Abstract: Given four polynomial or rational Bézier curves defining a curvilinear rectangle, we consider the problem of constructing polynomial or rational tensor-product Bézier patches bounded by these curves, such that they are geodesics of the constructed surface. The existence conditions and interpolation scheme, developed in a general context in earlier studies, are adapted herein to ensure that the geodesic-bounded surface patches are compatible with the usual polynomial/rational representation schemes of CAD systems. Precise conditions for four Bézier curves to constitute geodesic boundaries of a polynomial or rational surface patch are identified, and an interpolation scheme for the construction of such surfaces is presented when these conditions are satisfied. The method is illustrated with several computed examples. [Copyright &y& Elsevier]

Published
2009
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2. Construction of Bézier surface patches with Bézier curves as geodesic boundaries

Author

Luc Biard, Nicolas Szafran, Rida T. Farouki, Department of Mechanical and Aeronautical Engineering (MAE), University of California [Davis] (UC Davis), University of California-University of California, Modélisation Géométrique & Multirésolution pour l'Image (MGMI), Laboratoire Jean Kuntzmann (LJK), and Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)

Subjects
Bézier surface, Surface (mathematics), Pure mathematics, Polynomial, Geodesic, 010103 numerical & computational mathematics, 02 engineering and technology, Bézier curves and surfaces, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], 01 natural sciences, Industrial and Manufacturing Engineering, Hermite/Coons interpolation, surface reconstruction, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Mathematics, Rational surface, Mathematical analysis, Interpolation (computer graphics), geodesic curves, 020207 software engineering, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Computer Graphics and Computer-Aided Design, Computer Science Applications, Computer Science::Graphics, Geometric design, [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], Rational representation
Abstract

International audience; Given four polynomial or rational Bézier curves defining a curvilinear rectangle, we consider the problem of constructing polynomial or rational tensor-product Bézier patches bounded by these curves, such that they are geodesics of the constructed surface. The existence conditions and interpolation scheme, developed in a general context in earlier studies, are adapted herein to ensure that the geodesic-bounded surface patches are compatible with the usual polynomial/rational representation schemes of CAD systems. Precise conditions for four Bézier curves to constitute geodesic boundaries of a polynomial or rational surface patch are identified, and an interpolation scheme for the construction of such surfaces is presented when these conditions are satisfied. The method is illustrated with several computed examples.

Published
2009
Full Text
View/download PDF

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