Construction of rational surface patches bounded by lines of curvature
| Autor: | Luc Biard, Rida T. Farouki, Nicolas Szafran |
|---|---|
| Přispěvatelé: | Modélisation Géométrique & Multirésolution pour l'Image (MGMI), Laboratoire Jean Kuntzmann (LJK), 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), Department of Mechanical and Aeronautical Engineering (MAE), University of California [Davis] (UC Davis), University of California-University of California |
| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: |
Surface (mathematics)
Darboux frame rotation-minimizing frame Aerospace Engineering Boundary (topology) Geometry Bézier curve 010103 numerical & computational mathematics 02 engineering and technology Pythagorean-hodograph curve Curvature 01 natural sciences Principal curvature 0202 electrical engineering electronic engineering information engineering 0101 mathematics Mathematics rational surface patch Rational surface Mathematical analysis 020207 software engineering Computer Graphics and Computer-Aided Design [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation Quintic function Computer Science::Graphics [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] Modeling and Simulation Automotive Engineering angular velocity lines of curvature |
| Zdroj: | Computer Aided Geometric Design Computer Aided Geometric Design, Elsevier, 2010, 27 (5), pp.359-371. ⟨10.1016/j.cagd.2010.03.002⟩ |
| ISSN: | 0167-8396 |
| DOI: | 10.1016/j.cagd.2010.03.002⟩ |
| Popis: | International audience; The fact that the Darboux frame is rotation-minimizing along lines of curvature of a smooth surface is invoked to construct rational surface patches whose boundary curves are lines of curvature. For given patch corner points and associated frames defining the surface normals and principal directions, the patch boundaries are constructed as quintic RRFM curves, i.e, spatial Pythagorean-hodograph (PH) curves that possess rational rotation-minimizing frames. The interior of the patch is then defined as a Coons interpolant, matching the boundary curves and their associated rotation-minimizing frames as surface Darboux frames. The surface patches are compatible with the standard rational Bézier/B-spline representations, and G^1 continuity between adjacent patches is easily achieved. Such patches are advantageous in surface design with more precise control over the surface curvature properties. |
| Databáze: | OpenAIRE |
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