Construction and smoothing of triangular Coons patches with geodesic boundary curves
| Autor: | Nicolas Szafran, Luc Biard, Rida T. Farouki |
|---|---|
| Přispěvatelé: | 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), 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) |
| Rok vydání: | 2010 |
| Předmět: |
Pure mathematics
Geodesic Coordinate system Aerospace Engineering 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Combinatorics 0202 electrical engineering electronic engineering information engineering Regular space Geodesic curves 0101 mathematics Mathematics Curvilinear coordinates 020207 software engineering [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation Computer Graphics and Computer-Aided Design Coons interpolation Spline (mathematics) Tensor product [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] Modeling and Simulation Bounded function Automotive Engineering Surface reconstruction Smoothing |
| Zdroj: | Computer Aided Geometric Design Computer Aided Geometric Design, Elsevier, 2010, 27 (4), pp.301-312. ⟨10.1016/j.cagd.2010.01.004⟩ |
| ISSN: | 0167-8396 |
| DOI: | 10.1016/j.cagd.2010.01.004 |
| Popis: | International audience; Given three regular space curves r1(t), r2(t), r3(t) for t in [0,1] that define a curvilinear triangle, we consider the problem of constructing a triangular surface patch R(u1,u2,u3) bounded by these three curves, such that they are geodesics of the constructed surface. Results from a prior study (Farouki et al., 2009a) concerned with tensor-product patches are adapted to identify constraints on the given curves for the existence of such geodesic-bounded triangular surface patches. For curves satisfying these conditions, the patch is constructed by means of a cubically-blended triangular Coons interpolation scheme. A formulation of thin-plate spline energy in terms of barycentric coordinates with respect to a general domain triangle is also derived, and used to optimize the smoothness of the geodesic-bounded triangular surface patches. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect