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Détermination géométrique de chemins géodésiques sur des surfaces du subdivision

Abstract : Geodesic paths between two points on a surface of R³ are local shortest paths.We propose two methods to compute them ; these ones are innovative because they use Computer Aided Geometric Design tools in this context of differential geometry.The minimisation method considers parametric surfaces and studies the problem in the parameter domain. Bezier and spline curves represent there the approximation class. Their control points are the variables for the minimization of the length of the image path on the surface. The implementation of this approximation method and its validation are developed.The subdivision method considers subdivision surfaces, limits of a sequence of control nets generated by a subdivision scheme.An iterative and exact method to compute geodesic paths on polyhedral surfaces is developed. This leads to the computation of a sequence of geodesic paths on the polyhedral surfaces associated to the successiv control nets. The convergence of the path sequence is discussed and we present results illustrated by examples.Some applications are finally given : surface mesh computation and myocardium fibres modelling in a medical context.
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Submitted on : Monday, February 16, 2004 - 6:03:23 PM
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Valérie Pham-Trong. Détermination géométrique de chemins géodésiques sur des surfaces du subdivision. Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 2001. Français. ⟨tel-00004698⟩

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