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Habilitation à diriger des recherches

Modélisation géométrique de surfaces lisses: Design et Fairing

Abstract : The present habilitation thesis deals with two aspects of geometric modeling
of smooth surfaces. The first part is about interpolation of arbitrary triangle meshes
by a smooth piecewise polynomial parametric surface. We introduce a new splitting method
which is based on a regular 4-split of the input triangles. Different interpolation and modeling
methods are then developed. We focus in particular on the problem how to join an arbitrary number
of patches at a common vertex with tangent plane continuity, and how to choose the degrees
of freedom in order to get a globally smooth surface. One of our schemes is subdivision invariant.
We therefore have a parametric surface model which allows for multiresolution applications and
which allows representing surfaces of arbitrary topological type. The application domains vary from
CAD/CAM, virtual reality to medical applications.
The second part of this thesis is on fairing of B-spline surfaces. Two different approaches are
presented. They both aim to decrease the curvature variation of the surfaces. The first approach
uses heuristic search strategies, like simulated annealing and best first search. The second
approach is based on a convolution of the surface control net with discrete fairing filters.
Document type :
Habilitation à diriger des recherches
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Contributor : Stefanie Hahmann <>
Submitted on : Thursday, January 19, 2006 - 12:03:05 PM
Last modification on : Wednesday, July 28, 2021 - 3:57:07 AM
Long-term archiving on: : Saturday, April 3, 2010 - 9:34:40 PM


  • HAL Id : tel-00011422, version 1



Stefanie Hahmann. Modélisation géométrique de surfaces lisses: Design et Fairing. Interface homme-machine [cs.HC]. Institut National Polytechnique de Grenoble - INPG, 2001. ⟨tel-00011422⟩



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