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Digital geometry and algorithmic geometry for interactive 3D design

Abstract : While 3D surfaces are essentially represented using triangle meshes in the domain of digital geometry, the structures that allow to interact with those are various and adapted to the different geometry processing tasks that are targetted by the user.This thesis presents results on structures of various dimension and various geometrical representations, going from internal structures like analytical curve skeletons for shape modeling, to on-surface structures allowing automatic selection of feature handles for shape deformation, and external control structures known as “cages” offering a high-level representation of animated 3D data stemming from performance capture. Results on spatial functions are also presented, in particular for the Mean-Value Coordinates, for which the analytical formulae of the gradients and the Hessians are provided, and biharmonic functions, for which a finite elements basis is given for the resolution of the biharmonic Laplace problem with mixed Dirichlet/Neumann boundary conditions, as well as their applications to 3D shapes deformation.
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Submitted on : Monday, October 27, 2014 - 4:56:50 PM
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  • HAL Id : tel-01078038, version 1



Jean-Marc Thiery. Digital geometry and algorithmic geometry for interactive 3D design. Other. Télécom ParisTech, 2012. English. ⟨NNT : 2012ENST0070⟩. ⟨tel-01078038⟩



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