Free-Form Deformation (FFD) is a well established technique for deforming arbitrary object shapes in space. Although more recent deformation techniques have been introduced, among them skeleton-based deformation and cage-based deformation, the simple and versatile nature of FFD is a strong advantage, and justifies its presence in nowadays leading commercial geometric modeling and animation software systems. Since its introduction in the late 1980s, many improvements have been proposed to the FFD paradigm, including control lattices of arbitrary topology, direct shape manipulation and GPU implementation. Several authors have addressed the problem of volume-preserving FFD. These previous approaches either make use of expensive nonlinear optimization techniques, or resort to first order approximation suitable only for small-scale deformations. In this paper we take advantage of the multi-linear nature of the volume constraint in order to derive a simple, exact and explicit solution to the problem of volume-preserving FFD. Two variants of the algorithm are given, without and with direct shape manipulation. Moreover, the linearity of our solution enables to implement it efficiently on GPU.

A new approach for the interactive simulation of viscoelastic object cutting is presented. Two synchronized geometrical models at different resolutions are used, both derived from medical images. In contrast with most previous approaches, the blade deforms the object, and cutting occurs once a contact pressure threshold is exceeded. Moreover, we achieve interactive simulation rates by embedding a high-resolution geometry within a regular grid with arbitrary resolution. This allows to trade off accuracy for speed in the computation of deformations. The input data is a high-resolution volumetric model of the objects. The surface model of the object, used for rendering as well as collision detection and response, is a polygonal level set of the volumetric data. It is embedded in the volume model using barycentric coordinates. Cutting is performed by removing voxels at the fine level, and updating the surface and volume models accordingly. We introduce a new data structure, which we call a Dynamic Branched Grid, in order to preserve the fine-level topology at the coarse level. When an element of the coarse volumetric model is cut, it is replaced by a number of superimposed elements with the same size and at the same rest position as the original one. Each new element is assigned a part of material contained in the original one, and the mass and stiffness are recomputed accordingly. The well-known problem of creating small, ill-shaped finite elements while remeshing is thus completely avoided.

Generating smooth surfaces of arbitrary topology is still a challenge. This paper considers the problem of creating a smooth parametric polynomial surface interpolating the vertices of an irregular triangular or quadrilateral mesh of arbitrary topological type. The surface is overall tangent plane continuous without any singular points and without any singular parameterizations. We particularly focus on design issues related to this spline model which offers several degrees of freedom. In particular, an exhaustive description of all available degrees of freedom is given and their geometric interpretation for shape design is specified. An extension of the model allows for additional normal vector interpolation and increases thus the number of design parameters. Finally several design issues are discussed and illustrated.

We present a new image-based method to process contacts between objects bounded by triangular surfaces. Unlike previous methods, it relies on image-based volume minimization, which eliminates complex geometrical computations and robustly handles deep intersections. The surfaces are rasterized in three orthogonal directions, and intersections are detected based on pixel depth and normal orientation. Per-pixel contact forces are computed and accumulated at the vertices. We show how to compute pressure forces which serve to minimize the intersection volume, as well as friction forces. No geometrical precomputation is required, which makes the method efficient for both deformable and rigid objects. We demonstrate it on rigid, skinned, and particle-based physical models with detailed surfaces in contacts at interactive frame rates.

Direct Volume Rendering is one of the most popular visualization techniques. Although approaches such as ray-casting or slicing are fast and well-implemented on graphics hardware for regular and irregular grids, cell projection techniques are still time-consuming for large tetrahedral meshes. We propose improvements to the pipeline of cell projection techniques based on the SXMPVO [4] and the Projected Tetrahedra [8] (PT) algorithms. Specifically, we exploit new functionalities of the latest graphics hardware to remove bottlenecks in the sorting and rendering phases.

L'exploration et l'analyse visuelle de grands maillages tétraédriques restent des tâches coûteuses en temps lorsque les ensembles de données sont affichés dans leur globalité. Pourtant, dans la plupart des cas, l'utilisateur n'explorera que de petites zones compactes où se concentrent les informations qu'il juge remarquables. Se basant sur ce constat, nous proposons une approche focus+contexte reposant sur une double résolution des données. Dans l'espace objet, une Région Locale d'Intérêt (RLI) - le focus - est extraite du maillage précis originel et est entourée par une représentation grossière globale - le contexte. Pour unir les deux résolutions, une connexion topologiquement valide est créée interactivement. Les techniques de rendu classiques y sont intégrées. De plus, quand le focus est déplacé, l'extraction de la RLI ainsi que son affichage sont accélérés en utilisant la cohérence temporelle. Les dernières cartes graphiques sont utilisées afin d'accélérer le Rendu Volumique Direct. Notre approche focus+contexte réduit de manière significative le nombre de primitives affichées ce qui permet une exploration interactive de grands maillages tétraédriques.

L'exploration et l'analyse visuelle de grands maillages tetraedriques restent des tâches couteuses en temps lorsque les ensembles de donnees sont affiches dans leur globalite. Pourtant, dans la plupart des cas, l'utilisateur n'explorera que de petites zones compactes ou se concentrent les informations qu'il juge remarquables. Se basant sur ce constat, nous proposons une approche focus+contexte reposant sur une double resolution des donnees. Dans l'espace objet, une Region Locale d'Interet (RLI) - le focus - est extraite du maillage precis originel et est entouree par une representation grossiere globale - le contexte. Pour unir les deux resolutions, une connexion topologiquement valide est creee interactivement. Les techniques de rendu classiques y sont integrees. De plus, quand le focus est deplace, l'extraction de la RLI ainsi que son affichage sont acceleres en utilisant la coherence temporelle. Les dernieres cartes graphiques sont utilisees afin d'accelerer le Rendu Volumique Direct. Notre approche focus+contexte reduit de maniere significative le nombre de primitives affichees ce qui permet une exploration interactive de grands maillages tetraedriques.