Flexible G1 Interpolation of Quad Meshes

International audienceTransforming an arbitrary mesh into a smooth G1 surface has been the subject of intensive research works. To get a visual pleasing shape without any imperfection even in the presence of extraordinary mesh vertices is still a challenging problem in particular when interpolation of the mesh vertices is required. We present a new local method, which produces visually smooth shapes while solving the interpolation problem. It consists of combining low degree biquartic Bézier patches with minimum number of pieces per mesh face, assembled together with G1-continuity. All surface control points are given explicitly. The construction is local and free of zero-twists. We further show that within this economical class of surfaces it is however possible to derive a sufficient number of meaningful degrees of freedom so that standard optimization techniques result in high quality surfaces

Multiresolution Analysis with Non-Nested Spaces

International audienceTwo multiresolution analyses (MRA) intended to be used in scientiic visualization, and that are both based on a non-nested set of approximating spaces, are presented. The notion of approximated r eenement is introduced to deal with non nested spaces. The rst MRA scheme, referred to as BLaC (Blending of Linear and Constant) wavelets is based on a one parameter family of wavelet bases that realizes a blend between the Haar and the linear wavelet bases. The approximated reenement is applied in the last part to build a second MRA scheme for data deened on an arbitrary planar triangular mesh

Topology Preserving Simplification of 2D Non-Manifold Meshes with Embedded Structures

International audienceMesh simplification has received tremendous attention over the past years. Most of the previous works deal with a proper choice of error measures to guide the simplification. Preserving the topological characteristics of the mesh and possibly of data attached to the mesh is a more recent topic, the present paper is about.We introduce a new topology preserving simplification algorithm for triangular meshes, possibly non-manifold, with embedded polylines. In this context embedded means that the edges of the polylines are also edges of the mesh. The paper introduces a robust test to detect if the collapse of an edge in the mesh modifies either the topology of the mesh or the topology of the embedded polylines. This validity test is derived using combinatorial topology results. More precisely we define a so-called extended complex from the input mesh and the embedded polylines. We show that if an edge collapse of the mesh preserves the topology of this extended complex, then it also preserves both the topology of the mesh and the embedded polylines. Our validity test can be used for any 2-complex mesh, including non-manifold triangular meshes. It can be combined with any previously introduced error measure. Implementation of this validity test is described. We demonstrate the power and versatility of our method with scientific data sets from neuroscience, geology and CAD/CAM models from mechanical engineering

Automatic lighting design from photographic rules

International audienceLighting design is crucial in 3D scenes modeling for its ability to provide cues to understand the objects shape. However a lot of time, skills, trials and errors are required to obtain a desired result. Existing automatic lighting methods for conveying the shape of 3D objects are based either on costly optimizations or on non-realistic shading effects. Also they do not take the material information into account. In this paper, we propose a new method that automatically suggests a lighting setup to reveal the shape of a 3D model, taking into account its material and its geometric properties. Our method is independent from the rendering algorithm. It is based on lighting rules extracted from photography books, applied through a fast and simple geometric analysis. We illustrate our algorithm on objects having different shapes and materials, and we show by both visual and metric evaluation that it is comparable to optimization methods in terms of lighting setups quality. Thanks to its genericity our algorithm could be integrated in any rendering pipeline to suggest appropriate lighting

Visualisation Focus+Contexte pour l'Exploration Interactive de Maillages Tétraèdriques

in Revue Électronique Francophone d'Informatique Graphique (REFIG) , Vol 2, Num 1, http://www.irit.fr/REFIG/index.php/refig/issue/view/2National audienceL'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

Visualization of uncertain scalar data fields using color scales and perceptually adapted noise

Session: VisualizationInternational audienceWe present a new method to visualize uncertain scalar data fields by combining color scale visualization techniques with animated, perceptually adapted Perlin noise. The parameters of the Perlin noise are controlled by the uncertainty information to produce animated patterns showing local data value and quality. In order to precisely control the perception of the noise patterns, we perform a psychophysical evaluation of contrast sensitivity thresholds for a set of Perlin noise stimuli. We validate and extend this evaluation using an existing computational model. This allows us to predict the perception of the uncertainty noise patterns for arbitrary choices of parameters. We demonstrate and discuss the efficiency and the benefits of our method with various settings, color maps and data sets

Smooth Interpolation of Curve Networks with Surface Normals

International audienceRecent surface acquisition technologies based on microsensors produce three-space tangential curve data which can be transformed into a network of space curves with surface normals. This paper addresses the problem of surfacing an arbitrary closed 3D curve network with given surface normals.Thanks to the normal vector input, the patch finding problem can be solved unambiguously and an initial piecewise smooth triangle mesh is computed. The input normals are propagated throughout the mesh and used to compute mean curvature vectors. We then introduce a new variational optimization method in which the standard bi-Laplacian is penalized by a term based on the mean curvature vectors. The intuition behind this original approach is to guide the standard Laplacian-based variational methods by the curvature information extracted from the input normals. The normal input increases shape fidelity and allows to achieve globally smooth and visually pleasing shapes

Piecewise polynomial monotonic interpolation of 2D gridded data

International audienceA method for interpolating monotone increasing 2D scalar data with a monotone piecewise cubic C$^1$-continuous surface is presented. Monotonicity is a sufficient condition for a function to be free of critical points inside its domain. The standard axial monotonicity for tensor-product surfaces is however too restrictive. We therefore introduce a more relaxed monotonicity constraint. We derive sufficient conditions on the partial derivatives of the interpolating function to ensure its monotonicity. We then develop two algorithms to effectively construct a monotone C$^1$ surface composed of cubic triangular Bézier surfaces interpolating a monotone gridded data set. Our method enables to interpolate given topological data such as minima, maxima and saddle points at the corners of a rectangular domain without adding spurious extrema inside the function domain. Numerical examples are given to illustrate the performance of the algorithm

Length Constrained Multiresolution Deformation for Surface Wrinkling

International audienceWe present a method for deforming piescewise linear 3D curves on surfaces with constant length constraint. We show how this constraint can be integrated into a multiresolution editing tool allowing an intuitive control of the deformation's extent and aspect. The constraint is enforced following two steps. A first step consists in approximating the initial length by modifying the multiresolution decomposition at some specified scale. In a second step the constraint is axactly enforced by constrained minimization of a smoothness criterion. This process then provides the core of an integrated wrinkling tool for soft tissues modelling. A curve on the mesh is deformed, providing a deformation profile which is propagated in a user-defined neighbourhood

Subdivision Invariant Polynomial Interpolation

International audienceIn previous works a polynomial interpolation method for triangular meshes has been introduced. This interpolant can be used to design smooth surfaces of arbitrary topological type. In a design process, it is very useful to be able to locate the deformation made on a geometric model. The previously introduced interpolant has the so-called strict locality property: when a mesh vertex is changed, only the surface patches containing this vertex are changed. This enables to locate the deformation at the size of the input triangles. Unfortunately this is not sufficient if the designer wants to add some detail at a smaller size than that of the input triangles. In this paper, we propose a modification of our interpolant, that enables to arbitrary refine the input triangulation, without changing the resulting surface. We call this property the subdivision invariance. After refinement of the input triangulation, the modification of one of the vertices will change the shape of the interpolant at the scale of the refined triangulation. In this way, it is possible to add details at an arbitrary fine scale