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

Methods for Feature Detection in Point Clouds

This paper gives an overview over several techniques for detection of features, and in particular sharp features, on point-sampled geometry. In addition, a new technique using the Gauss map is shown. Given an unstructured point cloud, this method computes a Gauss map clustering on local neighborhoods in order to discard all points that are unlikely to belong to a sharp feature. A single parameter is used in this stage to control the sensitivity of the feature detection

08221 Abstracts Collection -- Geometric Modeling

From May 26 to May 30 2008 the Dagstuhl Seminar 08221 ``Geometric Modeling\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

A 2D Shape Structure for Decomposition and Part Similarity

International audienceThis paper presents a multilevel analysis of 2D shapes and uses it to find similarities between the different parts of a shape. Such an analysis is important for many applications such as shape comparison, editing, and compression. Our robust and stable method decomposes a shape into parts, determines a parts hierarchy, and measures similarity between parts based on a salience measure on the medial axis, the Weighted Extended Distance Function, providing a multi-resolution partition of the shape that is stable across scale and articulation. Comparison with an extensive user study on the MPEG-7 database demonstrates that our geometric results are consistent with user perception

Interactively animating crumpling paper

International audienceWe present the first method in computer graphics to animate sheets of paper at interactive rates while automatically generating a plausible set of sharp features when the sheet is crumpled. Our hybrid, geometric and physical, model is based on a high-level understanding of the physical constraints that act on real sheets of paper, and of their geometric counterparts. This understanding enables us to use an adaptive mesh carefully representing the main geometric features of paper in terms of singular points and developability

Synthèse de son de papier adaptée au mouvement et à la géométrie de la surface

National audienceNous présentons une méthode pour générer en temps réel un son plausible pour une animation d'un papier virtuel que l'on froisse. Pour cela, nous analysons l'animation géométrique de la surface du papier pour détecter les événements à l'origine de sons puis calculons géométriquement les zones du papier qui vibrent de part la propagation des ondes au travers de la surface. Le son résultant est ensuite synthétisé à partir à la fois d'extraits pré-enregistrés, et d'une synthèse procédurale, tenant compte de la forme géométrique de la surface et de sa dynamique. Nous validons nos résultats en comparant le son généré par notre modèle virtuel par rapport à des enregistrements réels pour un ensemble de cas d'animations caractéristiques. Abstract In this article, we present a method to generate plausible sounds for an animation of crumpling paper in real-time. We analyse the geometrical animation of the deformed surface to detect sound-producing events and compute the regions which resonate due to the propagation of the vibrations though the paper. The resulting sound is synthesized from both pre-recorded sounds and procedural generation taking into account the geometry of the surface and its dynamic. Our results are validated by comparing the generated sound of the virtual model with respect to real recording for a set of specific deformations

Idealized models for FEA derived from generative modeling processes based on extrusion primitives

International audienceShape idealization transformations are very common when adapting a CAD component to FEA requirements. Here, an idealization approach is proposed that is based on generative shape processes used to decompose an initial B-Rep object, i.e. extrusion processes. The corresponding primitives form the basis of candidate sub domains for idealization and their connections conveyed through the generative processes they belong to, bring robustness to set up the appropriate connections between idealized sub domains. Taking advantage of an existing construction tree as available in a CAD software does not help much because it may be complicated to use it for idealization processes. Using generative processes attached to an object that are no longer reduced to a single construction tree but to a graph containing all non trivial construction trees, is more useful for the engineer to evaluate variants of idealization. From this automated decomposition, each primitive is analyzed to define whether it can idealized or not. Subsequently, geometric interfaces between primitives are taken into account to determine more precisely the idealizable sub domains and their contours when primitives are incrementally merged to come back to the initial object

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

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

Real-time sound synthesis for paper material based on geometric analysis

International audienceIn this article, we present the first method to generate plausible sounds while animating crumpling virtual paper in real time. Our method handles shape-dependent friction and crumpling sounds which typically occur when manipulating or creasing paper by hand. Based on a run-time geometric analysis of the deforming surface, we identify resonating regions characterizing the sound being produced. Coupled to a fast analysis of the surrounding elements, the sound can be efficiently spatialized to take into account nearby wall or table reflectors. Finally, the sound is synthesized in real time using a pre-recorded database of frequency- and time-domain sound sources. Our synthesized sounds are evaluated by comparing them to recordings for a specific set of paper deformations