## Project-Team : evasion

## Section: New Results

## New representations and deformation techniques for shape modelling

**Participants:**Alexis Angelidis, Georges-Pierre Bonneau, Antoine Bouthors, Marie-Paule Cani, Franck Hétroy, Fabrice Neyret, Basile Sauvage, Alex Yvart.

### Detection of geometrical and topological characteristics in shapes

**Participant:**Franck Hétroy.

This work has just started this Fall with the arrival of a new assistant professor in EVASION.

The purpose of this research is to modelize and compute several geometrical or topological characteristics on surfaces or in volumes. The first part of this work, currently carried out, is the detection of "constriction areas" on a closed surface. We define constrictions as simple closed curves with locally minimal length, and use simple curve and path computation algorithms to construct them.

Applications of this work are widespread, from classification of shapes to object decomposition into simple parts, and to detection of singularities.

### Multiresolution surfaces

**Participants:**Georges-Pierre Bonneau, Alex Yvart.

This research is done in collaboration with Stefanie Hahmann from the LMC/IMAG. The aim is to define a representation of surfaces that combines the advantages of subdivision surfaces and NURBS surfaces, for use in CAD/CAM systems, or Animation software. Subdivision surfaces can represent surfaces of arbitrary topology, with the ability to efficiently encode local detail information. But they suffer from the lack of an explicit parametric formulation, which is required by many techniques in CAD/CAM systems, including surface interrogation, trimming, offsetting... On the other hand, NURBS surfaces are not efficient for representing surfaces of arbitrary topology. A new surface model has been developed, that is defined by low degree polynomial patches that connect smoothly with G1-continuity. Last year it has been shown how this model can be hierarchically refined in order to compactly add local detail on the surface. A paper on this topic has been submitted for publication at ACM Transactions On Graphics. Figure 1 illustrates a dog's head designed with a geometric modelling software based on our new surface model. Thereafter automatic reconstruction techniques have been developed, that takes as input a dense triangular mesh, and outputs a compact surface representation using our new model. The reconstruction method has been submitted for publication at SMI'05. Figure 2 illustrates the reconstruction of the Max Planck model. Alex Yvart has defended his PhD on this topic in December 2004.

### Multiresolution geometric modelling with constraints

**Participants:**Georges-Pierre Bonneau, Basile Sauvage.

This work is done in collaboration with Stefanie Hahmann from LMC/IMAG. A collaboration has also started on this topic with Prof. Gershon Elber from Technion, in the framework of the Aim@Shape Network of Excellence (see Section 8.3.1). The purpose of this research is to allow complex non-linear geometric constraints in a multiresolution geometric modelling environment. Two kinds of constraints have been investigated so far: constraints of constant area and constant length, both for the modelling of curves. For the area constraint, a wavelet decomposition of the curve has been used, and the bilinear form corresponding to the area enclosed by the curve has been expressed in this wavelet basis. This enables us to enforce a constant area constraint in real time, even for complex curves with an order of 1000 control points. This work has been submitted for publication in the journal Computer Aided Geometric Design. Concerning the constraint of constant length, a multiresolution editing tool for planar curves which allows maintaining a constant length has been developed. One possible application is the modelling of folds and wrinkles. This work has been published in [8].

The generalization of these results to constraint of constant volume and constant area in the modelling of surfaces is currently under investigation.

### Space deformations

**Participants:**Alexis Angelidis, Marie-Paule Cani.

We developed a new method based on space deformations for interactively sculpting a shape while keeping its topological genius unchanged: the user interactively sweeps tools that deform space along their path. The objects that overlap with the deformed part of the space are re-meshed in real-time for always being accurately displayed. Our method insures that the resulting deformations are fold over-free, which prevents self-intersections between parts of the deformed shapes. Our paper [11] got the best paper award at the Shape Modelling International'2004 conference. The extension of this work to constant volume space deformations makes the interaction even more intuitive, since objects now deform as if they were made of real material (see Figure 3). This work was presented as a technical sketch at SIGGRAPH [29], and the full paper [10] got the best paper award at the Pacific Graphics'2004 conference.

### Cumulus clouds shape model

**Participants:**Antoine Bouthors, Fabrice Neyret.

During his Master thesis Antoine Bouthors has developed a model of cumulus cloud shape which is surface based. The mesh of the surface is produced from hierarchical implicit blobs on top of each other. Blobs are associated to particles repulsing each other. Their shape is defined by a potential keeping their well-separated and spherical aspect while ensuring continuity through blobs. A dedicated shader allows us to provide a fuzzy apparence to the surface (see figure 4). This work has been published as a short presentation [13] at Eurographics'04. Antoine Bouthors is now continuing his work as a PhD student.