## Section: New Results

### New representations and deformation techniques for shape modelling

Participants : Alexis Angelidis, Georges-Pierre Bonneau, Antoine Bouthors, Marie-Paule Cani, François Faure, Franck Hétroy, Fabrice Neyret, François Faure, Lionel Reveret, Jamie Wither.

#### Detection of geometrical and topological characteristics in shapes

Participants : Franck Hétroy, François Faure, Lionel Revéret.

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 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. We have developed a new algorithm to compute major constrictions on closed polyhedral surfaces, which overcomes the drawbacks of previous approaches (for example, the computation time has been significantly reduced) using curvature directions and values. This work has been published as a short paper [24] at Eurographics'05.

Applications of this work are widespread, from classification of shapes to object decomposition into simple parts, and to detection of singularities. We currently focus on two main applications: the quantification of aneurysms in volumetric medical images (with François Faure) and the automatic detection of articulations on animal models, to simplify the animation of these models (with Lionel Revéret).

#### 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. It has been shown how this model can be hierarchically refined in order to compactly add local detail on the surface. Figure 1 illustrates a dog's head designed with a geometric modelling software based on our new surface model. A paper on this topic has been published in the journal ACM Transactions On Graphics [18] .

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. Special care has to be dedicated to the proper parameterization of the dense mesh over the base domain of the reconstructed surface. Figure 2 illustrates the reconstruction of the Max Planck model. Alex Yvart has defended his PhD on this topic in December 2004. The reconstruction method has been published in the conference SMI'05 [31] .

Alex Yvart has defended his PhD thesis December 4, 2004. He is now working in the R& D department of Renault, as a chief engineer.

#### 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 is also taking place 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 nonlinear geometric constraints in a multiresolution geometric modelling environment. Two kinds of constraints have been firstly investigated: 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 published in the journal Computer Aided Geometric Design [13] .

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 [12] .

Lately, constraints of constant volume for the multiresolution deformation of BSpline tensor-product surfaces as well as subdivision surfaces have been investigated. Fig. 3 illustrates the deformation of a subdivision surface with constant volume.

Basile Sauvage has defended his PhD thesis on December 5, 2005 [6] .

#### Space deformations

Participants : Alexis Angelidis, Marie-Paule Cani.

We developed a 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. After getting the best paper price in a conference in 2004, a revised version of our paper was published in the journal Graphical Models [9] . This work and its extension to constant volume space deformations (see Figure 4 ) was presented at the Summer School on Interactive shape modeling organized by the network of excellence Aim@shape 8.3.1 and in the EUROGRAPHICS'2005 tutorial on Interactive Shape Modelling [1] .

#### Cumulus clouds shape model

Participants : Antoine Bouthors, Fabrice Neyret.

Antoine Bouthors continues his PhD on Cumulus clouds. This year, he worked with a student on dynamic remeshing of implicit surfaces [35] (a paper has been submitted to SMI'06, see fig. 5 ), and he studied statistics of photon-tracing and analytical models.

#### Modeling by sketching

Participants : Marie-Paule Cani, Jamie Wither.

Participants: Marie-Paule Cani, Jamie Wither

Easily creating 3D models by using sketch-based techniques is attracting more and more attention.

In collaboration with the computer graphics group at IRIT (Toulouse), we created a user-friendly modeling system that enables non-expert users to generae a wide range of free-form shapes from interactive sketching. A skeleton, in the form of a graph of branching polylines and polygons, is first extracted from the user's sketch. The 3D shape is then defined as a convolution surface generated by this skeleton. The subsequent 2D stokes are used to infer new parts of the object, which are combined with the prior ones using smooth CSG operators, the range of blending being adapted to the scale. This work appear in Pacific Graphics [19] .

A new PhD student, Jamie Wither, funded by the European project visitor, joined the group in november to work on sketch and annotation techniques for the design and animation of natural scenes.

#### Automatic computation of an animation skeleton

Participant : Franck Hétroy.

Animation of a 3D model is usually made using a hierarchical representation of its articulations called the animation skeleton. Creation of this animation skeleton is a laborious task since it is made by hand. We aim at simplifying this task, using geometrical information on the model to first compute a geometric skeleton, which later can be converted into an animation skeleton.

The first part of this work is thus to compute a geometric skeleton containing relevant information and which can easily be converted into an animation skeleton. To do so, we focus on Reeb graphs, because such skeletons are simple edge-vertex graphs, their structure is closely related to the model's geometry and topology, and their computation is fast. This work has started this summer, with the test several kinds of Reeb graphs, and how they can be modified.