## Section: New Results

### Creation of digital content and geometry processing

Participants : Grégoire Aujay, Georges-Pierre Bonneau, Marie-Paule Cani, Christine Depraz, François Faure, Laurent Favreau, Franck Hétroy, Paul Kry, Olivier Palombi, Lionel Reveret, Jamie Wither.

#### Multiresolution geometric modeling with constraints

Participant : Georges-Pierre Bonneau.

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 8.1.1 ). The purpose of this research is to allow complex nonlinear geometric constraints in a multiresolution geometric modeling environment. Two kinds of constraints have been firstly investigated: constraints of constant area and constant length, both for the modeling of curves.

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 modeling of folds and wrinkles. This work has been published in [31] .

Lately, constraints of constant volume for the multiresolution deformation of BSpline tensor-product surfaces as well as subdivision surfaces have been investigated. Fig. 2 illustrates the deformation of a subdivision surface with constant volume.

A survey on integrating constraints into multiresolution models has been written in collaboration with Prof. Elber, and published in [11] .

#### Virtual sculpture

Participants : Marie-Paule Cani, Paul Kry.

We compared two alternative approaches for interactively sculpting a 3D shape: a geometric approach based on space deformations and the use of a physically-based model for virtual clay.

The space deformation technique called ``sweepers'' [5] , developed in collaboration with the University of Otago in New Zealand, is controlled by gesture: the user interactively sweeps tools that deform space along their path. The objects overlapping with the deformed part of space are locally re-meshed in real-time for accurate display. The resulting deformations are fold over-free: self-intersections are prevented, and the objects topological genius is preserved. This technique was extended to constant volume deformations, called ``swirling sweepers'' [4] : preserving volume makes the deformation even more intuitive, giving the user the impression of interacting with clay.

This approach was compared with different models for physically-based virtual clay within in a tutorial on ``Interactive shape editing'' we gave this summer at SIGGRAPH [6] . We concluded that the layered volumetric model we previously developed for clay achieves the desired plausibility in real-time, but opens the problem of providing intuitive interaction modes. We are currently working on this point with a master student, following the work Paul Kry presented at SIGGRAPH on interaction capture [25] .

#### Modeling by sketching

Participants : Grégoire Aujay, Marie-Paule Cani, Jamie Wither.

Sketch-based techniques are currently attracting more and more attention as a fast and intuitive way to create digital content. We are exploring these techniques with two different view-points:

A first class of sketching techniques directly infer free-form shapes in 3D from arbitrary progressive sketches, without any a priori knowledge on the objects being represented. Following a collaboration started last year with IRIT in Toulouse, we are studying the use of convolution surfaces for achieving this goal. This done within a direct industrial contract with the firm Axiatec (see Section 7.3 ), on which we hired an engineer: Grégoire Aujay.

A second class of sketching techniques create complex shapes from one or two sketches only (for instance a front and a back view), using some a priori knowledge on the object being sketched for inferring 3D. This is the topic of Jamie Wither's PhD. He first extended a previous work on sketching for fashion design by introducing the sketching of cloth folds [16] (see figure 3 ), and is now working towards the extension of this kind of technique for natural objects: we are developing a sketching interface for realistic hair in collaboration with UBC, Canada and will address sketch-based modeling of trees within the ANR project Natsim(see Sections 6.2.7 and 8.2.2 ).

#### Mesh repair with topology control

Participant : Franck Hétroy.

Meshes created from 3D laser scanned acquisition of real models often contain singularities (intersecting faces, holes, ...), due to defect during measures (for example, hidden parts of the model) or during the mesh creation process. The goal of this work is to transform a mesh with singularities into a "clean" mesh – mathematically speaking, a 2-manifold – with user control of the topology of the output (number of connected components and number of holes). It is a joint work between EVASION and the MOVING Group of the Technical University of Catalonia (UPC, Barcelona: Carlos Andújar, Pere Brunet, Jordi Esteve and Álvar Vinacua).

During her internship this summer, Stéphanie Rey has implemented an algorithm which computes and lets the user modify the topology of a voxel representation of the mesh, named ``discrete membrane'' [34] . Contrary to previous approaches, it allows the user to add or remove selected handles (of different sizes), in only a few seconds.

#### 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. During his Master thesis, Grégoire Aujay has developed an algorithm which uses geometrical information on the model to automatically compute a hierarchical geometric skeleton, which can be converted into an animation skeleton [36] , [19] . User intervention is restricted to the selection of one or a few points at the very beginning of the process, but the algorithm is customizable and users can adjust the skeleton to their needs. This work has been done in collaboration with Francis Lazarus, from the Laboratoire des Images et des Signaux (LIS) in Grenoble. A result is shown on figure 4 .

#### Morphable model of quadruped skeletons for animating 3D animals

Participants : Lionel Reveret, Laurent Favreau, Christine Depraz, Marie-Paule Cani.

Skeletons are at the core of 3D character animation. The goal of this work is to design a morphable model of 3D skeleton for four footed animals, controlled by a few intuitive parameters. This model enables the automatic generation of an animation skeleton, ready for character rigging, from a few simple measurements performed on the mesh of the quadruped to animate (see fig. 4 ). Quadruped animals - usually mammals - share similar anatomical structures, but only a skilled animator can easily translate them into a simple skeleton convenient for animation. Our approach for constructing the morphable model thus builds on the statistical learning of reference skeletons designed by an expert animator. This raises the problems of coping with data that includes both translations and rotations, and of avoiding the accumulation of errors due to its hierarchical structure. Our solution relies on a quaternion representation for rotations and the use of a global frame for expressing the skeleton data. We then explore the dimensionality of the space of quadruped skeletons, which yields the extraction of three intuitive parameters for the morphable model, easily measurable on any 3D mesh of a quadruped. We evaluate our method by comparing the predicted skeletons with user-defined ones on one animal example that was not included into the learning database. We finally demonstrate the usability of the morphable skeleton model for animation. Laurent Favreau has defended his PhD [2] on this topic in November 2006.

#### Detection and quantification of brain aneurysms

Participants : François Faure, Franck Hétroy, Olivier Palombi.

Aneurysms are excrescences on blood vessels. They can break, letting the blood propagate outside the vessel, which often leads to death. In some cases, the blood clots sufficiently fast so that people survive. However, a neurosurgeon or a neuroradiologist should intervene very quickly in order to repare the vessel before the aneurysm breaks once more.

The purpose of this research is to help neurosurgeons and neuroradiologists to plan surgery, by giving them quantitative information about the size, shape and geometry position of aneurysms. The first part of this work has been done this summer during the internship of Sahar Hassan [39] : we have developed a simple algorithm for the automatic detection of aneurysms on CTA images.

This work will continue in 2007 with the Master thesis of Sahar Hassan.