Section: New Results

Representing, creating and processing geometry

Participants : Adrien Bernhardt, Dobrina Boltcheva, Georges-Pierre Bonneau, Marie-Paule Cani, Jean-Rémy Chardonnet, Sahar Hassan, Franck Hétroy, Jean-Claude Léon, Olivier Palombi, Adeline Pihuit, Damien Rohmer.

Multiresolution geometric modeling with constraints

Participant : Georges-Pierre Bonneau.

Figure 4. Multiresolution Morphing between France and Germany, at 5 levels of resolution.

This work is done in collaboration with Stefanie Hahmann from LJK. The purpose of this research is to allow complex nonlinear geometric constraints in a multiresolution geometric modeling. This year we have worked on a multiresolution morphing algorithm using "as-rigid-as-possible" shape interpolation combined with an angle-length based multiresolution decomposition of simple 2D piecewise curves. This novel multiresolution representation is defined intrinsically and has the advantage that the details' orientation follows any deformation naturally. The multiresolution morphing algorithm consists of transforming separately the coarse and detail coefficients of the multiresolution decomposition. The results are illustrated in Figure 4 . This work has been published in [18] .

Hand-on interaction for Virtual Sculpture

Participants : Marie-Paule Cani, Jean-Rémy Chardonnet, Jean-Claude Léon, Damien Rohmer.

The different deformation models we developed in the past few years open the problem of providing intuitive interaction tools for specifying the desired deformation in real-time. Our recent work therefore focused on developing new interfaces for interacting with the model to deform.

After experimenting a soft ball connected to a phantom device, serving as a proxy for the model to deform, we developed an interface similar to a mouse, called the hand-navigator , enabling to control simultaneously all the degrees of freedom of a virtual hand. This device, which provides some passive haptic feedback, needs no calibration and enables interrupting the tasks anytime, is patented by INRIA. It extends a standard pace-navigator using petals that support sensors for the fingers, to control the opening and closure gestures of the virtual hand as well as its position and orientation.

This year, thanks to a pre-industrialization project funded by the incubator GRAVIT (see Section  7.1 ), we extended the first prototype by testing new captors and new shapes for the device. We also interfaced it with a constant volume skinning method (see Section  6.1.5 ) and demonstrated it at Grenoble Innivation Fair and in various conferences [30] , [19] .

Note that this work is also part of our contribution to the PPF "Multimodal interaction" (see Section  8.3.3 ).

Implicit Modeling

Participants : Adrien Bernhardt, Marie-Paule Cani, Olivier Palombi, Adeline Pihuit.

Implicit surfaces are a very good representation for smooth, organic-like, free-form shapes. In addition to being able to represent objects of arbitrary topological genius, they have the ability to be constructed by successively blending different components, which eases interactive modelling tasks. Lead by our needs of an adequate surface representation for sketch-based modelling (see  6.1.4 ), re-started this year some fundamental research on implicit modelling, leading to three new contributions:

Firstly, we designed a method for reconstructing 3D implicit surfaces from 2D regions painted in parallel planes. This method, applied to the reconstruction of anatomic shapes, first uses convolution surfaces to reconstruct a field function whose iso-surface fits a single contour, and then uses a combination of interpolation and extrapolation for computing field values outside the planes, leading to a full 3D reconstruction of the shape. Adeline Pihuit received the best student paper award at the French computer graphics conference (AFIG) for this work [29] . See Figure 5 .

Figure 5. Mixed interpolation and extrapolation for the implicit reconstruction of vertebra from 2D regions sketched in parallel planes.

This method has been used to reconstruct the shape of the precerebellar linear nucleus in the mouse. This neuroanatomical study has been successfully completed in collaboration with the laboratory of Pr. Paxinos in Sydney (POWMRI, UNSW, Australia) [7] .

Secondly, we collaborated with a researcher in formal computation to improve and extend the analytical methods for computing closed form solutions for convolution surfaces [35] .

Lastly, we revisited implicit blending, to enable implicit surfaces to blend in regions where they intersect, but to be able to come as close to each other as desired without blending in other regions. See Figure 6 . This work has been accepted for publication at Eurographics in 2010.

Sketch-Based Modeling

Participants : Adrien Bernhardt, Marie-Paule Cani, Jean-Claude Léon, Olivier Palombi, Adeline Pihuit.

3D modeling from a sketch is a fast and intuitive way of creating digital content. We are exploring this technique from two different view-points:

A first class of methods directly infer free-form shapes in 3D from arbitrary progressive sketches, without any a priori knowledge on the objects being represented. Our work relies on implicit, convolution surfaces for doing so: the user paints a 2D projection of the shape. A skeleton (or medial axis), taking the form of a set of branching curves, is reconstructed from this 2D region. It is converted into a close form convolution surface whose radius varies along the skeleton. The resulting 3D shape can be extended by sketching over it from a different viewpoint, while the blending operator used adapts its action so that blending remains local and no detail is blurred during the process (see figure 6 ). This work was supported by a direct industrial contract with Axiatec (see Section  7.2 ), leading to the development of the Azalic studio software (see Section  5.5 ).

Figure 6. Interactive modelling using Azalic Studio, our sketch-based modelling software: the different shape component are successively created using implicit surfaces and locally blended to the shape.

Another research direction is sketch-based modelling is to create a complex shape from a single sketch, using some a priori knowledge on the object being drawn for inferring the missing 3D information. This idea was exploited for the sketch-based modeling of trees [15] , in collaboration with the INRIA project-team Virtual Plants (see Figure 7 ). This work in the same spirit is currently conducted within Adeline Pihuit's PhD thesis, co-supervised by Olivier Palombi and Marie-Paule Cani, and focusing on the use of sketch-based interfaces for the interactive teaching of anatomy. We are also investigating the design of realistic terrains from a single sketch, within the PhD thesis of Adrien Bernhardt.

Figure 7. Tree designed in less than 2mn using a multi-resolution sketching system which incorporates some a priori knowledge from botany.

Geometrical methods for skinning character animations

Participants : Marie-Paule Cani, Franck Hétroy, Damien Rohmer.

Skinning, which consists in computing how vertices of a character mesh (representing its skin) are moved during a deformation w.r.t. the skeleton bones, is currently the most tedious part in the skeleton-based character animation process. We propose [21] new geometrical tools to enhance current methods. First, we developed a new skinning framework inspired from the mathematical concept of atlas of charts: we segment a 3D model of a character into overlapping parts, each of them being anatomically meaningful (e.g., a region for each arm, leg, etc., with overlaps around joints), then during deformation the position of each vertex in an overlapping area is updated thanks to the movement of neighboring bones. This work was done in collaboration with Boris Thibert from the MGMI team of the LJK, Cédric Gérot from the GIPSA-Lab in Grenoble, and Lin Lu from the University of Hong Kong.

Secondly, we developed, in collaboration with Stefanie Hahmann from the MGMI team of the LJK, a post-correction method for preserving volume in the standard smooth-skinning pipeline [25] . As usual, the character is defined by a skin mesh at some rest pose and an animation skeleton. At each animation step, skin deformations are first computed using standard SSD. Our method corrects the result using a set of local deformations which model the fold-over-free, constant volume behaviour of soft tissues. This is done within an exact geometrical computation in three passes. This new methods has the benefits to allow the specification of a profile curve through which the user controls the shape of the deformation. See figure 8 .

Figure 8. Constant volume skinning with shape control.

Ontology-based mesh segmentation

Participants : Sahar Hassan, Franck Hétroy, Olivier Palombi.

Patient-specific 3D virtual models of anatomical organs are becoming more and more useful in medicine, for instance for diagnosis or follow-up care purposes. These models are usually created from 2D scan OR MRI images. However, small or thin geometrical features, such as ligaments, are sometimes not visible on these images. We propose to use an anatomical ontology, called MyCorporisFabrica [11] and developed in the team (see Section  5.6 ), to add missing parts to reconstructed virtual organs. This ontology describes definitions of and relationships between organs: e.g., femur is part of the leg. The first step towards the full achievement of this process is to segment virtual models, often represented by 2D meshes, into meaningful parts. In our case, “meaningful” means “related to the ontology”: each part should refer to an organ defined in the ontology. The general outline to create this segmentation has been proposed this year [27] : first, we approximate organ's shapes by geometric primitives, then we segment a given organ mesh by optimizing objective functions which are related to these primitives.

Topological classification of non-manifold singularities

Participants : Dobrina Boltcheva, Franck Hétroy, Jean-Claude Léon.

In computer graphics, as in many other cases (CAD, civil engineering, ...), idealized virtual representations of real models are used. For instance in case of a complex big building, a single wall will be seen as a planar surface, instead of a thin volume. However, most processing algorithms suppose these data to be globally coherent: surfacic meshes are for instance supposed to be 2-manifolds. Together with colleagues from the university of Genova in Italy, we aim at classifying non-manifold singularities of used idealized models (we restrict to simplicial complexes), in order to exhibit global topological properties that can then be used to enhance or modify current processing algorithms. A first step towards this goal has been achieved this year, with a first classification proposal [22] , [28] . Two examples of non-manifold singularities are shown on figure 9 .

Figure 9. Two shapes with non-manifold singularities: pinched sphere (left) and squeezed torus (right).

Mesh repair

Participant : Franck Hétroy.

This work is done in collaboration with Carlos Andujar, Pere Brunet and Alvar Vinacua from Universitat Politecnica de Barcelona, Spain. The purpose is to propose an efficient method to create 2-manifold meshes from real data, obtained as soups of polygons with combinatorial, geometrical and topological noise. We propose to use a voxel structure called a discrete membrane and morphological operators to compute possible topologies, between which the user chooses. It has been submitted to publication.