### Research Activities:

In computer graphics, researches are usually conducted independently on two main areas that are geometric modeling and rendering. The research group VORTEX/AGGA develops research at the interface of these two fields to construct a coherent chain of processing and efficient data representation for image synthesis.

This joint approach geometry/rendering was mainly conducted on the following topics:

**Real time rendering and expressivity.** Real time rendering, with its interactive applications for exploration and analysis of 3D data, requires the establishment of appropriate and effective algorithms to allow efficient perception of computer-generated images. The main results over the period concern expressive rendering, through the stylization of line drawings based on a differential geometry analysis, for efficient content perception [12439], and also realistic rendering through geometry-based shadow algorithm [10771].

**Models and algorithms for lighting simulation.** When image quality is of first interest for applications, computing an image requires solving the general integral equation of rendering. Due to its nature, this recursive integral equation is solved using Monte Carlo techniques. By expressing the light transport equation not only in 3D space but also in infinite dimensional path-space two main problems arise: how to minimize the variance of the Monte Carlo estimator and how to minimize computational complexity when exploring infinite dimensional space. The main results obtained by the group in this field concern efficient sampling of path-space [12265] and parallelization of the algorithm using both CPU and GPU [12266].

**Implicit surfaces modeling and rendering.** 3D object modeling remains an open problem as far as efficient user manipulation and adaptation of the 3D surface description for rendering is concerned. By studying implicit surfaces as an alternative representation of 3D objects, the group aims to provide the user intuitive control over its creation process. Implicit modeling relies on the ability to blend several implicit surfaces to define a global geometry. We have solved old problems of implicit blending by defining a gradient-based blending operator [14354] that allows an efficient control over the final shape. Efficient algorithms were also developed to render implicit surfaces by ray-tracing 11842] and, thanks to the properties of our blending operator, we have proposed a real-time skinning process for skeletal animation that simplifies the rigging and skinning workflow for content creation [14737].

**Meshes, B-Rep and CAD.** Meshes and B-Rep nevertheless remain the main surface representation for interactive applications or for CAD modeling. In order to improve the creation, edition and visualization process of such surface representation, we have developed robust algorithms allowing topologically consistent interactive remeshing of deformable surfaces [14355] but also fast and accurate adaptive meshing of B-REP surfaces for CAD visualization [15285].

### Research project :

Content creation for computer graphics remains a complex problem while the requirements and the expectations from the constantly increasing number of users are getting more and more prominent. On the one hand, the representation and the computation of the data required to combine 3D objects, animation parameters and lighting parameters into a computer generated picture leads to mathematical modeling, data structure and algorithmic complexity problems. On the other hand, creating, editing and exploiting such data relies on efficient user interactions with these objects and requires versatile creation and edition metaphors hiding the mathematical complexity of the 3D content. This ambivalent vision of content creation for computer graphics is at the heart of our scientific objectives for the next period: the definition of domain-centered content creation frameworks for animated computer graphics.

By relying on our joint geometry/appearance approach, we plan to address bottlenecks in geometric aspect of skeletal animation guided by visual objectives, efficient sampling strategies for stochastic algorithms and user editing method for picture generation. Efficient sampling and user editing of image synthesis. With the advance of widely available geometric modeling and content creation software, users can create wide detailed worlds with realistic appearance. Physically based rendering algorithms, such those presented in our scientific assessment, are now quite mature and allow the simulation of fine global illumination effects, even though the time and space footprint of these algorithms still need improvements.

Efficient sampling and reconstruction methods for picture generation. Light transport integral equation used by physically based renderers is nowadays commonly solved using Monte Carlo based techniques. As these rely on sampling of the integration domain (light-path space), we plan to analyze the spatial and frequency properties of the light transport equations to define a sampling scheme that minimize the number of nD samples (light paths) required to reconstruct the light signal in image space. Some works already use frequency analysis or differential analysis of light transport to reduce the sampling rate of the integration domain. Built on our Monte-Carlo techniques expertise for lighting simulation, we plan to study how compressive sensing will help to obtain efficient evaluation of light transport for the computation of consistent images.

User control. From a user point of view, the parameterization of rendering algorithms and the edition of the resulting picture to obtain a particular visual aspect to depict a scene is still a major issue: the user modifies the 3D scene definition and updating the finale image needs time consuming re-computation; editing appearance and lighting involves the understanding and control of light propagation on a perceptual point of view. By exploiting the light-path space formulation of rendering algorithms, we currently work on a geometric metaphor to edit light propagation paths and the characterization of local appearance properties. Our objective is to provide efficient editing approach, with perceptually motivated algorithms. Taking benefit from the efficient sampling, our middle term goal is to provide real-time editing of image synthesis.

Geometric aspect of skeletal animation guided by visual objectives. At short-term, we will follow the new line of research opened by the implicit skinning technique. It is a new approach for the computation of plausible skin deformations during animations and several researches have to be carried out in order to adapt the technique to the users needs and to increase its robustness and versatility. In parallel, we work with the SATT Toulouse Tech Transfer in order to transfer our technology in the simulation and animation industry. At medium and long-term, we will investigate around the joint use of implicit surfaces and meshes. We see this association as extremely promising as soon as collisions and deformations are to be computed and treated in a 3D application. From a higher level, we will study the definition of "interactors" that would define the way objects geometrically interact when they come into contact in a dynamic 3D environment. Often binary, this concept could be studied up to its limits, when a very large number of collisions are to be treated in the same interactor. Computing and treating collisions in an interactive way remains a very challenging open problem that a dedicated instantiation of the theoretical interactors could solve.

### Research Contributions :

We present a general method enhancing the robustness of estimators based on multiple importance sampling (MIS) in a numerical integration context. MIS minimizes variance of estimators for a given sampling configuration, but when this configuration is less adapted to the integrand, the resulting estimator suffers from extra variance. We address this issue by introducing the notion of "representativity’’ of a sampling strategy, and demonstrate how it can be used to increase robustness of estimators, by adapting them to the integrand. We first show how to compute representativities using common rendering informations such as BSDF, photon maps or caches in order to choose the best sampling strategy for MIS. We then give hints to generalize our method to any integration problem and demonstrate that it can be used successfully to enhance robustness in different common rendering algorithms. | |

For each location of the test scene (left picture), the right picture shows the MSE of our estimator are in red, and MSE of the other estimators are with a color gradient ranging from dark blue to cyan. Dark blue means rhob = 0.1, cyan means rhob = 1.0, that is pure BSDF-based path-tracing. The x axis corresponds to the number of samples generated to perform one estimation of the value of a pixel, from 2^1 to 2^10. | |

IEEE Transactions On Visualization and Computer Graphics, August 2011, pp1108-1121 |

Many methods in computer graphics require the integration of functions on low- to-middle-dimensional spaces. However, no available method can handle all the possible integrands accurately and rapidly. This paper presents a robust numerical integration method, able to handle arbitrary non-singular scalar or vector-valued functions defined on low-to-middle-dimensional spaces. Our method combines control variate, globally adaptive subdivision and Monte-Carlo estimation to achieve fast and accurate computations of any non-singular integral. The runtime is linear with respect to standard deviation while standard Monte-Carlo methods are quadratic. We additionally show through numerical tests that our method is extremely stable from a computation time and memory footprint point-of-view, assessing its robustness. We demonstrate our method on a participating media voxelization application, which requires the computation of several millions integrals for complex media. |

When computing the integral of a function g over a multidimensional domain Omega, our algorithm build an evaluation tree where each node represents an analytically integrable approximation of the function g. When the approximation error is small enough, the node is the considered as a leaf of the evaluation tree and the local integral is approximated as the sum of the analytically computed approximation of the integral and a Monte-Carlo estimation of the integral of the approximation error. |

SIAM Journal on Scientific Computing, 36(4), pages A1708-A1730, 2014 |

Geometric skinning techniques, such as smooth blending or dualquaternions, are very popular in the industry for their high performances, but fail to mimic realistic deformations. Other methods make use of physical simulation or control volume to better capture the skin behavior, yet they cannot deliver real-time feedback. In this paper, we present the first purely geometric method handling skin contact effects and muscular bulges in real-time. The insight is to exploit the advanced composition mechanism of volumetric, implicit representations for correcting the results of geometric skinning techniques. The mesh is first approximated by a set of implicit surfaces. At each animation step, these surfaces are combined in real-time and used to adjust the position of mesh vertices, starting from their smooth skinning position. This deformation step is done without any loss of detail and seamlessly handles contacts between skin parts. As it acts as a post-process, our method fits well into the standard animation pipeline. Moreover, it requires no intensive computation step such as collision detection, and therefore provides real-time performance. |

(a) Real-time animation of the index finger of a hand model composed of 31750 vertices. Two poses are shown in each column: (b) standard smooth skinning with linear blending at 95 frames per second (fps), (c) our method which compensates the loss of volume on top of joints and models contact in the fold at 37 fps, (d) our method with an additional bulge mimicking tissues inflation at 35 fps, and (e) a picture of a real bent finger. |

ACM Transactions on Graphics, 32(4), proc. of ACM SIGGRAPH, 2013 |