Rendering a complex surface accurately and without aliasing requires the evaluation of an integral for each pixel, namely a weighted average of the outgoing radiance over the pixel footprint on the surface. The outgoing radiance is itself given by a local illumination equation as a function of the incident radiance and of the surface properties. Computing all this numerically during rendering can be extremely costly. For efficiency, especially for real-time rendering, it is necessary to use precomputations. When the fine scale surface geometry, reflectance and illumination properties are specified with maps on a coarse mesh (such as color maps, normal maps, horizon maps or shadow maps), a frequently used simple idea is to pre-filter each map linearly and separately. The averaged outgoing radiance, i.e., the average of the values given by the local illumination equation is then estimated by applying this equation to the averaged surface parameters. But this is really not accurate because this equation is non-linear, due to self-occlusions, self-shadowing, non-linear reflectance functions, etc. Some methods use more complex pre-filtering algorithms to cope with these non-linear effects. In we presented a a survey of these methods. We have started with a general presentation of the problem of pre-filtering complex surfaces. We then present and classify the existing methods according to the approximations they make to tackle this difficult problem. Finally, an analysis of these methods allows us to highlight some generic tools to pre-filter maps used in non-linear functions, and to identify open issues to address the general problem.

We have developed an extension to Hachisuka et al.'s Progressive Photon Mapping (or PPM) algorithm in which we estimate the radius of the density estimation kernels using frequency analysis of light transport . We predict the local radiance frequency at the surface of objects using a Gaussian approximation, and use it to drive the size of the density estimation kernels, in order to accelerate convergence (see Figure  . The key is to add frequency information to a small proportion of photons: frequency photons. In addition to contributing to the density estimation, they will provide frequency information. This work has been published in .

This work is the result of a collaboration with S. Hahmann from the EVASION team-project and Prof. Hans Hagen partly done during a sabbatical of G.-P. Bonneau in the University of Kaiserslautern, Germany. Interdisciplinary efforts in modeling and simulating phenomena have led to complex multi-physics models involving different physical properties and materials in the same system. Within a 3d domain, substructures of lower dimensions appear at the interface between different materials. Correspondingly, an unstructured tetrahedral mesh used for such a simulation includes 2d and 1d substructures embedded in the vertices, edges and faces of the mesh. The simplification of such tetrahedral meshes must preserve (1) the geometry and the topology of the 3d domain, (2) the simulated data and (3) the geometry and topology of the embedded substructures. This work focuses on the preservation of the topology of 1d and 2d substructures embedded in an unstructured tetrahedral mesh, during edge collapse simplification. We derive a robust algorithm, based on combinatorial topology results, in order to determine if an edge can be collapsed without changing the topology of both the mesh and all embedded substructures. Based on this algorithm we have developed a system for simplifying scientific datasets defined on irregular tetrahedral meshes with substructures, illustrated in Figure  . We presented and demonstrated the power of our system with real world scientific datasets from electromagnetism simulations in the Springer book chapter .

We have developed an algorithm to render objects of transparent materials with rough surfaces in real-time, under distant illumination. Rough surfaces cause wide scattering as light enters and exits objects, which significantly complicates the rendering of such materials. We present two contributions to approximate the successive scattering events at interfaces, due to rough refraction : First, an approximation of the Bidirectional Transmittance Distribution Function (BTDF), using spherical Gaussians, suitable for real-time estimation of environment lighting using pre-convolution; second, a combination of cone tracing and macro-geometry filtering to efficiently integrate the scattered rays at the exiting interface of the object. We demonstrate in I3D paper the quality of our approximation by comparison against stochastic raytracing. This work is illustrated in Figure  .

Indirect illumination is an important element for realistic image synthesis, but its computation is expensive and highly dependent on the complexity of the scene and of the BRDF of the involved surfaces. While off-line computation and pre-baking can be acceptable for some cases, many applications (games, simulators, etc.) require real-time or interactive approaches to evaluate indirect illumination. We present in the Pacific Graphics paper a novel algorithm to compute indirect lighting in real-time that avoids costly precomputation steps and is not restricted to low-frequency illumination. An illustration is given in Figure  . It is based on a hierarchical voxel octree representation generated and updated on the fly from a regular scene mesh coupled with an approximate voxel cone tracing that allows for a fast estimation of the visibility and incoming energy. Our approach can manage two light bounces for both Lambertian and glossy materials at interactive framerates (25-70FPS). It exhibits an almost scene-independent performance and can handle complex scenes with dynamic content thanks to an interactive octree-voxelization scheme. In addition, we demonstrate that our voxel cone tracing can be used to efficiently estimate Ambient Occlusion. A primer of this work has been published as a poster (Best Poster Award ). Insights of the method were given in the Siggraph Talk 2011 .

The publication has received the Best Poster Awardat I3D'2011.

Shading complex materials such as acquired reflectances in multi-light environments is computationally expensive. Estimating the shading integral involves stochastic sampling of the incident illumination independently at several pixels. The number of samples required for this integration varies across the image, depending on an intricate combination of several factors. Ignoring visibility, adaptively distributing computational budget across the pixels for shading is already a challenging problem. In the paper we present a systematic approach to accelerate shading, by rapidly predicting the approximate spatial and angular variation in the local light field arriving at each pixel. Our estimation of variation is in the form of local bandwidth, and accounts for combinations of a variety of factors: the reflectance at the pixel, the nature of the illumination, the local geometry and the camera position relative to the geometry and lighting. An illustration is given in Figure  .The speed-up, using our method, is from a combination of two factors. First, rather than shade every pixel, we use this predicted variation to direct computational effort towards regions of the image with high local variation. Second, we use the predicted variance of the shading integrals, to cleverly distribute a fixed total budget of shading samples across the pixels. For example, reflection off specular objects is estimated using fewer samples than off diffuse objects.

Non-photorealistic rendering (NPR) algorithms allow the creation of images in a variety of styles, ranging from line drawing and pen-and-ink to oil painting and watercolor. These algorithms provide greater flexibility, control and automation over traditional drawing and painting. Despite significant progress over the past 15 years, the application of NPR to the generation of stylized animations remains an active area of research. The main challenge of computer generated stylized animations is to reproduce the look of traditional drawings and paintings while minimizing distracting flickering and sliding artifacts present in hand-drawn animations. These goals are inherently conflicting and any attempt to address the temporal coherence of stylized animations is a trade-off. We have published the state-of-the-art report motivated by the growing number of methods proposed in recent years and the need for a comprehensive analysis of the trade-offs they propose. We formalize the problem of temporal coherence in terms of goals and compare existing methods accordingly. We propose an analysis for both line and region stylization methods and discuss initial steps toward their perceptual evaluation. The goal of our report is to help uninformed readers to choose the method that best suits their needs, as well as motivate further research to address the limitations of existing methods.

This work is the result of a collaboration with EdF R&D and Jacques Droulez, Director of Research at CNRS in Collège de France. In his PhD work, Alexandre Coninx has introduced a new method to visualize uncertain scalar data fields by combining color scale visualization techniques with animated, perceptually adapted Perlin noise. The parameters of the Perlin noise are controlled by the uncertainty information to produce animated patterns showing local data value and quality, as illustrated in Figure  . In order to precisely control the perception of the noise patterns, we perform a psychophysical evaluation of contrast sensitivity thresholds for a set of Perlin noise stimuli. We validate and extend this evaluation using an existing computational model. This allows us to predict the perception of the uncertainty noise patterns for arbitrary choices of parameters. We demonstrate and discuss the efficiency and the benefits of our method with various settings, color maps and data sets. This work has been published at APGV'2011 .

Computer tomography (CT) has wide application in medical imaging and reverse engineering. Due to the limited number of projections used in reconstructing the volume, the resulting 3D data is typically noisy. Contouring such data, for surface extraction, yields surfaces with localised artifacts of complex topology. To avoid such artifacts, we propose a method for feature-preserving smoothing of CT data, illustrated in Figure  . The smoothing is based on anisotropic diffusion, with a diffusion tensor designed to smooth noise up to a given scale, while preserving features. We compute these diffusion kernels from the directional histograms of gradients around each voxel, using a fast GPU implementation. This work has been published as a Siggraph'2011 Poster .

In this work, we propose a new method to automatically and consistently convert 3D splines into dynamic rods at rest under gravity, bridging the gap between the modeling of 3D strands (such as hair, plants) and their physics-based animation. An illustration is given in Figure  . This work is done in collaboration with F. Bertails from the BIPOP team-project. It has been published in a Siggraph'2011 poster .

Texturing an animated fluid is a useful way to augment the visual complexity of pictures without increasing the simulation time. But texturing flowing fluids is a complex issue, as it creates conflicting requirements: we want to keep the key texture properties (features, spectrum) while advecting the texture with the underlying flow — which distorts it. In this context we present a new, Lagrangian, method for advecting textures: the advected texture is computed only locally and follows the velocity field at each pixel (see Figure  ). The texture retains its local properties, including its Fourier spectrum, even though it is accurately advected. Due to its Lagrangian nature, our algorithm can perform on very large, potentially infinite scenes in real time. Our experiments show that it is well suited for a wide range of input textures, including, but not limited to, noise textures. This work has been published in the IEEE Transactions on Visualization and Computer Graphics (TVCG)  .

We have developed a method for simulating local water waves caused by obstacles in water streams for real-time graphics applications. Given a low-resolution water surface and velocity field, our method is able to decorate the input water surface with high resolution detail for the animated waves around obstacles. We construct and animate a vector representation of the waves. It is then converted to feature-aligned meshes for capturing the surfaces of the waves (see Figure  ). Results demonstrate that our method has the benefits of real-time performance and easy controllability. The method also fits well into a state-of-the-art river animation system. This work has been published in the Journal of Computer Animation and Virtual Worlds .

This work is the result of a collaboration with S. Hahmann from the EVASION team-project, Prof. Gershon Elber from Technion and Prof. Hans Hagen from the University of Kaiserslautern.

Free Form Deformation (FFD) is a well established technique for deforming arbitrary object shapes in space. Although more recent deformation techniques have been introduced, amongst them skeleton-based deformation and cage based deformation, the simple and versatile nature of FFD is a strong advantage, and justifies its presence in nowadays leading commercial geometric modeling and animation software systems. Since its introduction in the late 80's, many improvements have been proposed to the FFD paradigm, including control lattices of arbitrary topology, direct shape manipulation and GPU implementation. Several authors have addressed the problem of volume preserving FFD. These previous approaches either make use of expensive non-linear optimization techniques, or resort to first order approximation suitable only for small-scale deformations. In this work we take advantage from the multi-linear nature of the volume constraint in order to derive a simple, exact and explicit solution to the problem of volume preserving FFD (see Figure  ). Two variants of the algorithm are given, without and with direct shape manipulation. Moreover, the linearity of our solution enables to implement it efficiently on GPU. The results have been published in a Visual Computer journal paper .