Abstract We present a novel approach to the multi‐scale analysis of point‐sampled manifolds of co‐dimension 1. It is based on a variant of Moving Least Squares, whereby the evolution of a geometric descriptor at increasing scales is used to locate pertinent locations in scale‐space, hence the name “Growing Least Squares”. Compared to existing scale‐space analysis methods, our approach is the first to provide acontinuoussolution in space and scale dimensions, without requiring any parametrization, connectivity or uniform sampling. An important implication is that we identifymultiple pertinentscales for any point on a manifold, a property that had not yet been demonstrated in the literature. In practice, our approach exhibits an improved robustness to change of input, and is easily implemented in a parallel fashion on the GPU. We compare our method to state‐of‐the‐art scale‐space analysis techniques and illustrate its practical relevance in a few application scenarios.

Over the last two decades, much effort has been devoted to accurately measuring Bidirectional Reflectance Distribution Functions (BRDFs) of real-world materials and to use efficiently the resulting data for rendering. Because of their large size, it is difficult to use directly measured BRDFs for real-time applications, and fitting the most sophisticated analytical BRDF models is still a complex task. In this paper, we introduce Rational BRDF, a general-purpose and efficient representation for arbitrary BRDFs, based on Rational Functions (RFs). Using an adapted parametrization, we demonstrate how Rational BRDFs offer 1) a more compact and efficient representation using low-degree RFs, 2) an accurate fitting of measured materials with guaranteed control of the residual error, and 3) efficient importance sampling by applying the same fitting process to determine the inverse of the Cumulative Distribution Function (CDF) generated from the BRDF for use in Monte-Carlo rendering.

The recent widespread of RGBD cameras such as Kinect® device from Microsoft® opens many new interaction metaphors available to the general public. In this poster we introduce a tabletop interaction metaphor using the depth map from the Kinect: each element on the table is included as a set of physical constraints in a virtual environment. We briefly discuss visualization methods and present a gaming genre adapted to this framework: action-construction games.

Abstract We introduce a new technique called Implicit Brushes to render animated 3D scenes with stylized lines in realtime with temporal coherence. An Implicit Brush is defined at a given pixel by the convolution of a brush footprint along a feature skeleton; the skeleton itself is obtained by locating surface features in the pixel neighborhood. Features are identified via image‐space fitting techniques that not only extract their location, but also their profile, which permits to distinguish between sharp and smooth features. Profile parameters are then mapped to stylistic parameters such as brush orientation, size or opacity to give rise to a wide range of line‐based styles.

Based on the observation that shading conveys shape information through intensity gradients, we present a new technique called Radiance Scaling that modifies the classical shading equations to offer versatile shape depiction functionalities. It works by scaling reflected light intensities depending on both surface curvature and material characteristics. As a result, diffuse shading or highlight variations become correlated with surface feature variations, enhancing concavities and convexities. The first advantage of such an approach is that it produces satisfying results with any kind of material for direct and global illumination: we demonstrate results obtained with Phong and Ashikmin-Shirley BRDFs, Cartoon shading, sub-Lambertian materials, perfectly reflective or refractive objects. Another advantage is that there is no restriction to the choice of lighting environment: it works with a single light, area lights, and interreflections. Third, it may be adapted to enhance surface shape through the use of precomputed radiance data such as Ambient Occlusion, Prefiltered Environment Maps or Lit Spheres. Finally, our approach works in real time on modern graphics hardware making it suitable for any interactive 3D visualization.

We present a novel technique called Radiance Scaling for the depiction of surface shape through shading. It adjusts reflected light intensities in a way dependent on both surface curvature and material characteristics. As a result, diffuse shading or highlight variations become correlated to surface feature variations, enhancing surface concavities and convexities. This approach is more versatile compared to previous methods. First, it produces satisfying results with any kind of material: we demonstrate results obtained with Phong and Ashikmin BRDFs, Cartoon shading, sub-Lambertian materials, and perfectly reflective or refractive objects. Second, it imposes no restriction on lighting environment: it does not require a dense sampling of lighting directions and works even with a single light. Third, it makes it possible to enhance surface shape through the use of precomputed radiance data such as Ambient Occlusion, Prefiltered Environment Maps or Lit Spheres. Our novel approach works in real-time on modern graphics hardware.

Abstract The usual approach to design subdivision schemes for curves and surfaces basically consists in combining proper rules for regular configurations, with some specific heuristics to handle extraordinary vertices. In this paper, we introduce an alternative approach, called Least Squares Subdivision Surfaces (LS), where the key idea is to iteratively project each vertex onto a local approximation of the current polygonal mesh. While the resulting procedure haves the same complexity as simpler subdivision schemes, our method offers much higher visual quality, especially in the vicinity of extraordinary vertices. Moreover, we show it can be easily generalized to support boundaries and creases. The fitting procedure allows for a local control of the surface from the normals, making LS3very well suited for interactive freeform modeling applications. We demonstrate our approach on diadic triangular and quadrangular refinement schemes, though it can be applied to any splitting strategies.

Recent research on the human visual system shows that our perception of object shape relies in part on compression and stretching of the reflected lighting environment onto its surface. We use this property to enhance the shape depiction of 3D objects by locally warping the environment lighting around main surface features. Contrary to previous work, which require specific illumination, material characteristics and/or stylization choices, our approach enhances surface shape without impairing the desired appearance. Thanks to our novel local shape descriptor, salient surface features are explicitly extracted in a view-dependent fashion at various scales without the need of any pre-process. We demonstrate our system on a variety of rendering settings, using object materials ranging from diffuse to glossy, to mirror or refractive, with direct or global illumination, and providing styles that range from photorealistic to non-photorealistic. The warping itself is very fast to compute on modern graphics hardware, enabling real-time performance in direct illumination scenarios. Note: Third-Party Material Attribution Third-party material used in ACM Transactions on Graphics 28(3), Article 25 - "Light Warping for Enhanced Surface Depiction," by Vergne, Pacanowski, Barla, Granier, and Schlick - was used without proper attribution. The 3D model used in Figures 1, 3, and 5, as well as in the cover image of this volume of the journal, was downloaded from the Shape Repository of AIM@SHAPE Project (http://shapes.aimatshape.net) and is the property of CNR-IMATI. We regret this oversight.

Abstract We present a flexible GPU kernel for adaptive on‐the‐fly refinement of meshes with arbitrary topology. By simply reserving a small amount of GPU memory to store a set of adaptive refinement patterns, on‐the‐fly refinement is performed by the GPU, without any preprocessing nor additional topology data structure. The level of adaptive refinement can be controlled by specifying a per‐vertex depth‐tag, in addition to usual position, normal, color and texture coordinates. This depth‐tag is used by the kernel to instanciate the correct refinement pattern, which will map a refined connectivity on the input coarse polygon. Finally, the refined patch produced for each triangle can be displaced by the vertex shader, using any kind of geometric refinement, such as Bezier patch smoothing, scalar valued displacement, procedural geometry synthesis or subdivision surfaces. This refinement engine does neither require multipass rendering nor any use of fragment processing nor special preprocess of the input mesh structure. It can be implemented on any GPU with vertex shading capabilities.

We introduce QAS, an efficient quadratic approximation of subdivision surfaces which offers a very close appearance compared to the true subdivision surface but avoids recursion, providing at least one order of magnitude faster rendering. QAS uses enriched polygons, equipped with edge vertices, and replaces them on-the-fly with low degree polynomials for interpolating positions and normals. By systematically projecting the vertices of the input coarse mesh at their limit position on the subdivision surface, the visual quality of the approximation is good enough for imposing only a single subdivision step, followed by our patch fitting, which allows real-time performances for million polygons output. Additionally, the parametric nature of the approximation offers an efficient adaptive sampling for rendering and displacement mapping. Last, the hexagonal support associated to each coarse triangle is adapted to geometry processors.

Particle systems, as originally proposed by Witkin and Heckbert, are a powerful way to sample implicit surfaces since they generate almost evenly distributed samples over the surface, thanks to a global minimization of an energy criterion. Nonetheless, due to the computational cost of the relaxation process, the sampling process becomes rather expensive when the number of samples exceeds a few thousands. In this paper, we propose a technique that only relies on a pure geometry processing which enables us to rapidly generate the set of final particles (e.g., half a second to generate 5,000 particles for an analytic implicit surface) with near-optimal positions. Because of its characteristics, the technique does not need the usual split-and-death criterion any more and only about ten relaxation steps are necessary to get a high quality sampling. Either uniform or non-uniform sampling can be performed with our technique

Abstract Many algorithms in computer graphics improve their efficiency by using Hierarchical Space Subdivision Schemes (HS3), such as octrees, kD‐trees or BSP trees. Such HS3 usually provide an axis‐aligned subdivision of the 3D space embedding a scene or an object. However, the purely volume‐based behavior of these schemes often leads to strongly imbalanced surface clustering. In this article, we introduce the VS‐Tree, an alternative HS3 providing efficient and accurate surface‐based hierarchical clustering via a combination of a global 3D decomposition at coarse subdivision levels, and a local 2D decomposition at fine levels near the surface. First, we show how to efficiently construct VS‐Trees over meshes and point‐based surfaces, and analyze the improvement it offers for cluster‐based surface simplification methods. Then we propose a new surface reconstruction algorithm based on the volume‐surface classification of the VS‐Tree. This new algorithm is faster than state‐of‐the‐art reconstruction methods and provides a final semi‐regular mesh comparable to the output of remeshing algorithms.

Point-based surfaces (i.e. surfaces represented by discrete point sets which are either directly obtained by current 3D acquisition devices or converted from other surface representations) are well designed for multiresolution storage and transmission of complex objects. Unfortunately, visualization of point-based surfaces requires to develop specific rendering techniques (e.g. splatting) as point sets are not well adapted to existing graphics hardware which are optimized for polygonal meshes. In this paper, we propose an efficient reconstruction and visualization technique of point-based surfaces that takes full benefit from the whole optimized pipeline implemented in graphics hardware. The basic idea is to generate a set of independent meshes using a local 2D Delaunay triangulation of the point set. These meshes are then glued together to get a " visual continuity" by using a subdivision process.

This paper presents some experimental results on the comparison of users performance for different kinds of 3D interaction tasks (travel, manipulation), when using either a standard desktop display or a large immersive display. The main results of our experimentation are the following: first, not all users benefit similarly from the use of large displays, and second, the gains of performance strongly depend on the nature of the interaction task. To explain these results, we borrow some tools from cognitive science in order to identify one cognitive factor (visual attention) that is involved in the difference of performance that can be observed.

We present a new method for the multi-scale reconstruction of implicit surfaces with attributes from large unorganized point sets. The implicit surface is reconstructed by subdividing the global domain into overlapping local subdomains using a perfectly balanced binary tree, reconstructing the surface parts in the local subdomains from non-disjunct subsets of the points by variational techniques using radial basis functions, and hierarchically blending together the surface parts of the local subdomains by using a family of functions called partition of unity. The subsets of the points in the inner nodes of the tree for intermediate resolutions are obtained by thinning algorithms. The reconstruction is particularly robust since the number of data points in the partition of unity blending zones can be specified explicitly. Furthermore, the new reconstruction method is valid for discrete datasets in any dimension, so we can use it also to reconstruct continuous functions for the surface's attributes. In a short discussion, we evaluate the advantages and drawbacks of our reconstruction method compared to existing reconstruction methods for implicit surfaces.

Abstract The concept of solid texturing is extended in two directions: constructive modeling of space partitions for texturing and modeling of multidimensional textured objects called hypervolumes. A hypervolume is considered as a point set with attributes of both physical (density, temperature, etc.) and photometric (color, transparency, diffuse and specular reflections, etc.) nature. The point set geometry and attributes are modeled independently using real‐valued scalar functions of several variables. Each real‐valued function defining geometry or an attribute is evaluated at the given point by a procedure traversing a constructive tree structure with primitives in the leaves and operations in the nodes of the tree. This approach provides a framework for modeling, texturing and visualization of 3D solids, time‐dependent and multidimensional objects in a completely uniform manner. We introduced a special modeling language and implemented software tools supporting the proposed approach. The concept of constructive hypervolume textures is independent of the geometry representation. We provide examples of textured Frep and BRep objects as illustrations. Copyright © 2002 John Wiley & Sons, Ltd.

This paper proposes to study a spline model, called HB‐splines, that is in fact a B‐spline representation of Hermite splines, combined with some restriction on the differential values at segment boundaries. Although this model does not appear able to offer something new to the computer graphics community, we think that HB‐splines deserve to be considered for themselves because they embed many interesting features. First, they include all the classical properties required in a geometric modeling environment (convex hull, local control, arbitrary orders of parametric or geometric continuity). Second, they have a nice aptitude for direct manipulation (i.e. manipulation without using control points). For this purpose, we propose a new graphic widget, called control sails, that offers the user an intuitive way to specify local properties (position, tangent, curvature) of a curve or a surface. Finally, they provide an elegant formulation of a biorthogonal wavelet family, that permits multiresolution manipulations of the resulting curves or surfaces, in a very efficient way.

this paper, all these models will be grouped under the generic name: iso-surfaces. In the iso-surface model, an object is defined by a set of primitives that can be considered as potential fields. The boundary surface of the object is then represented by the set of points for which the sum of the potential values equates a given isovalue. Two competitive approaches can be taken to create complex shapes with the iso-surface model. Either the object may be described by a very large number of simple primitives (e.g. spheres or ellipsoids) or by a small number of complex ones (e.g. distance or convolution surfaces). The first approach is well adapted to the automatic matching of 3D experimental data [11] while the second one is merely used in a design process which allows the user to define interactively each primitive

This paper presents a new model of spline curves and surfaces. The main characteristic of this model is that it has been created from scratch by using a kind of mathematical engineering process. In a first step, a list of specifications was established. This list groups all the properties that a spline model should contain in order to appear intuitive to a non-mathematician end-user. In a second step, a new family of blending functions was derived, trying to fulfill as many items as possible of the previous list. Finally, the degrees of freedom offered by the model have been reduced to provide only shape parameters that have a visual interpretation on the screen. The resulting model includes many classical properties such as affine and perspective invariance, convex hull, variation diminution, local controlandC2=G2 orC2=G0 continuity. But it also includesoriginal features such as a continuum between B-splines and Catmull-Rom splines, or the ability to define approximation zones and interpolation zones in the same curve or surface.

Abstract Since the beginning of computer graphics, three decades ago, a large number of models intended to describe the behaviour of light on a given point of a surface have been proposed. Almost every author uses his own terminology and/or notation. To understand clearly the similarities and the differences between existing models, reformulating them with a unified notation is essential. This has been done by Hall in 1986. This paper is a new survey of shading and reflectance models, including the most recent models. Moreover, after the lengthy enumeration, some original models are proposed, which attempt to include interesting features of previous disjointed work into new formulations.

Abstract: A new BRDF model is presented which can be viewed as an kind of intermediary model between empirism and theory. Main results of physics are observed (energy conservation, reciprocity rule, microfacet theory) and numerous phenomena involved in light reflection are accounted for, in a physically plausible way (incoherent and coherent reflection, spectrum modifications, anisotropy, self‐shadowing, multiple surface and subsurface reflection, differences between homogeneous and heterogeneous materials). The model has been especially intended for computer graphics applications and therefore includes two main features: simplicity (a small number of intuitively understandable parameters controls the model) and efficiency (the formulation provides adequation to Monte‐Carlo rendering techniques and/or hardware implementations).

Abstract: We present a new algorithm for simulating the effect of light travelling through volume objects. Such objects (haze, fog, clouds…) are usually modelized by voxel grids which define their density distribution in a discrete tridimensional space. The method we propose is a two‐pass Monte‐Carlo ray‐tracing algorithm that does not make any restrictive assumptions neither about the characteristics of the objects (both arbitrary density distributions and phase functions are allowed) nor about the physical phenomena included in the rendering process (multiple scattering is accounted for). The driving idea of the algorithm is to use the phase function for Monte‐Carlo sampling, in order to modify the direction of the ray during scattering.