Abstract Spectral rendering is essential for the production of physically‐plausible synthetic images, but requires to introduce several changes in the content generation pipeline. In particular, the authoring of spectral material properties (e.g., albedo maps, indices of refraction, transmittance coefficients) raises new problems. While a large panel of computer graphics methods exists to upsample a RGB color to a spectrum, they all provide a one‐to‐one mapping. This limits the ability to control interesting color changes such as the Usambara effect or metameric spectra. In this work, we introduce a one‐to‐many mapping in which we show how we can explore the set of all spectra reproducing a given input color. We apply this method to different colour changing effects such as vathochromism – the change of color with depth, and metamerism.

We present a purely geometric, time-independent deformer resolving local contacts between elastic objects, including self-collisions between adjacent parts of the same object that often occur in character skinning animation. Starting from multiple meshes in intersection, our deformer first computes the parts of the surfaces remaining in contact, and then applies a procedural displacement with volume preservation. Although our deformer processes each frame independently, it achieves temporally continuous deformations with artistic control of the bulge through few pseudo-stiffness parameters. The plausibility of the deformation is further enhanced by anisotropically spreading the volume-preserving bulge. The result is a robust, real-time deformer that can handle complex geometric configurations such as a ball squashed by a hand, colliding lips, bending fingers, etc.

In this paper, we introduce a novel and extremely fast algorithm to compute continuous transport maps between 2D probability densities discretized on uniform grids. The core of our method is a novel iterative solver computing the L 2 optimal transport map from a grid to the uniform density in the 2D Euclidean plane. A transport map between arbitrary densities is then recovered through numerical inversion and composition. In this case, the resulting map is only approximately optimal, but it is continuous and density preserving. Our solver is derivative-free, and it converges in a few cheap iterations. We demonstrate interactive performance in various applications such as adaptive sampling, feature sensitive remeshing, and caustic design.

Abstract The area of surface reconstruction has seen substantial progress in the past two decades. The traditional problem addressed by surface reconstruction is to recover the digital representation of a physical shape that has been scanned, where the scanned data contain a wide variety of defects. While much of the earlier work has been focused on reconstructing a piece‐wise smooth representation of the original shape, recent work has taken on more specialized priors to address significantly challenging data imperfections, where the reconstruction can take on different representations—not necessarily the explicit geometry. We survey the field of surface reconstruction, and provide a categorization with respect to priors, data imperfections and reconstruction output. By considering a holistic view of surface reconstruction, we show a detailed characterization of the field, highlight similarities between diverse reconstruction techniques and provide directions for future work in surface reconstruction.

Abstract Hardware tessellation is de facto the preferred mechanism to adaptively control mesh resolution with maximal performances. However, owing to its fixed and uniform pattern, leveraging tessellation for feature‐aware LOD rendering remains a challenging problem. We relax this fundamental constraint by introducing a new spatial and temporal blending mechanism of tessellation levels, which is built on top of a novel hierarchical representation of multi‐resolution meshes. This mechanism allows to finely control topological changes so that vertices can be removed or added at the most appropriate location to preserve geometric features in a continuous and artifact‐free manner. We then show how to extend edge‐collapse based decimation methods to build feature‐aware multi‐resolution meshes that match the tessellation patterns. Our approach is fully compatible with current hardware tessellators and only adds a small overhead on memory consumption and tessellation cost.

We introduce a Spatially-Varying BRDF model tailored to the multi-scale rendering of scratched materials such as metals, plastics or finished woods. Our approach takes advantage of the regular structure of scratch distributions to achieve high performance without compromising visual quality. We provide users with controls over the profile, micro-BRDF, density and orientation of scratches, while updating our material model at interactive rates. The BRDF for a single scratch is simulated using an optimized 2D ray-tracer and compactly stored in a three-component 2D texture. In contrast to existing models, our approach takes into account all interreflections inside a scratch, including Fresnel effects. At render time, the SV-BRDF for the scratch distribution under a pixel or ray footprint is obtained by linear combination of individual scratch BRDFs. We show how to evaluate it using both importance and light sampling, in direct and global illumination settings.

Abstract This paper presents a tool that enables the direct editing of surface features in large point‐clouds or meshes. This is made possible by a novel multi‐scale analysis of unstructured point‐clouds that automatically extracts the number of relevant features together with their respective scale all over the surface. Then, combining this ingredient with an adequate multi‐scale decomposition allows us to directly enhance or reduce each feature in an independent manner. Our feature extraction is based on the analysis of the scale‐variations of locally fitted surface primitives combined with unsupervised learning techniques. Our tool may be applied either globally or locally, and millions of points are handled in real‐time. The resulting system enables users to accurately edit complex geometries with minimal interaction.

Abstract This paper introduces a system for the direct editing of highlights produced by anisotropic BRDFs, which we call anisotropic highlights. We first provide a comprehensive analysis of the link between the direction of anisotropy and the shape of highlight curves for arbitrary object surfaces. The gained insights provide the required ingredients to infer BRDF orientations from a prescribed highlight tangent field. This amounts to a non‐linear optimization problem, which is solved at interactive framerates during manipulation. Taking inspiration from sculpting software, we provide tools that give the impression of manipulating highlight curves while actually modifying their tangents. Our solver produces desired highlight shapes for a host of lighting environments and anisotropic BRDFs.

We present a novel approach to interactive character skinning, which is robust to extreme character movements, handles skin contacts and produces the effect of skin elasticity (sliding). Our approach builds on the idea of implicit skinning in which the character is approximated by a 3D scalar field and mesh-vertices are appropriately re-projected. Instead of being bound by an initial skinning solution used to initialize the shape at each time step, we use the skin mesh to directly track iso-surfaces of the field over time. Technical problems are two-fold: firstly, all contact surfaces generated between skin parts should be captured as iso-surfaces of the implicit field; secondly, the tracking method should capture elastic skin effects when the joints bend, and as the character returns to its rest shape, so the skin must follow. Our solutions include: new composition operators enabling blending effects and local self-contact between implicit surfaces, as well as a tangential relaxation scheme derived from the as-rigid-as possible energy to solve the tracking problem.

Abstract We introduce a new approach for defining continuous non‐oriented gradient fields from discrete inputs, a fundamental stage for a variety of computer graphics applications such as surface or curve reconstruction, and image stylization. Our approach builds on a moving least square formalism that computes higher‐order local approximations of non‐oriented input gradients. In particular, we show that our novel isotropic linear approximation outperforms its lower‐order alternative: surface or image structures are much better preserved, and instabilities are significantly reduced. Thanks to its ease of implementation (on both CPU and GPU) and small performance overhead, we believe our approach will find a widespread use in graphics applications, as demonstrated by the variety of our results.

Geometric skinning techniques, such as smooth blending or dual-quaternions, 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 performances.

Abstract In this paper, we present an analysis technique that leverages the complexity found in detailed 3D models for illustrative shading purposes. Given a smooth base surface with relief, it locates relief features (concavities, convexities and inflections) around each surface point and at multiple scales, using cubic‐polynomial fitting. This object‐space, per‐vertex information is then used to guide a variety of shading techniques including normal enhancement, feature visualization, accessibility shading and radiance scaling. Thanks to this approach, features at multiple scales are easily combined, filtered and shaded, allowing users to explore surface relief in real‐time.

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.

The creation of free-form vector drawings has been greatly improved in recent years with techniques based on (bi)-harmonic interpolation. Such methods offer the best trade-off between sparsity (keeping the number of control points small) and expressivity (achieving complex shapes and gradients). In this paper, we introduce a vectorial solver for the computation of free-form vector gradients. Based on Finite Element Methods (FEM), its key feature is to output a low-level vector representation suitable for very fast GPU accelerated rasterization and close-form evaluation. This intermediate representation is hidden from the user: it is dynamically updated using FEM during drawing when control points are edited. Since it is output-insensitive, our approach enables novel possibilities for (bi)-harmonic vector drawings such as instancing, layering, deformation, texture and environment mapping. Finally, in this paper we also generalize and extend the set of drawing possibilities. In particular, we show how to locally control vector gradients.

Abstract In this paper we present a novel image based algorithm to render visually plausible anti‐aliased soft shadows in a robust and efficient manner. To achieve both high visual quality and high performance, it employs an accurate shadow map filtering method which guarantees smooth penumbrae and high quality anisotropic anti‐aliasing of the sharp transitions. Unlike approaches based on pre‐filtering approximations, our approach does not suffer from light bleeding or losing contact shadows. Discretization artefacts are avoided by creating virtual shadow maps on the fly according to a novel shadow map resolution prediction model. This model takes into account the screen space frequency of the penumbrae via a perceptual metric which has been directly established from an appropriate user study. Consequently, our algorithm always generates shadow maps with minimal resolutions enabling high performance while guarantying high quality. Thanks to this perceptual model, our algorithm can sometimes be faster at rendering soft shadows than hard shadows. It can render game‐like scenes at very high frame rates, and extremely large and complex scenes such as CAD models at interactive rates. In addition, our algorithm is highly scalable, and the quality versus performance trade‐off can be easily tweaked.

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.

Abstract Efficiently computing robust soft shadows is a challenging and time consuming task. On the one hand, the quality of image‐based shadows is inherently limited by the discrete property of their framework. On the other hand, object‐based algorithms do not exhibit such discretization issues but they can only efficiently deal with triangles having a constant transmittance factor. This paper addresses this limitation. We propose a general algorithm for the computation of robust and accurate soft shadows for triangles with a spatially varying transmittance. We then show how this technique can be efficiently included into object‐based soft shadow algorithms. This results in unified object‐based frameworks for computing robust direct shadows for both standard and perforated triangles in fully animated scenes.

Abstract Moving least squares (MLS) is a very attractive tool to design effective meshless surface representations. However, as long as approximations are performed in a least square sense, the resulting definitions remain sensitive to outliers, and smooth‐out small or sharp features. In this paper, we address these major issues, and present a novel point based surface definition combining the simplicity of implicit MLS surfaces [ SOS04 , Kol05 ] with the strength of robust statistics. To reach this new definition, we review MLS surfaces in terms of local kernel regression, opening the doors to a vast and well established literature from which we utilize robust kernel regression. Our novel representation can handle sparse sampling, generates a continuous surface better preserving fine details, and can naturally handle any kind of sharp features with controllable sharpness. Finally, it combines ease of implementation with performance competing with other non‐robust approaches.

Abstract Recent soft shadow mapping techniques based on back‐projection can render high quality soft shadows in real time. However, real time high quality rendering of large penumbrae is still challenging, especially when multilayer shadow maps are used to reduce single light sample silhouette artifact. In this paper, we present an efficient algorithm to attack this problem. We first present a GPU‐friendly packet‐based approach rendering a packet of neighboring pixels together to amortize the cost of computing visibility factors. Then, we propose a hierarchical technique to quickly locate the contour edges, further reducing the computation cost. At last, we suggest a multi‐view shadow map approach to reduce the single light sample artifact. We also demonstrate its higher image quality and higher efficiency compared to the existing depth peeling approaches.

Abstract Algebraic Point Set Surfaces (APSS) define a smooth surface from a set of points using local moving least‐squares (MLS) fitting of algebraic spheres. In this paper we first revisit the spherical fitting problem and provide a new, more generic solution that includes intuitive parameters for curvature control of the fitted spheres. As a second contribution we present a novel real‐time rendering system of such surfaces using a dynamic up‐sampling strategy combined with a conventional splatting algorithm for high quality rendering. Our approach also includes a new view dependent geometric error tailored to efficient and adaptive up‐sampling of the surface. One of the key features of our system is its high degree of flexibility that enables us to achieve high performance even for highly dynamic data or complex models by exploiting temporal coherence at the primitive level. We also address the issue of efficient spatial search data structures with respect to construction, access and GPU friendliness. Finally, we present an efficient parallel GPU implementation of the algorithms and search structures.

The method of Moving Least Squares (MLS) is a popular framework for reconstructing continuous functions from scattered data due to its rich mathematical properties and well-understood theoretical foundations. This paper applies MLS to volume rendering, providing a unified mathematical framework for ray casting of scalar data stored over regular as well as irregular grids. We use the MLS reconstruction to render smooth isosurfaces and to compute accurate derivatives for high-quality shading effects. We also present a novel, adaptive preintegration scheme to improve the efficiency of the ray casting algorithm by reducing the overall number of function evaluations, and an efficient implementation of our framework exploiting modern graphics hardware. The resulting system enables high-quality volume integration and shaded isosurface rendering for regular and irregular volume data.

Abstract The recent soft shadow mapping technique [ GBP06 ] allows the rendering in real‐time of convincing soft shadows on complex and dynamic scenes using a single shadow map. While attractive, this method suffers from shadow overestimation and becomes both expensive and approximate when dealing with large penumbrae. This paper proposes new solutions removing these limitations and hence providing an efficient and practical technique for soft shadow generation. First, we propose a new visibility computation procedure based on the detection of occluder contours, that is more accurate and faster while reducing aliasing. Secondly, we present a shadow map multi‐resolution strategy keeping the computation complexity almost independent on the light size while maintaining high‐quality rendering. Finally, we propose a view‐dependent adaptive strategy, that automatically reduces the screen resolution in the region of large penumbrae, thus allowing us to keep very high frame rates in any situation.

In this paper we present a new Point Set Surface (PSS) definition based on moving least squares (MLS) fitting of algebraic spheres. Our surface representation can be expressed by either a projection procedure or in implicit form. The central advantages of our approach compared to existing planar MLS include significantly improved stability of the projection under low sampling rates and in the presence of high curvature. The method can approximate or interpolate the input point set and naturally handles planar point clouds. In addition, our approach provides a reliable estimate of the mean curvature of the surface at no additional cost and allows for the robust handling of sharp features and boundaries. It processes a simple point set as input, but can also take significant advantage of surface normals to improve robustness, quality and performance. We also present an novel normal estimation procedure which exploits the properties of the spherical fit for both direction estimation and orientation propagation. Very efficient computational procedures enable us to compute the algebraic sphere fitting with up to 40 million points per second on latest generation GPUs.

Abstract In recent years it has been shown that, above a certain complexity, points become the most efficient rendering primitives. Although the programmability of the lastest graphics hardware allows efficient implementation of high quality surface splatting algorithms, their performance remains below those obtained with simpler point based rendering algorithms when they are used for scenes of high complexity. In this paper, our goal is to apply high quality point based rendering algorithms on complex scenes. For this purpose, we show how to take advantage of temporal coherency in a very accurate hardware accelerated point selection algorithm allowing the expensive computations to be peformed only on visible points. Our algorithm is based on a multi‐pass hardware accelerated EWA splatting. It is also suitable for any rendering application since no pre‐process is needed and no assumption is made on the data structure. In addition, we briefly discuss the association of our method with other existing culling techniques and optimization for particular applications. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Viewing algorithms