Abstract The prevailing model in virtual 3D scenes is a 3D surface, which a texture is mapped onto, through a parameterization from the texture plane. We focus on accounting for the parameterization during the texture creation process, to control the deformations and remove the cuts induced by the mapping. We rely on the tiling and blending, a real‐time and parallel algorithm that generates an arbitrary large texture from a small input example. Our first contribution is to enhance the tiling and blending with a deformation field, which controls smooth spatial variations in the texture plane. Our second contribution is to derive, from a parameterized triangle mesh, a deformation field to compensate for texture distortions and to control for the texture orientation. Our third contribution is a technique to enforce texture continuity across the cuts, thanks to a proper tile selection. This opens the door to interactive sessions with artistic control, and real‐time rendering with improved visual quality.

While precise spectral control can be achieved through sparse convolution, corresponding state of the art noise models are typically too expensive for solid noise. We introduce an alternative, wave-based procedural noise model, fast enough to be used in any dimension. We express the noise in the spectral domain and then apply an inverse Fourier transform (FT), requiring the computation of a multidimensional integral. Our contribution is a novel, efficient way to perform this computation, using a sum of precomputed complex-valued hyperplanar wave-functions, oriented in random directions. We show that using suitable wave profiles and combination operators, our model is able to extend to 3D a number of Gaussian and non-Gaussian noises, including Gabor, by-example and Phasor noises, as well as generate novel cellular noises. Our versatile and controllable solid noise model is very compact, a key feature for complex power spectrum and animated noises. We illustrate this through the design of 2D, 3D, and 3D+t materials using color, transparency and style transfer functions.

Abstract Mixing textures is a basic and ubiquitous operation in data‐driven algorithms for real‐time texture generation and rendering. It is usually performed either by linear blending, or by cutting. We propose a new mixing operator which encompasses and extends both, creating more complex transitions that adapt to the texture's contents. Our mixing operator takes as input two or more textures along with two or more priority maps, which encode how the texture patterns should interact. The resulting mixed texture is defined pixel‐wise by selecting the maximum of both priorities. We show that it integrates smoothly into two widespread applications: transition between two different textures, and texture synthesis that mixes pieces of the same texture. We provide constant‐time and parallel evaluation of the resulting mix over square footprints of MIP‐maps, making our operator suitable for real‐time rendering. We also develop a micro‐priority model, inspired by micro‐geometry models in rendering, which represents sub‐pixel priorities by a statistical distribution, and which allows for tuning between sharp cuts and smooth blend.

Abstract Assisting the authoring of virtual terrains is a perennial challenge in the creation of convincing synthetic landscapes. Particularly, there is a need for augmenting artist‐controlled low‐resolution models with consistent relief details. We present a structured noise that procedurally enhances terrains in real time by adding spatially varying erosion patterns. The patterns can be cascaded, i.e. narrow ones are nested into large ones. Our model builds upon the Phasor noise, which we adapt to the specific characteristics of terrains (water flow, slope orientation). Relief details correspond to the underlying terrain characteristics and align with the slope to preserve the coherence of generated landforms. Moreover, our model allows for artist control, providing a palette of control maps, and can be efficiently implemented in graphics hardware, thus allowing for real‐time synthesis and rendering, therefore permitting effective and intuitive authoring.

Abstract By‐example aperiodic tilings are popular texture synthesis techniques that allow a fast, on‐the‐fly generation of unbounded and non‐periodic textures with an appearance matching an arbitrary input sample called the “exemplar”. But by relying on uniform random sampling, these algorithms fail to preserve the autocovariance function, resulting in correlations that do not match the ones in the exemplar. The output can then be perceived as excessively random. In this work, we present a new method which can well preserve the autocovariance function of the exemplar. It consists in fetching contents with an importance sampler taking the explicit autocovariance function as the probability density function (pdf) of the sampler. Our method can be controlled for increasing or decreasing the randomness aspect of the texture. Besides significantly improving synthesis quality for classes of textures characterized by pronounced autocovariance functions, we moreover propose a real‐time tiling and blending scheme that permits the generation of high‐quality textures faster than former algorithms with minimal downsides by reducing the number of texture fetches.

Abstract Stochastic micro‐patterns successfully enhance the realism of virtual scenes. Procedural models using noise combined with transfer functions are extremely efficient. However, most patterns produced today employ 1D transfer functions, which assign color, transparency, or other material attributes, based solely on the single scalar quantity of noise. Multi‐dimensional transfer functions have received widespread attention in other fields, such as scientific volume rendering. But their potential has not yet been well explored for modeling micro‐patterns in the field of procedural texturing. We propose a new procedural model for stochastic patterns, defined as the composition of a bi‐dimensional transfer function (a.k.a. color‐map) with a stochastic vector field. Our model is versatile, as it encompasses several existing procedural noises, including Gaussian noise and phasor noise. It also generates a much larger gamut of patterns, including locally structured patterns which are notoriously difficult to reproduce. We leverage the Gaussian assumption and a tiling and blending algorithm to provide real‐time generation and filtering. A key contribution is a real‐time approximation of the second order statistics over an arbitrary pixel footprint, which enables, in addition, the filtering of procedural normal maps. We exhibit a wide variety of results, including Gaussian patterns, profiled waves, concentric and non‐concentric patterns.

Abstract Digital terrains are a foundational element in the computer‐generated depiction of natural scenes. Given the variety and complexity of real‐world landforms, there is a need for authoring solutions that achieve perceptually realistic outcomes without sacrificing artistic control. In this paper, we propose setting aside the elevation domain in favour of modelling in the gradient domain. Such a slope‐based representation is height independent and allows a seamless blending of disparate landforms from procedural, simulation, and real‐world sources. For output, an elevation model can always be recovered using Poisson reconstruction, which can include Dirichlet conditions to constrain the elevation of points and curves. In terms of authoring our approach has numerous benefits. It provides artists with a complete toolbox, including: cut‐and‐paste operations that support warping as needed to fit the destination terrain, brushes to modify region characteristics, and sketching to provide point and curve constraints on both elevation and gradient. It is also a unifying representation that enables the inclusion of tools from the spectrum of existing procedural and simulation methods, such as painting localised high‐frequency noise or hydraulic erosion, without breaking the formalism. Finally, our constrained reconstruction is GPU optimized and executes in real‐time, which promotes productive cycles of iterative authoring.

Abstract Stationary Gaussian processes have been used for decades in the context of procedural noises to model and synthesize textures with no spatial organization. In this paper we investigate cyclostationary Gaussian processes, whose statistics are repeated periodically. It enables the modeling of noises having periodic spatial variations, which we call “cyclostationary Gaussian noises”. We adapt to the cyclostationary context several stationary noises along with their synthesis algorithms: spot noise, Gabor noise, local random‐phase noise, high‐performance noise, and phasor noise. We exhibit real‐time synthesis of a variety of visual patterns having periodic spatial variations.

Abstract Physically based rendering of glittering surfaces is a challenging problem in computer graphics. Several methods have proposed off‐line solutions, but none is dedicated to high‐performance graphics. In this work, we propose a novel physically based BRDF for real‐time rendering of glints. Our model can reproduce the appearance of sparkling materials (rocks, rough plastics, glitter fabrics, etc.). Compared to the previous real‐time method [ZK16], which is not physically based, our BRDF uses normalized NDFs and converges to the standard microfacet BRDF [CT82] for a large number of microfacets. Our method procedurally computes NDFs with hundreds of sharp lobes. It relies on a dictionary of 1D marginal distributions: at each location two of them are randomly picked and multiplied (to obtain a NDF), rotated (to increase the variety), and scaled (to control standard deviation/roughness). The dictionary is multiscale, does not depend on roughness, and has a low memory footprint (less than 1 MiB).

Abstract We propose a bi‐layer representation for textures which is suitable for on‐the‐fly synthesis of unbounded textures from an input exemplar. The goal is to improve the variety of outputs while preserving plausible small‐scale details. The insight is that many natural textures can be decomposed into a series of fine scale Gaussian patterns which have to be faithfully reproduced, and some non‐homogeneous, larger scale structure which can be deformed to add variety. Our key contribution is a novel, bi‐layer representation for such textures. It includes a model for spatially‐varying Gaussian noise, together with a mechanism enabling synchronization with a structure layer. We propose an automatic method to instantiate our bi‐layer model from an input exemplar. At the synthesis stage, the two layers are generated independently, synchronized and added, preserving the consistency of details even when the structure layer has been deformed to increase variety. We show on a variety of complex, real textures, that our method reduces repetition artifacts while preserving a coherent appearance.

Geometric modifications of three-dimensional (3D) digital models are commonplace for the purpose of efficient rendering or compact storage. Modifications imply visual distortions that are hard to measure numerically. They depend not only on the model itself but also on how the model is visualized. We hypothesize that the model’s light environment and the way it reflects incoming light strongly influences perceived quality. Hence, we conduct a perceptual study demonstrating that the same modifications can be masked, or conversely highlighted, by different light-matter interactions. Additionally, we propose a new metric that predicts the perceived distortion of 3D modifications for a known interaction. It operates in the space of 3D meshes with the object’s appearance, that is, the light emitted by its surface in any direction given a known incoming light. Despite its simplicity, this metric outperforms 3D mesh metrics and competes with sophisticated perceptual image-based metrics in terms of correlation to subjective measurements. Unlike image-based methods, it has the advantage of being computable prior to the costly rendering steps of image projection and rasterization of the scene for given camera parameters.

Texture synthesis is a well-established area, with many important applications in computer graphics and vision. However, despite their success, synthesis techniques are not used widely in practice because the creation of good exemplars remains challenging and extremely tedious. In this paper, we introduce an unsupervised method for analyzing texture content across multiple scales that automatically extracts good exemplars from natural images. Unlike existing methods, which require extensive manual tuning, our method is fully automatic. This allows the user to focus on using texture palettes derived from their own images, rather than on manual interactions dictated by the needs of an underlying algorithm. Most natural textures exhibit patterns at multiple scales that may vary according to the location (non-stationarity). To handle such textures many synthesis algorithms rely on an analysis of the input and a guidance of the synthesis. Our new analysis is based on a labeling of texture patterns that is both (i) multi-scale and (ii) unsupervised -- that is, patterns are labeled at multiple scales, and the scales and the number of labeled clusters are selected automatically. Our method works in two stages. The first builds a hierarchical extension of superpixels and the second labels the superpixels based on random walk in a graph of similarity between superpixels and a nonnegative matrix factorization. Our label-maps provide descriptors for pixels and regions that benefit state-of-the-art texture synthesis algorithms. We show several applications including guidance of non-stationary synthesis, content selection and texture painting. Our method is designed to treat large inputs and can scale to many megapixels. In addition to traditional exemplar inputs, our method can also handle natural images containing different textured regions.

Abstract Semi‐regular triangle remeshing algorithms convert irregular surface meshes into semi‐regular ones. Especially in the field of computer graphics, semi‐regularity is an interesting property because it makes meshes highly suitable for multi‐resolution analysis. In this paper, we survey the numerous remeshing algorithms that have been developed over the past two decades. We propose different classifications to give new and comprehensible insights into both existing methods and issues. We describe how considerable obstacles have already been overcome, and discuss promising perspectives.

Local random-phase noise is a noise model for procedural texturing. It is defined on a regular spatial grid by local noises, which are sums of cosines with random phase. Our model is versatile thanks to separate sampling in the spatial and spectral domains. Therefore, it encompasses Gabor noise and noise by Fourier series. A stratified spectral sampling allows for a faithful yet compact and efficient reproduction of an arbitrary power spectrum. Noise by example is therefore obtained faster than state-of-the-art techniques. As a second contribution we address texture by example and generate not only Gaussian patterns but also structured features present in the input. This is achieved by fixing the phase on some part of the spectrum. Generated textures are continuous and non-repetitive. Results show unprecedented framerates and a flexible visual result: users can control with one parameter the blending between noise by example and structured texture synthesis.

Abstract Two‐dimensional (2D) parametric colour functions are widely used in Image‐Based Rendering and Image Relighting. They make it possible to express the colour of a point depending on a continuous directional parameter: the viewing or the incident light direction. Producing such functions from acquired data is promising but difficult. Indeed, an intensive acquisition process resulting in dense and uniform sampling is not always possible. Conversely, a simpler acquisition process results in sparse, scattered and noisy data on which parametric functions can hardly be fitted without introducing artefacts. Within this context, we present two contributions. The first one is a robust least‐squares‐based method for fitting 2D parametric colour functions on sparse and scattered data. Our method works for any amount and distribution of acquired data, as well as for any function expressed as a linear combination of basis functions. We tested our fitting for both image‐based rendering (surface light fields) and image relighting using polynomials and spherical harmonics. The second one is a statistical analysis to measure the robustness of any fitting method. This measure assesses a trade‐off between precision of the fitting and stability with respect to input sampling conditions. This analysis along with visual results confirm that our fitting method is robust and reduces reconstruction artefacts for poorly sampled data while preserving the precision for a dense and uniform sampling.

In computer graphics, rendering visually detailed scenes is often achieved through texturing. We propose a method for on-the-fly non-periodic infinite texturing of surfaces based on a single image. Pattern repetition is avoided by defining patches within each texture whose content can be changed at runtime. In addition, we consistently manage multi-scale using one input image per represented scale. Undersampling artifacts are avoided by accounting for fine-scale features while colors are transferred between scales. Eventually, we allow for relief-enhanced rendering and provide a tool for intuitive creation of height maps. This is done using an ad-hoc local descriptor that measures feature self-similarity in order to propagate height values provided by the user for a few selected texels only. Thanks to the patch-based system, manipulated data are compact and our texturing approach is easy to implement on GPU. The multi-scale extension is capable of rendering finely detailed textures in real-time.

Abstract Geometric constraints have proved to be efficient for enhancing the realism of shape animation. The present paper addresses the computation and the preservation of the volume enclosed by multiresolution meshes. A wavelet based representation allows the mesh to be handled at any level of resolution. The key contribution is the calculation of the volume as a trilinear form with respect to the multiresolution coefficients. Efficiency is reached thanks to the pre‐processing of a sparse 3D data structure involving the transposition of the filters while represented as a lifting scheme. A versatile and interactive method for preserving the volume during a deformation process is then proposed. It is based on a quadratic minimization subject to a linearization of the volume constraint. A closed form of the solution is derived.

We present a method for deforming piecewise linear 3D curves with constant length constraint. We show how this constraint can be integrated into a multiresolution editing tool allowing an intuitive control of the deformation’s extent and aspect. The constraint is enforced following two steps. A first step consists in approximating the initial length by modifying the multiresolution decomposition at some specified scale. In a second step the constraint is exactly enforced by constrained minimization of a smoothness criterion. This process then provides the core of an integrated wrinkling tool for soft tissues modelling. A curve on the mesh is deformed, providing a deformation profile which is propagated in a user-defined neighbourhood on the surface.