A Physically‐based Appearance Model for Special Effect Pigments

An appearance model for materials adhered with massive collections of special effect pigments has to take both high‐frequency spatial details (e.g., glints) and wave‐optical effects (e.g., iridescence) due to thin‐film interference into account. However, either phenomenon is challenging to characterize and simulate in a physically accurate way. Capturing these fascinating effects in a unified framework is even harder as the normal distribution function and the reflectance term are highly correlated and cannot be treated separately. In this paper, we propose a multi‐scale BRDF model for reproducing the main visual effects generated by the discrete assembly of special effect pigments, enabling a smooth transition from fine‐scale surface details to large‐scale iridescent patterns. We demonstrate that the wavelength‐dependent reflectance inside the pixel's footprint follows a Gaussian distribution according to the central limit theorem, and is closely related to the distribution of the thin‐film's thickness. We efficiently determine the mean and the variance of this Gaussian distribution for each pixel whose closed‐form expressions can be derived by assuming that the thin‐film's thickness is uniformly distributed. To validate its effectiveness, the proposed model is compared against some previous methods and photographs of actual materials. Furthermore, since our method does not require any scene‐dependent precomputation, the distribution of thickness is allowed to be spatially‐varying.     

A Stationary SVBRDF Material Modeling Method Based on Discrete Microsurface

Microfacet theory is commonly used to build reflectance models for surfaces. While traditional microfacet‐based models assume that the distribution of a surface's microstructure is continuous, recent studies indicate that some surfaces with tiny, discrete and stochastic facets exhibit glittering visual effects, while some surfaces with structured features exhibit anisotropic specular reflection. Accordingly, this paper proposes an efficient and stationary method of surface material modeling to process both glittery and non‐glittery surfaces in a consistent way. Our method comprises two steps: in the preprocessing step, we take a fixed‐size sample normal map as input, then organize 4D microfacet trees in position and normal space for arbitrary‐sized surfaces; we also cluster microfacets into 4D K‐lobes via the adaptive k‐means method. In the rendering step, moreover, surface normals can be efficiently evaluated using pre‐clustered microfacets. Our method is able to efficiently render any structured, discrete and continuous micro‐surfaces using a precisely reconstructed surface NDF. Our method is both faster and uses less memory compared to the state‐of‐the‐art glittery surface modeling works.     

On‐the‐Fly Power‐Aware Rendering

Power saving is a prevailing concern in desktop computers and, especially, in battery‐powered devices such as mobile phones. This is generating a growing demand for power‐aware graphics applications that can extend battery life, while preserving good quality. In this paper, we address this issue by presenting a real‐time power‐efficient rendering framework, able to dynamically select the rendering configuration with the best quality within a given power budget. Different from the current state of the art, our method does not require precomputation of the whole camera‐view space, nor Pareto curves to explore the vast power‐error space; as such, it can also handle dynamic scenes. Our algorithm is based on two key components: our novel power prediction model, and our runtime quality error estimation mechanism. These components allow us to search for the optimal rendering configuration at runtime, being transparent to the user. We demonstrate the performance of our framework on two different platforms: a desktop computer, and a mobile device. In both cases, we produce results close to the maximum quality, while achieving significant power savings.     

Fiber‐Level On‐the‐Fly Procedural Textiles

Procedural textile models are compact, easy to edit, and can achieve state‐of‐the‐art realism with fiber‐level details. However, these complex models generally need to be fully instantiated (aka. realized ) into 3D volumes or fiber meshes and stored in memory, We introduce a novel realization‐minimizing technique that enables physically based rendering of procedural textiles, without the need of full model realizations. The key ingredients of our technique are new data structures and search algorithms that look up regular and flyaway fibers on the fly, efficiently and consistently. Our technique works with compact fiber‐level procedural yarn models in their exact form with no approximation imposed. In practice, our method can render very large models that are practically unrenderable using existing methods, while using considerably less memory (60–200× less) and achieving good performance.     

A Low‐Dimensional Function Space for Efficient Spectral Upsampling

We present a versatile technique to convert textures with tristimulus colors into the spectral domain, allowing such content to be used in modern rendering systems. Our method is based on the observation that suitable reflectance spectra can be represented using a low‐dimensional parametric model that is intrinsically smooth and energy‐conserving, which leads to significant simplifications compared to prior work. The resulting spectral textures are compact and efficient: storage requirements are identical to standard RGB textures, and as few as six floating point instructions are required to evaluate them at any wavelength. Our model is the first spectral upsampling method to achieve zero error on the full sRGB gamut. The technique also supports large‐gamut color spaces, and can be vectorized effectively for use in rendering systems that handle many wavelengths at once.     

Attribute‐preserving gamut mapping of measured BRDFs

Reproducing the appearance of real‐world materials using current printing technology is problematic. The reduced number of inks available define the printer's limited gamut, creating distortions in the printed appearance that are hard to control. Gamut mapping refers to the process of bringing an out‐of‐gamut material appearance into the printer's gamut, while minimizing such distortions as much as possible. We present a novel two‐step gamut mapping algorithm that allows users to specify which perceptual attribute of the original material they want to preserve (such as brightness, or roughness). In the first step, we work in the low‐dimensional intuitive appearance space recently proposed by Serrano et al. [ SGM*16 ], and adjust achromatic reflectance via an objective function that strives to preserve certain attributes. From such intermediate representation, we then perform an image‐based optimization including color information, to bring the BRDF into gamut. We show, both objectively and through a user study, how our method yields superior results compared to the state of the art, with the additional advantage that the user can specify which visual attributes need to be preserved. Moreover, we show how this approach can also be used for attribute‐preserving material editing.     

Glint Rendering based on a Multiple‐Scattering Patch BRDF

Rendering materials such as metallic paints, scratched metals and rough plastics requires glint integrators that can capture all micro‐specular highlights falling into a pixel footprint, faithfully replicating surface appearance. Specular normal maps can be used to represent a wide range of arbitrary micro‐structures. The use of normal maps comes with important drawbacks though: the appearance is dark overall due to back‐facing normals and importance sampling is suboptimal, especially when the micro‐surface is very rough. We propose a new glint integrator relying on a multiple‐scattering patch‐based BRDF addressing these issues. To do so, our method uses a modified version of microfacet‐based normal mapping [SHHD17] designed for glint rendering, leveraging symmetric microfacets. To model multiple‐scattering, we re‐introduce the lost energy caused by a perfectly specular, single‐scattering formulation instead of using expensive random walks. This reflectance model is the basis of our patch‐based BRDF, enabling robust sampling and artifact‐free rendering with a natural appearance. Additional calculation costs amount to about 40% in the worst cases compared to previous methods [YHMR16, CCM18].     

Generating Stochastic Wall Patterns On‐the‐fly with Wang Tiles

The game and movie industries always face the challenge of reproducing materials. This problem is tackled by combining illumination models and various textures (painted or procedural patterns). Generating stochastic wall patterns is crucial in the creation of a wide range of backgrounds (castles, temples, ruins…). A specific Wang tile set was introduced previously to tackle this problem, in an iterative fashion. However, long lines may appear as visual artifacts. We use this tile set in a new on‐the‐fly procedure to generate stochastic wall patterns. For this purpose, we introduce specific hash functions implementing a constrained Wang tiling. This technique makes possible the generation of boundless textures while giving control over the maximum line length. The algorithm is simple and easy to implement, and the wall structure we get from the tiles allows to achieve visuals that reproduce all the small details of artist painted walls.     

Real‐time Indirect Illumination of Emissive Inhomogeneous Volumes using Layered Polygonal Area Lights

Indirect illumination involving with visually rich participating media such as turbulent smoke and loud explosions contributes significantly to the appearances of other objects in a rendering scene. However, previous real‐time techniques have focused only on the appearances of the media directly visible from the viewer. Specifically, appearances that can be indirectly seen over reflective surfaces have not attracted much attention. In this paper, we present a real‐time rendering technique for such indirect views that involves the participating media. To achieve real‐time performance for computing indirect views, we leverage layered polygonal area lights (LPALs) that can be obtained by slicing the media into multiple flat layers. Using this representation, radiance entering each surface point from each slice of the volume is analytically evaluated to achieve instant calculation. The analytic solution can be derived for standard bidirectional reflectance distribution functions (BRDFs) based on the microfacet theory. Accordingly, our method is sufficiently robust to work on surfaces with arbitrary shapes and roughness values. In addition, we propose a quadrature method for more accurate rendering of scenes with dense volumes, and a transformation of the domain of volumes to simplify the calculation and implementation of the proposed method. By taking advantage of these computation techniques, the proposed method achieves real‐time rendering of indirect illumination for emissive volumes.     

Multi‐Pose Interactive Linkage Design

We introduce an interactive tool for novice users to design mechanical objects made of 2.5D linkages. Users simply draw the shape of the object and a few key poses of its multiple moving parts. Our approach automatically generates a one‐degree‐of freedom linkage that connects the fixed and moving parts, such that the moving parts traverse all input poses in order without any collision with the fixed and other moving parts. In addition, our approach avoids common linkage defects and favors compact linkages and smooth motion trajectories. Finally, our system automatically generates the 3D geometry of the object and its links, allowing the rapid creation of a physical mockup of the designed object.     

Real‐time Image‐based Lighting of Microfacet BRDFs with Varying Iridescence

Iridescence is a natural phenomenon that is perceived as gradual color changes, depending on the view and illumination direction. Prominent examples are the colors seen in oil films and soap bubbles. Unfortunately, iridescent effects are particularly difficult to recreate in real‐time computer graphics. We present a high‐quality real‐time method for rendering iridescent effects under image‐based lighting. Previous methods model dielectric thin‐films of varying thickness on top of an arbitrary micro‐facet model with a conducting or dielectric base material, and evaluate the resulting reflectance term, responsible for the iridescent effects, only for a single direction when using real‐time image‐based lighting. This leads to bright halos at grazing angles and over‐saturated colors on rough surfaces, which causes an unnatural appearance that is not observed in ground truth data. We address this problem by taking the distribution of light directions, given by the environment map and surface roughness, into account when evaluating the reflectance term. In particular, our approach prefilters the first and second moments of the light direction, which are used to evaluate a filtered version of the reflectance term. We show that the visual quality of our approach is superior to the ones previously achieved, while having only a small negative impact on performance.     

A Composite BRDF Model for Hazy Gloss

We introduce a bidirectional reflectance distribution function (BRDF) model for the rendering of materials that exhibit hazy reflections, whereby the specular reflections appear to be flanked by a surrounding halo. The focus of this work is on artistic control and ease of implementation for real‐time and off‐line rendering. We propose relying on a composite material based on a pair of arbitrary BRDF models; however, instead of controlling their physical parameters, we expose perceptual parameters inspired by visual experiments [ VBF17 ]. Our main contribution then consists in a mapping from perceptual to physical parameters that ensures the resulting composite BRDF is valid in terms of reciprocity, positivity and energy conservation. The immediate benefit of our approach is to provide direct artistic control over both the intensity and extent of the haze effect, which is not only necessary for editing purposes, but also essential to vary haziness spatially over an object surface. Our solution is also simple to implement as it requires no new importance sampling strategy and relies on existing BRDF models. Such a simplicity is key to approximating the method for the editing of hazy gloss in real‐time and for compositing.     

Practical Foldover‐Free Volumetric Mapping Construction

In this paper, we present a practically robust method for computing foldover‐free volumetric mappings with hard linear constraints. Central to this approach is a projection algorithm that monotonically and efficiently decreases the distance from the mapping to the bounded conformal distortion mapping space. After projection, the conformal distortion of the updated mapping tends to be below the given bound, thereby significantly reducing foldovers. Since it is non‐trivial to define an optimal bound, we introduce a practical conformal distortion bound generation scheme to facilitate subsequent projections. By iteratively generating conformal distortion bounds and trying to project mappings into bounded conformal distortion spaces monotonically, our algorithm achieves high‐quality foldover‐free volumetric mappings with strong practical robustness and high efficiency. Compared with existing methods, our method computes mesh‐based and meshless volumetric mappings with no prescribed conformal distortion bounds. We demonstrate the efficacy and efficiency of our method through a variety of geometric processing tasks.     

Computing Surface PolyCube‐Maps by Constrained Voxelization

We present a novel method to compute bijective PolyCube‐maps with low isometric distortion. Given a surface and its pre‐axis‐aligned shape that is not an exact PolyCube shape, the algorithm contains two steps: (i) construct a PolyCube shape to approximate the pre‐axis‐aligned shape; and (ii) generate a bijective, low isometric distortion mapping between the constructed PolyCube shape and the input surface. The PolyCube construction is formulated as a constrained optimization problem, where the objective is the number of corners in the constructed PolyCube, and the constraint is to bound the approximation error between the constructed PolyCube and the input pre‐axis‐aligned shape while ensuring topological validity. A novel erasing‐and‐filling solver is proposed to solve this challenging problem. Centeral to the algorithm for computing bijective PolyCube‐maps is a quad mesh optimization process that projects the constructed PolyCube onto the input surface with high‐quality quads. We demonstrate the efficacy of our algorithm on a data set containing 300 closed meshes. Compared to state‐of‐the‐art methods, our method achieves higher practical robustness and lower mapping distortion.     

Sequences with Low‐Discrepancy Blue‐Noise 2‐D Projections

Distributions of samples play a very important role in rendering, affecting variance, bias and aliasing in Monte‐Carlo and Quasi‐Monte Carlo evaluation of the rendering equation. In this paper, we propose an original sampler which inherits many important features of classical low‐discrepancy sequences (LDS): a high degree of uniformity of the achieved distribution of samples, computational efficiency and progressive sampling capability. At the same time, we purposely tailor our sampler in order to improve its spectral characteristics, which in turn play a crucial role in variance reduction, anti‐aliasing and improving visual appearance of rendering. Our sampler can efficiently generate sequences of multidimensional points, whose power spectra approach so‐called Blue‐Noise (BN) spectral property while preserving low discrepancy (LD) in certain 2‐D projections. In our tile‐based approach, we perform permutations on subsets of the original Sobol LDS. In a large space of all possible permutations, we select those which better approach the target BN property, using pair‐correlation statistics. We pre‐calculate such “good” permutations for each possible Sobol pattern, and store them in a lookup table efficiently accessible in runtime. We provide a complete and rigorous proof that such permutations preserve dyadic partitioning and thus the LDS properties of the point set in 2‐D projections. Our construction is computationally efficient, has a relatively low memory footprint and supports adaptive sampling. We validate our method by performing spectral/discrepancy/aliasing analysis of the achieved distributions, and provide variance analysis for several target integrands of theoretical and practical interest.     

A Color‐Pair Based Approach for Accurate Color Harmony Estimation

Harmonious color combinations can stimulate positive user emotional responses. However, a widely open research question is: how can we establish a robust and accurate color harmony measure for the public and professional designers to identify the harmony level of a color theme or color set. Building upon the key discovery that color pairs play an important role in harmony estimation, in this paper we present a novel color‐pair based estimation model to accurately measure the color harmony. It first takes a two‐layer maximum likelihood estimation (MLE) based method to compute an initial prediction of color harmony by statistically modeling the pair‐wise color preferences from existing datasets. Then, the initial scores are refined through a back‐propagation neural network (BPNN) with a variety of color features extracted in different color spaces, so that an accurate harmony estimation can be obtained at the end. Our extensive experiments, including performance comparisons of harmony estimation applications, show the advantages of our method in comparison with the state of the art methods.     

Position‐Based Simulation of Elastic Models on the GPU with Energy Aware Gauss‐Seidel Algorithm

In this paper, we provide a smooth extension of the energy aware Gauss‐Seidel iteration to the Position‐Based Dynamics (PBD) method. This extension is inspired by the kinetic and potential energy changes equalization and uses the foundations of the recent extended version of PBD algorithm (XPBD). The proposed method is not meant to conserve the total energy of the system and modifies each position constraint based on the equality of the kinetic and potential energy changes within the Gauss‐Seidel process of the XPBD algorithm. Our extension provides an implicit solution for relatively better stiffness during the simulation of elastic objects. We apply our solution directly within each Gauss‐Seidel iteration and it is independent of both simulation step‐size and integration methods. To demonstrate the benefits of our proposed extension with higher frame rates, we develop an efficient and practical mesh coloring algorithm for the XPBD method which provides parallel processing on a GPU. During the initialization phase, all mesh primitives are grouped according to their connectivity. Afterwards, all these groups are computed simultaneously on a GPU during the simulation phase. We demonstrate the benefits of our method with many spring potential and strain‐based continuous material constraints. Our proposed algorithm is easy to implement and seamlessly fits into the existing position‐based frameworks.     

Real‐time Locomotion Controller using an Inverted‐Pendulum‐based Abstract Model

In this paper, we propose a novel motion controller for the online generation of natural character locomotion that adapts to new situations such as changing user control or applying external forces. This controller continuously estimates the next footstep while walking and running, and automatically switches the stepping strategy based on situational changes. To develop the controller, we devise a new physical model called an inverted‐pendulum‐based abstract model (IPAM). The proposed abstract model represents high‐dimensional character motions, inheriting the naturalness of captured motions by estimating the appropriate footstep location, speed and switching time at every frame. The estimation is achieved by a deep learning based regressor that extracts important features in captured motions. To validate the proposed controller, we train the model using captured motions of a human stopping, walking, and running in a limited space. Then, the motion controller generates human‐like locomotion with continuously varying speeds, transitions between walking and running, and collision response strategies in a cluttered space in real time.