Figure 1: A high dynamic range 1024×512 environment map [Debevec 98] sampled with 3000 point lights. In this image, importance density is represented by the lightness of the background. It took 0.064 seconds on a 2.6 GHz P4 to generate this point set. Similar results using a hardware accelerated Lloyd relaxation [Hoff et al. 1999] required 1 second, while Structured Importance Sampling [Agarwal et al. 2003] took 1393 seconds. This paper presents a novel method for efficiently generating a good sampling pattern given an importance density over a 2D domain. A Penrose tiling is hierarchically subdivided creating a sufficiently large number of sample points. These points are numbered using the Fibonacci number system, and these numbers are used to threshold the samples against the local value of the importance density. Pre-computed correction vectors, obtained using relaxation, are used to improve the spectral characteristics of the sampling pattern. The technique is deterministic and very fast; the sampling time grows linearly with the required number of samples. We illustrate our technique with importance-based environment mapping, but the technique is versatile enough to be used in a large variety of computer graphics applications, such as light transport calculations, digital halftoning, geometry processing, and various rendering techniques.

High-quality Monte Carlo image synthesis requires the ability to importance sample realistic BRDF models. However, analytic sampling algorithms exist only for the Phong model and its derivatives such as Lafortune and Blinn-Phong. This paper demonstrates an importance sampling technique for a wide range of BRDFs, including complex analytic models such as Cook-Torrance and measured materials, which are being increasingly used for realistic image synthesis. Our approach is based on a compact factored representation of the BRDF that is optimized for sampling. We show that our algorithm consistently offers better efficiency than alternatives that involve fitting and sampling a Lafortune or Blinn-Phong lobe, and is more compact than sampling strategies based on tabulating the full BRDF. We are able to efficiently create images involving multiple measured and analytic BRDFs, under both complex direct lighting and global illumination.

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In this paper, we present a procedural object distribution function, a new texture basis function that distributes procedurally generated objects over a procedurally generated texture. The objects are distributed uniformly over the texture, and are guaranteed not to overlap. The scale, size and orientation of the objects can be easily manipulated. The texture basis function is efficient to evaluate, and is suited for real-time applications. The new texturing primitive we present extends the range of textures that can be generated procedurally. The procedural object distribution function we propose is based on Poisson disk tiles and a direct stochastic tiling algorithm for Wang tiles. Poisson disk tiles are square tiles filled with a precomputed set of Poisson disk distributed points, inspired by Wang tiles. A single set of Poisson disk tiles enables the real-time generation of an infinite amount of Poisson disk distributions of arbitrary size. With the direct stochastic tiling algorithm, these Poisson disk distributions can be evaluated locally, at any position in the Euclidean plane. Poisson disk tiles and the direct stochastic tiling algorithm have many other applications in computer graphics. We briefly explore applications in object distribution, primitive distribution for illustration, and environment map sampling.

+ 0.2 sin 2 (πx) sin 2 (πy); (Right) 4096 points with a density function extracted from a grayscale image. We present a new general-purpose method for optimizing existing point sets. The resulting distributions possess high-quality blue noise characteristics and adapt precisely to given density functions. Our method is similar to the commonly used Lloyd’s method while avoiding its drawbacks. We achieve our results by utilizing the concept of capacity, which for each point is determined by the area of its Voronoi region weighted with an underlying density function. We demand that each point has the same capacity. In combination with a dedicated optimization algorithm, this capacity constraint enforces that each point obtains equal importance in the distribution. Our method can be used as a drop-in replacement for Lloyd’s method, and combines enhancement of blue noise characteristics and density function adaptation in one operation.

We present an interactive system for fully dynamic scene lighting using captured high dynamic range (HDR) video environment maps. The key component of our system is an algorithm for efficient decomposition of HDR video environment map captured over hemisphere into a set of representative directional light sources, which can be used for the direct lighting computation with shadows using graphics hardware. The resulting lights exhibit good temporal coherence and their number can be adaptively changed to keep a constant framerate while good spatial distribution (stratification) properties are maintained. We can handle a large number of light sources with shadows using a novel technique which reduces the cost of BRDF-based shading and visibility computations. We demonstrate the use of our system in a mixed reality application in which real and synthetic objects are illuminated by consistent lighting at interactive framerates.

Figure 1: Different views of a “VW New Beetle ” car rendered with a measured and fitted “Polaris Silber” car paint, lighted from Paul Debevec’s HDR environment map of the Uffizi Gallery in Florence [5]. The outside appearance of cars is mostly defined through only two distinct materials – glass and car paint. While glass can rather easily be simulated by the simple physical laws of reflection and refraction, modelling car paint is more challenging. In this paper we present a framework for the efficient acquisition and realistic rendering of realworld car paint. This is achieved by building an easy-to-reproduce measuring setup, fitting the measured data to a general BRDF model for car paint, adding a component for simulating the sparkling effect of metallic paints, and rendering using a specially designed shader in a realtime ray tracer. 1

One of the most important, still unsolved problems in computer graphics is the generation of predictive imagery, i.e., images that represent perfect renditions of reality. Such perfect images are required in application areas like Virtual Prototyping for making reliable decisions in the costly design development of novel products like cars and airplanes. Recently, measured material properties received significant attention since they enable generation of highly accurate images that appear to be predictive at a first glance. In this work we investigate the degree of realism that can be achieved using measured bidirectional texture functions (BTFs) by comparing photographs and rendered images at two scales. To analyze the realism of rendered images at a coarse scale, we compare the light distribution resulting from standard materials to the one from measured BTFs by automatic procedures. At a fine scale, accurate reproduction of material structures is checked by a psychophysical study. Our results show that measured BTFs lead to much more accurate results than standard materials at both scales. CR Categories: I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism—Color, shading, shadowing, and texture

Providing computer models that accurately characterize the appearance of a wide class of materials is of great interest to both the computer graphics and computer vision communities. The last ten years has witnessed a surge in techniques for measuring the optical properties of physical materials. As compared to conventional techniques that rely on hand-tuning parametric light reflectance functions, a data-driven approach is better suited for representing complex real-world appearance. However, incorporating these representations into existing rendering algorithms and a practical production pipeline has remained an open research problem. One common approach has been to fit the parameters of an analytic reflectance function to measured appearance data. This has the benefit of providing significant compression ratios and these analytic models are already fully integrated into modern rendering algorithms. However, this approach can lead to significant approximation errors for many materials and it requires computationally expensive and numerically unstable non-linear optimization. An alternative approach is to compress these datasets, using algorithms such as Principal Component Analysis, wavelet compression or matrix factorization. Although these techniques provide an accurate and compact representation, they do have several drawbacks. In particular,

This paper introduces a new method for building 2D lowdiscrepancy sequences and fast hierarchical importance sampling. Our approach is based on self-similar tiling of the plane with a set of aperiodic tiles having twelve-fold (dedecagonal) rotational symmetry. Sampling points of our low-discrepancy sequence are associated with tiles, one point per tiles. Each tile is recursively subdivided until the desired local density of samples is reached. A numerical code generated during the subdivision process is used for thresholding to accept or reject the sample. A special number system is specially tailored in order to allow linear numbering of the tiles. The resulting point distribution is more even, compared with that of popular Halton and Hammersley 2D low-discrepancy sequences. It can be successfully applied in a large variety of graphical applications, where fast sampling with good spectral and visual properties is required. Typical applications application are digital halftoning, rendering, geometry processing etc. 1