A separable decomposition of bidirectional reflectance distributions (BRDFs) is used to implement arbitrary reflectances from point sources on existing graphics hardware. Two-dimensional texture mapping and compositing operations are used to reconstruct samples of the BRDF at every pixel at interactive rates. A change of variables, the Gram-Schmidt halfangle/difference vector parameterization, improves separability. Two decomposition algorithms are also presented. The singular value decomposition (SVD) minimizes RMS error. The normalized decomposition is fast and simple, using no more space than what is required for the final representation.

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Contents 1 Introduction 1 2 Background 3 2.1 Reflectance Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 BRDF -- Bidirectional Reflectance Distribution Function . . . . . . . . . . . . . . 4 2.3 Hardware Rendering -- Prior Results . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.5 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3 Decomposition of BRDFs 8 3.1 Singular Value Decomposition of BRDFs . . . . . . . . . . . . . . . . . . . . . . 8 3.1.1 General SVD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.1.2 SVD of a BRDF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.1.3 Drawbacks of the SVD . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2 Approximate Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2.1 Serial Separation of Resi

We introduce a physically plausible mathematical model for a large class of BRDFs. The new model is as simple as the well-known Phong model, but eliminates its disadvantages. It gives a good visual approximation for many practical materials: coated metals, plastics, ceramics, retro-reflective paints, anisotropic and retro-reflective materials, etc. Because of its illustrative properties it can be used easily in most commercial software and because of its low computational cost it is practical for virtual reality. The model

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,

Figure 1: A synthetic image where our proposed BRDF model is used on a fluorescent orange surface that is being illuminated by several collimated monochrome light sources. The scene geometry is similar to that shown in figure 2. Note the colours of the directly viewed bright dots on the material itself, and the in some cases considerably different colours seen in the reflection patterns. It is noteworthy that the blue and green monochrome lights (second and third light from the left), which fall into the main area of the absorption curve shown in figure 4, exhibit the largest colour discrepancies between specular and diffuse reflection. Fluorescence is an interesting and visually prominent effect, which has not been fully covered by Computer Graphics research so far. While the physical phenomenon of fluorescence has been addressed in isolation, the actual reflection behaviour of real fluorescent surfaces has never been documented, and no analytical BRDF models for such surfaces have been published yet. This paper aims to illustrate the reflection properties typical for diffuse fluorescent surfaces, and provides a BRDF model based on a layered microfacet approach that mimics them.

Physically-based rendering methods represent the core of current realistic image synthesis frameworks. These methods, through a plausible simulation of the processes of light propagation and interaction with objects, have contributed considerably to the improvement of photorealistic rendering. The state of art research in this area includes the simulation of natural phenomena and the incorporation of biological aspects affecting light propagation in natural environments. The search for more efficient rendering solutions is also of major interest for the rendering community. In this dissertation biologically and physically-based models for light interaction with plant leaves are presented. Moreover, since the light that reach a plant leaf may be propagated directly from a light source or indirectly, due to multiple interactions with other objects in the environment, global illumination issues are also addressed, more specifically related to the radiosity method. This method is commonly...