Dynamic Materials Global Illumination Rendering Based on BRDF

When the materials in scene are invariant, a linear transformation occurs in the transmission change from lighting to outgoing radiance, which makes a real-time global illumination rendering achieved. However, such linear transformation does not hold when materials change. This paper presents an real-time rendering algorithm for scenes with editable materials under direct and indirect illumination. All materials in scenes are represented as various linear combinations of the BRDF base, from which, all outgoing radiance luminance of each conbination are precomputed. When it renders, linear combines the pre-computed data by the coefficient resulted from different materials projection on the base, the nonlinear problem is converted to a linear one, and the final effects of global illumination rendingering in real-time can be achieved. The algorithm only takes twice reflection into account, without viewing any refraction or translucency. Keywords-Global Illumination; graphics processing unit (GPU); Bi-Directional Reflectance Distribution Function (BRDF); Rendering Equation I. RELATED WORK AND BACKGROUND The fundamental task of global illumination aims at using the pre-placed three-dimensional scene to create an image with a completely strong sense of reality, which posts an inevitable development trend of real-time rendering. We have to simulate all kinds of physical phenomenon which happens when light transmit in scene. It not only needs specific illustration of geometrical properties and material features of all objects in scene, but also for the solves and calculates infinitesimal calculus problems brought about by many times reflection and refraction. The calculation complexity of global illumination needs very long time to render an image with strong sense of reality, therefore, many studies in the field of graphics focus on how to improve the algorithm of global illumination and render high quality images within shorter time. There are many non-real time algorithm for global illumination. Kajiya[1] first proposed the raytracing algorithm based on Monte Carlo’s method to solve rendering equation, which takes samples of lightrays reaching the surface of image and then estimates their contribution to the final image in order to create the actual image. After improvement, Arvo[2][3] proposed the equal backward particle tracing method. Later Veach[4] used the optimally combining sampling to greatly improve the adaptation and efficiency of the raytracing method. Lafortune[5] and Beach respectively proposed the Bidirectional path tracing, though which, a pair of eyes sub-path and light source sub-path are created, connecting through every node, to reduce the variance level of calculation. Soon, Vench[6] proposed Metropolis method that adjusted sampling according to illumination distribution, this method creates a highly effective calculation for the scene in which indirect illumination accounts for major part. Jesen[7] proposed Photon Mapping method, which is a two-step calculation for creating image of photons and photos collection. With the rapid development of graphics processing unit (GPU), some algorithms for real time rendering have been proposed. Sloan[8] proposed pre-computed radiance transfer (PRT) and Zhou Kun[9] put forward shadow fields. They disassembled the influences of some factors including illumination or reflection over linear base, and then transfered the integral calculation to the base coefficient and at the same time took advantage of GPU parallel computation to speed up the pace of rendering. Ben-Artzi used material properties as an independent dynamic change factor to operate real time rendering, supportive of direct illumination rendering of complicated light source, but not of indirect illumination rendering. II. BI-DIRECTIONAL REFLECTANCE DISTRIBUTION FUNCTION Bi-Directional Reflectance Distribution Function (BRDF) is a mathematical model to describe the reflectance properties of material. BRDF model describes a relation between incident light and reflectance rays on the surface (see Fig.1). They show that light rays can be reflected (specular or diffuse reflection) or absorbed or both. It is feasible to measure incident light and reflectance rays on the surface of a certain real object to describe this type of material and its BRDF. The measure results can be used in the CG program to create the material with the same surface properties. Reflectance model maybe precise or experimental. Figure 1. The BRDF Domain The nature of BRDF is, according to the surface properties, to calculate the incident light angle and viewer angle though vendor quantity to describe light reflectance. Considering illumination’s influence on scene and changes of color and brightness caused by the different observing position for the very same point in scene, BRDF in form performs three 978-1-4244-4994-1/09/$25.00 ©2009 IEEE dimensional functions through three angles: (a) the angle formed between illumination direction and surface normal direction; (b) the angle formed between viewer angle direction and surface normal direction; and (c) the angle formed between illumination direction on the surface which is vertical to normal and viewer angle direction. The surface normal of reflectance point in most of BRDF models is symmetrical, which is called isotropic BRDF, otherwise called anisotropic BRDF. Some BRDF models uses parameters to describe its form and are expressed by analytic functions, for example Phong, BlinnPhong, Cook-Torrance and Ward, etc. In this paper, it is assumed that light path is only changed on the object surface without considering refraction, therefore Blinn-Phong[10] of BRDF model is adopted to describe the object properties,the change of the object properties can be achieved through the change of the model parameters III. GLOBAL ILLUMINATION RENDERING OF DYNAMIC MATERIALS BASED ON BRDF A. Real -Time Global Illumination Rendering Rendering equation records the complete physical process of how lightrays transmit in scene. Rendering equation displays how light energy emits from light source, reflects and refracts for many times over the surface of a variety of types of materials and finally enters into viewers’ eyes. The classical rendering equation to describe how a ray of light starts off from a certain point x' in the surface, emits along the direction see Fig. 2) can be defined as below: