In this paper, we present a new mathematical foundation for image-based lighting. Using a simple manipulation of the local coordinate system, we derive a closed-form solution to the light integral equation under distant environment illumination. We derive our solution for different BRDF's such as lambertian and Phong-like. The method is free of noise, and provides the possibility of using the full spectrum of frequencies captured by images taken from the environment. This allows for the color of the rendered object to be toned according to the color of the light in the environment. Experimental results also show that one can gain an order of magnitude or higher in rendering time compared to Monte Carlo quadrature methods and spherical harmonics.
Currently, the closed-form solutions proposed in the literature mostly target specific scenarios. For example, the work done in @cite_5 targets linear light sources and provides a solution to the integral for diffuse and specular materials lit by such a light. The work done by Arvo @cite_114 provides analytic solutions to the light integral for polyhedral sources using the irradiance jacobian. @cite_62 introduced the use of B-splines to represent surface radiance in static scenes. A recent work by @cite_137 provides a closed-form solution to the light integral given isotropic point light sources. Their solution targets the scenarios of fog, mist and haze.
@cite_137 @cite_5 @cite_62 @cite_114
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We present a closed-form expression for the irradiance at a point on a surface due to an arbitrary polygonal Lambertian luminaire with linearly-varying radiant exitance. The solution consists of elementary functions and a single well-behaved special function that can be either approximated directly or computed exactly in terms of classical special functions such as Clausen’s integral or the closely related dilogarithm. We first provide a general boundary integral that applies to all planar luminaires and then derive the closed-form expression that applies to arbitrary polygons, which is the result most relevant for global illumination. Our approach is to express the problem as an integral of a simple class of rational functions over regions of the sphere, and to convert the surface integral to a boundary integral using a generalization of irradiance tensors. The result extends the class of available closed-form expressions for computing direct radiative transfer from finite areas to differential areas. We provide an outline of the derivation, a detailed proof of the resulting formula, and complete pseudo-code of the resulting algorithm. Finally, we demonstrate the validity of our algorithm by comparison with Monte Carlo. While there are direct applications of this work, it is primarily of theoretical interest as it introduces much of the machinery needed to derive closed-form solutions for the general case of luminaires with radiance distributions that vary polynomially in both position and direction. Abstract Existing two-stream approximations to radiative transfer theory for particulate media are shown to be represented by identical forms of coupled differential equations if the intensity is replaced by integrals of the intensity over hemispheres. One set of solutions thus suffices for all methods and provides convenient analytical comparisons. The equations also suggest modifications of the standard techniques so as to duplicate exact solutions for thin atmospheres and thus permit accurate determinations of the effects of typical aerosol layers. Numerical results for the plane albedos of plane-parallel atmospheres (single-scattering albedo = 0.8, 1.0; optical thickness = 0.25, 1, 4. 16; Henyey-Greenstein phase function with asymmetry factor 0.75) are given for conventional and modified Eddington approximations, conventional and modified two-point quadrature schemes, the hemispheric-constant method and the delta-function method, all for comparison with accurate discrete-ordinate solutions. A new two-... We present a theoretical analysis of the relationship between incoming radiance and irradiance. Specifically, we address the question of whether it is possible to compute the incident radiance from knowledge of the irradiance at all surface orientations. This is a fundamental question in computer vision and inverse radiative transfer. We show that the irradiance can be viewed as a simple convolution of the incident illumination, i.e., radiance and a clamped cosine transfer function. Estimating the radiance can then be seen as a deconvolution operation. We derive a simple closed-form formula for the irradiance in terms of spherical harmonic coefficients of the incident illumination and demonstrate that the odd-order modes of the lighting with order greater than 1 are completely annihilated. Therefore these components cannot be estimated from the irradiance, contradicting a theorem that is due to Preisendorfer. A practical realization of the radiance-from-irradiance problem is the estimation of the lighting from images of a homogeneous convex curved Lambertian surface of known geometry under distant illumination, since a Lambertian object reflects light equally in all directions proportional to the irradiance. We briefly discuss practical and physical considerations and describe a simple experimental test to verify our theoretical results. Abstract In virtually all rendering systems, linear light sources are modeled with a series of point light sources that require considerable computing resources to produce realistic looking results. A general solution for shading surfaces illuminated by a linear light source is proposed. A formulation allowing for faster computation of the diffuse component of light reflection is derived. By assuming Phong's specular component, simple, inexpensive and convincing results are produced with the use of a Chebyshev approximation. A shadowing algorithm is also presented. As shadowing from linear light sources is expensive, two acceleration schemes, extended from ray tracing, are evaluated.