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.
Some very interesting closed-form solutions have already been proposed to solve the light integral. The appeal of closed-form solutions lies in the fact that they provide complete elimination of noise. Furthermore, the availability of a closed-form solution expedites the rendering process significantly. For estimation methods such as Monte Carlo @cite_112 , many samples of the environment are required to render realistic low-noise images. On the other hand, several hours might be required to generate one single image.
@cite_112
2033102965
In a distributed ray tracer, the sampling strategy is the crucial part of the direct lighting calculation. Monte Carlo integration with importance sampling is used to carry out this calculation. Importance sampling involves the design of integrand-specific probability density functions that are used to generate sample points for the numerical quadrature. Probability density functions are presented that aid in the direct lighting calculation from luminaires of various simple shapes. A method for defining a probability density function over a set of luminaires is presented that allows the direct lighting calculation to be carried out with a number of sample points that is independent of the number of luminaires.