# Showing papers on "Illumination problem published in 1994"

•

15 Dec 1994TL;DR: This dissertation shows the equivalence of these hierarchical techniques to the use of a Haar wavelet basis in a general Galerkin framework and the correspondence of the geometric arguments underlying hierarchical methods to the theory of Calderon-Zygmund operators and their sparse realization in wavelet bases.

Abstract: One of the core problems of computer graphics is the computation of the equilibrium distribution of light in a scene. This distribution is given as the solution to a Fredholm integral equation of the second kind involving an integral over all surfaces in the scene. In the general case such solutions can only be numerically approximated, and are generally costly to compute, due to the geometric complexity of typical computer graphics scenes. For this computation both Monte Carlo and finite element techniques (or hybrid approaches) are typically used.
A simplified version of the illumination problem is known as radiosity, which assumes that all surfaces are diffuse reflectors. For this case hierarchical techniques, first introduced by Hanrahan et al. (32), have recently gained prominence. The hierarchical approaches lead to an asymptotic improvement when only finite precision is required. The resulting algorithms have cost proportional to $O(k\sp2 + n)$ versus the usual $O(n\sp2)$ (k is the number of input surfaces, n the number of finite elements into which the input surfaces are meshed). Similarly a hierarchical technique has been introduced for the more general radiance problem (which allows glossy reflectors) by Aupperle et al. (6).
In this dissertation we show the equivalence of these hierarchical techniques to the use of a Haar wavelet basis in a general Galerkin framework. By so doing, we come to a deeper understanding of the properties of the numerical approximations used and are able to extend the hierarchical techniques to higher orders. In particular, we show the correspondence of the geometric arguments underlying hierarchical methods to the theory of Calderon-Zygmund operators and their sparse realization in wavelet bases. The resulting wavelet algorithms for radiosity and radiance are analyzed and numerical results achieved with our implementation are reported. We find that the resulting algorithms achieve smaller and smoother errors at equivalent work.

25 citations

••

TL;DR: This paper presents a ray‐tracing based algorithm for adaptive mesh generation which resolves all the illumination problems without lengthening computation time too much and allows a small number of initial elements and increases element density in critical locations while solving the illumination problem.

Abstract: The radiosity method is one of the most popular rendering algorithms. It allows to simulate interreflections of light accurately between surfaces as energy transfers are well designed. However, this algorithm and its derivatives need to break scenes into a relatively large number of small elements to approximate the illumination function. Even with a very large number of elements, not all the illumination effects can be simulated. In fact, there are always artefacts when modelling sharp shadows, besides shadows falling between mesh vertices can be missed entirely. To reduce the computational cost of such methods and to increase the accuracy of the radiosity solution, adaptive mesh generation is well suited. In this paper, we present a ray-tracing based algorithm for adaptive mesh generation which resolves all the illumination problems without lengthening computation time too much. This method allows a small number of initial elements and increases element density in critical locations while solving the illumination problem.

3 citations