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Item An adaptive Discretization Method For Radiosity(Blackwell Science Ltd and the Eurographics Association, 1992) Languenou, Eric; Bouatouch, Kadi; Tellier, PierreWhen using radiosiiy, the visual quality of the rendered images strongly depends on the method employed for discretizing the scene into patches. A too fine discretization may give rise to artifacts, while with a coarse discretization areas with high radiosity gradient may appear. To overcome these problems, the discretization must adapt to the scene. That is, the interaction between two patches must account for the distance between them as well as their surface area. In other words, surfaces far away are discretized less finely than nearby surfaces. These aspects are considered by the new adaptive discretiration method described in this paper. It performs both discretization and system resolution at each iteration of the shooting process, allowing then interactivity.Item Computation of Higher Order Illumination with a Non-Deterministic Approach(Blackwell Science Ltd and the Eurographics Association, 1996) Bouatouch, Kadi; Pattanaik, S. N.; Zeghers, EricIn spite of the number of efforts made by the computer graphics researchers, till today the computation of view-independent global illumination in an environment containing non-diffusely reflecting objects is a non-resolved problem. In general, non-deterministic techniques seem to be capable of solving this problem. In this article we propose one such non-deterministic method which will permit such calculation by using a combined technique of higher order function approximation and particle tracing. We have used multi-wavelets as basis functions and have calculated the illumination function approximation coefficients by exploiting the adjointness between the radiance equation and the potential equation.Item Low Sampling Densities using a psychovisual approach(Eurographics Association, 1991) Bouville, Christian; Tellier, Pierre; Bouatouch, KadiIt has long been observed that the keenness of sight is lower for diagonal directions than for horizontal or vertical ones. This anisotropy of the human eye response can be exploited by using a non-orthogonal sampling pattern with a reduced sampling density. After an introduction to the two-dimensional sampling theory, it is shown that quincunx sampling is well suited to this characteristic. Then a sampling scheme based on this approach is described. This effectively leads to halving the sampling density and thereby the computing time of ray-traced pictures.Item Fast Wavelet Radiosity Method(Blackwell Science Ltd and the Eurographics Association, 1994) Pattanaik, Sumanta N.; Bouatouch, KadiWavelet analysis has been found [1] to be very useful for functional representation and accurate global solution of radiosity. In radiosity we deal with functions in 2D and 4D spaces. Under such conditions, the biggest bottleneck in applying this wavelet analysis seems to be the large number of multidimensional inner products. In this paper, we propose (i) the use of interpolating wavelets for fast inner product computation and consequently for faster wavelet radiosity solution (ii) the use of hierarchical decomposition technique for determining the smoothness of the radiosity function for optimal adaptive subdivision.