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Item Stochastic Motion-Motion Under the Influence of Wind(Blackwell Science Ltd and the Eurographics Association, 1992) Shinya, Mikio; Fournier, AlainStochastic approaches are very effective for modelling natural phenomena. This paper presents a motion model based on a stochastic process as well as physics, and proposes motion synthesis techniques for stochastic motion-motion under the influence of wind.The motion synthesis process is modelled by a cascade system of three components: wind model, dynamic model, and deformation model. Wind models produce spatio-temporal wind velocity fields using the power spectrum and auto-correlation of wind, just like fractal geometry. Dynamic models describe the dynamic response of the systems, using equation systems or response functions. Deformation models produce deformed shapes of objects according to the geometric models of the objects and the results of the dynamic systems.The biggest advantage of the model is its generality and consistency. The model is applicable to most of the existing trees and grass models, including structural models, particle systems, impressionist models, and 3D texture. It is demonstrated that the coupling of stochastic approaches and physically-based approaches can synthesize realistic motion of trees, grass and snow with modest computational cost.Item Tightly-Coupled Multiprocessing for a Global Illumination Algorithm(Eurographics Association, 1990) Drettakis, George; Fiume, Eugene; Fournier, AlainA prevailing trend in computer graphics is the demand for increasingly realistic global illumination models and algorithms. Despite the fact that the computational power of uniprocessors is increasing, it is clear that much greater computational power is required to achieve satisfactory throughput. The obvious next step is to employ parallel processing. The advent of affordable, tightly-coupled multiprocessors makes such an approach widely available for the first time. We propose a tightly-coupled parallel decomposition of FIAT, a global illumination algorithm, based on space subdivision and power balancing, that we have recently developed. This algorithm is somewhat ambitious, and severely strains existing uniprocessor environments. We discuss techniques for reducing memory contention and maximising parallelism. We also present empirical data on the actual performance of our parallel solution. Since the model of parallel computation that we have employed is likely to persist for quite some time, our techniques are applicable to other algorithms based on space subdivision.Item Chebyshev Polynomials for Boxing and Intersections of Parametric Curves and Surfaces(Blackwell Science Ltd and the Eurographics Association, 1994) Fournier, Alain; Buchanan, JohnParametric curves and surfaces are powerful and popular modelling tools in Computer Graphics and Computer Aided Design. Ray-tracing is a versatile and popular rendering technique. There is therefore a strong incentive in developing fast, accurate and reliable algorithms to intersect rays and parametric curves and surfaces.We propose and demonstrate the use of Chebyshev basis functions to speed up the computation of the intersections between rays and parametric curves or surfaces. The properties of Chebyshev polynomials result in the computation of better and tighter enclosing boxes. For surfaces they provide a better termination criterion to decide on the limits of subdivision, and allow the use of bilinear surfaces for the computation of the intersection when needed.The efficiency of the techniques used depends on the relative magnitude of the coefficients of the Chebyshev basis functions. We show from a statistical analysis of the characteristics of several thousands surfaces of different origin that these techniques will result most of the time in significant improvement in speed and accuracy over other other boxing and subdivision techniques.