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Item Growing and Animating Polygonal Models of Animals(Blackwell Publishers Ltd and the Eurographics Association, 1997) Walter, Marcelo; Fournier, AlainWhile there exist many computer models of animal bodies, as polygonal meshes and parametric surfaces, these are difficult to modify to take growth into account, or to animate. Growth data available from the literature usually is expressed as very sparse measurements over the body at various ages of the animal. We present here basic techniques to transfer growth data to computer models (especially polygonal meshes), which allows animation of the growth as well as animation of the body in the traditional sense.The main technique consists of defining local coordinate systems around the growing parts of the body, each one being transformed according to the relevant growth data while maintaining their relationship with the adjoining parts and the continuity of the surface. The local coordinates also permit ordinary animation mainly as relative rotation such as in articulated objects.We present examples with polygonal models of horses and cows, growth data from same, and motion from Muybridgeâ s classic photographic data.Item Wavelet Radiative Transfer and Surface Interaction(Blackwell Publishers Ltd and the Eurographics Association, 2000) Lewis, Robert R.; Fournier, AlainRecently, there has been considerable interest in the representation of radiance in terms of wavelet basis functions. We will present a coordinate system called Nusselt coordinates which, when combined with wavelets, considerably simplifies computation of radiative transport and surface interaction. It also provides straightforward computation of the physical quantities involved.We show how to construct a discrete representation of the radiative transport operator ? involving inner products of smoothing functions, discuss the possible numerical integration techniques, and present an application. We also show how surface interaction can be represented as a kind of matrix product of the wavelet projections of an incident radiance and a bidirectional reflectance distribution function (BRDF).Item Modelling the Garden of Perfect Brightness(Blackwell Publishers Ltd and the Eurographics Association, 1997) Wang, LiFeng; Botta, David; Ellefson, Chris; Fournier, AlainThe Yuan Ming Yuan, the Garden of Perfect Brightness, was the culmination of the art of Chinese Imperial gardens. Covering 350 hectares (875 acres) northwest of Beijing, it included 140 distinct sites, 2000 structures, thousands of pieces of furniture and precious objects, countless plants. It was almost totally destroyed in 1860 at the end of the second Opium War by English and French troops in one of the worst acts of cultural vandalism in recorded history.Rebuilding it has proven impossible, but now computer technology, based on 130 years of scholarly documentation makes it possible to build an accurate and detailed model, and will allow us to experience at least virtually the beauty and grandeur that was the Yuan Ming Yuan.This paper describes a project to build such a model, and details the main challenges and difficulties encountered. While commercially available graphics workstations and modelling software can take us most of the way in this task, they fall short with the modelling of natural phenomena such as plants, rocks and bodies of water. In addition the sheer size of the resulting database pushes rendering engines past their limits.Item Generating Reflected Directions from BRDF Data(Blackwell Publishers Ltd and the Eurographics Association, 1997) Lalonde, Paul; Fournier, AlainMonte-Carlo path tracing algorithms for computer graphics require that given an incident light ray at a surface an outgoing direction can be computed with a distribution given by the magnitude of the bidirectional reflectance distribution function (BRDF). For analytic reflectance functions this can be done using various techniques including inverting the function, or tabulating some representation of the inverse. However, measured BRDF data sets are too large for this to be practical.We present a method to generate reflection rays distributed according to the magnitude of the BRDF. The method relies on a wavelet-based representation of the BRDF. This representation is efficient and compact, allowing large, anisotropic measured BRDF data sets to be represented with a few thousand coefficients. In particular, we exploit the wavelet representation to quickly compute integrals over ranges of the BRDF.