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Item Mathematical Models for Semi-globalized Spectral Synthesis(Eurographics Association, 1990) Anjyo, Ken-ichiSemi-globalized spectral synthesis is proposed as a new tool for three-dimensional scene description consisting of many natural objects, such as terrain, sea waves, and clouds. The method is based on the mathematical theory of spectral representation of stochastic processes. In this paper, mathematical models in the method are presented under rigorous formulation and then their stochastic properties are shown. Some simple techniques for practical improvements of the original models in depicting scenes are also explained along with the examples obtained.Item A Simple Spectral Approach to Stochastic Modelling for Natural Objects(Eurographics Association, 1988) Anjyo, Ken-ichiStochastic modeling has been widely used in computer graphics to depict natural objects or phenomena. Various techniques are available, depending on what object is to be represented and what extent of realism to be achieved. This paper presents a simple approach to stochastic spectral synthesis for producing a large range of natural objects and scenes at low computational cost. By considering a wide class of power spectra, the method can provide twodimensional stochastic models for various objects, involving terrains, clouds and sea waves. Moreover, some functional operations and parameters for the models are introduced, which can make the models more flexible in describing a three-dimensional complex scene.