Explorations in Constructive Analytic Geometry

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The purpose of this Small Grants Exploratory Research (SGER) project is to determine the feasibility of combining tools from (discrete) computational geometry and (continuous) analytic computations using theory of R-functions. Specific tasks to be accomplished during this exploratory study are: 1. development and implementation of algorithms for automatic construction of (implicit) real-valued functions for objects represented by Boolean and/or boundary representations; 2. conduct experiments to verify computational and numerical properties of constructed functions predicted by the theory. The results of these explorations will be used to define and undertake a significantly larger scale effort to develop a computational environment for modeling and solving engineering and scientific problems. The unique feature of such an environment will be seamless integration of geometric and analytic computations.