Explorations in Constructive Analytic Geometry

这项小额拨款探索性研究（SGER）项目的目的是确定使用r函数理论结合（离散）计算几何和（连续）分析计算工具的可行性。本次探索性研究需要完成的具体任务是：1。为布尔和/或边界表示的对象自动构造（隐式）实值函数的算法的开发和实现；2. 通过实验验证理论预测的构造函数的计算和数值性质。这些探索的结果将用于定义和承担一个显著的更大规模的努力，以开发一个计算环境，用于建模和解决工程和科学问题。这种环境的独特之处在于几何计算和解析计算的无缝集成。

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.