Explorations in Constructive Analytic Geometry

这个小赠款探索性研究（SGER）项目的目的是确定从（离散）计算几何和（连续）分析计算使用R-函数理论相结合的工具的可行性。 本探索性研究期间要完成的具体任务包括： 1.开发和实现用于为布尔和/或边界表示表示的对象自动构造（隐式）实值函数的算法; 2.进行实验以验证理论预测的构造函数的计算和数值特性。 这些探索的结果将被用来定义和承担一个显着更大规模的努力，以开发一个计算环境，建模和解决工程和科学问题。 这样一个环境的独特之处将是几何和分析计算的无缝集成。

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.