Surface-Surface Intersection for Solid Modeling via Computerized Descriptive Geometry

本研究的目的是发展一种理论 框架和几何算法， 在几何和实体建模中使用的曲面的相交。 将使用符号计算。 也就是说， 应用代数或数值技术，使用基本的 一组几何例程（直线/直线交点、直线/圆 交叉点等）结合一套技术， 易于施工和连接交点， 应用。 该研究有以下重要成果： O 一套强大、快速和可靠的跨部门系统， 能够处理特殊情况，例如 接触和重叠的表面， O 一组视觉上可描述的算法， 包括在学术课程中， O 鲁棒的理论和计算基础 三维几何计算。

The objectives of this research are to develop a theoretical framework and geometrical algorithms for the robust and fast intersection of surfaces used in geometric and solid modeling. Symbolic computation will be used. That is, instead of applying algebraic or numerical techniques, the use of a basic set of geometry routines (line/line intersection, line/circle intersection, etc.) combined with a set of techniques for the easy construction and linkage of intersection points is applied. The research has the following significant output: o a set of robust, fast and reliable intersectors that are capable of handling special cases such as touching and overlapping surfaces, o a set of visually describable algorithms that can be included in an academic course, and o theoretical and computational foundation of robust three-dimensional geometric computations.