Surface-Surface Intersection for Solid Modeling via Computerized Descriptive Geometry

这项研究的目标是开发一个理论框架和几何算法，用于几何和实体造型中的曲面的健壮和快速相交。将使用符号计算。也就是说，不是应用代数或数值技术，而是使用一组基本的几何例程(直线/直线相交、直线/圆相交等)。并结合一套易于构造和连接交点的技术进行了应用。这项研究有以下重要成果：o一套坚固、快速和可靠的跨部门，能够处理特殊情况，如接触和重叠表面，O可以包括在学术课程中的一组视觉上可描述的算法，以及稳健三维几何计算的理论和计算基础。

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.