Abstract: It is important to trace back to the root of CAD technology and analyze the source of computing difficulty.The digital model of CAD is based on "shape".Thus,the original contradiction between the computing mechanism of "number" and the computing object of "shape" was examined,and a new computing mechanism of global,intuitive,simple and stable built with geometric approach was explored.A "shape computing" mechanism based on "geometrization of geometric problems" was introduced.The general idea and main strategy of shape computing were described.Application examples of shape computing were given and the performance of the algorithms was analyzed both theoretically and experimentally.Finally,the role of shape computing in CAD was discussed,and the computational basis of reconstruction CAD with shape computation was proposed.The implementation proposal and scheme were further given.Taking the advantages of shape computing in CAD,such as geometric representation,geometric computation,geometric relationship reorganization,geometric singularity processing,geometric transformation and dimension-reducing computation,the CAD root technology with shape computation as the theoretical basis was established to improve the geometric kernel in terms of algorithmic simplicity,computational robustness and computational efficiency.

Key words: CAD, industrial software, shape computing, geometry, geometric computing, algebraic computing, computational foundation

摘要： 追溯CAD技术之根,剖析计算难之源。CAD的数字化模型基于“形”。审视基于“数”的计算机制与“形”计算对象间的原始矛盾,探索用几何的思路去寻求全局、直观、简单、稳定的新计算机制。介绍了一种基于“几何问题几何化”的“形计算”机制。阐述了形计算的总体思想和主要策略,给出了形计算的应用实例,对算法性能作了理论与实验分析。最后,讨论了形计算在CAD中的作用,提出以形计算重构CAD的计算基础,给出了实施建议和方案,在CAD中发挥形计算在几何表示、几何计算、几何关系重组、几何奇异处理,以及几何变换、降维计算等方面的特色与优势,建设以形计算作为理论基础的CAD根技术,实现几何内核在算法简单化、计算稳定性和计算效率上有大的提升。

关键词: CAD, 工业软件, 形计算, 几何, 几何计算, 代数计算, 计算基础