几何计算及其理论研究

Reseurch of Geometric Computing and Its Theory

提出了一种新的几何计算理论.在几何基础层,充分利用笛卡儿创立的坐标几何思想,用几何代数化方法构建二、三维基本的几何代数基(简称几何基),可利用它的序列建立高一层次的几何基.在几何处理层,用几何方法解决几何问题,寻求几何问题的几何基求解序列.对几何引入方向性,统一几何的表示,简化几何基序列的求解过程.并从理论上探索解决几何奇异问题的完整解决方案,形成一个统一、规范的几何计算体系.由此实现莱布尼茨式的通过几何语言直接处理几何体的宏伟设想.

A new geometric computing theory was proposed.On the definition level of geometric elements,using the Cartesian coordinates ideology as reference,2D and 3D ＂geometric algebra elements＂（or（＂geometric） elements＂ for short,which could construct an upper-level element in the solving sequence） were constructed by geometry algebraization methods.On the processing level of geometries,geometric（problems） were solved with geometry methods,by which a geometric element solving sequence could be（constructed.） Directional property was introduced into geometries in this theory and geometries were represented in a unified format.They help to simplify the processing of finding the geometric element solving sequence for a geometry problem.The paper also tried to theoretically find out an integrated solution for geometry ambiguity issues,and established a unified,standardized geometry computing architecture.The Leibniz＇s mind——to process geometric objects with geometric language——was implemented in an indirect way!