关键词: 几何计算, 几何代数化, 几何基, 几何数

Abstract: Discussion for centuries about geometry and algebra was reexamined, problems caused by algebraization of geometry were also analysed. Progress of “geometry problems should be solved geometrically”was explored with angle of human cognition. Common problems of geometry and descriptive geometry are stated. Effects by descriptive geometry theory on geometry computing were discussed. Geometry computing problems were considered under “large geometry” concept formed by geometry and descriptive geometry. From the view of construction, “Geometry quality” and fundamentality of geometry singularity are set forth, key points of geometry computing are seized. When discussing geometry computing, stable juncture (geometry problems should be solved geometrically) should be found based on mathematics (geometry and algebra), engineering (descriptive geometry), computer (algorithm) and so on. A framework of this topic was then built with “primary geometric functions” and “geometric numeric”. Base theory and execution method of geometry computing were established.

Key words: geometry computing, geometry algebraization, primary geometric functions, geometric numeric