中心投影与平行投影椭圆对应关系的研究  

Research on Relationship of Centre Projection and Parallel Projection Ellipse

作　　者：杨道富[1] 

机构地区：[1]黄河水利职业技术学院,河南开封475001

出　　处：《河南大学学报（自然科学版）》2006年第4期110-114,共5页Journal of Henan University:Natural Science

基　　金：河南省科技攻关项目(20025700002)

摘　　要：根据同素性、从属性和等简比、等交比的特性,研究了透视对应中空间圆与投影椭圆之间的特性和变化规律,得出了同族变化定理、视角交比相关定理、等交比定理、平行二重直线对应线段的等简比定理、双心几何定理、透视椭圆定理,建立了中心投影和平行投影之间的几何对应关系,解决了透视椭圆的作图问题.Based on the features of similar elements, subordination, brief ratio and equianharmonic cross ratio, this paper analyses the features and changing rules of spacial circle and perspective ellipse, and gets the similar family changing theorem, view cross ratio theorem, equianharmonic cross ratio theorem, corresponding section brief ratio theorem of two parallel lines, dual-center geometry theorem, perspective ellipse theorem. In addition, it builds up geometry relationship between centre projection and parallel projection and then solves the problems of drawing about perspective ellipse.

关 键 词：中心投影 平行投影 透视椭圆 仿射变换 等交比性 双心定理 

分 类 号：TU204[建筑科学—建筑设计及理论]