透视投影研究  

An Investigation of Perspective Projection

作　　者：陈自强[1] 

机构地区：[1]华东理工大学材料工程学院,上海200237

出　　处：《华东理工大学学报（自然科学版）》2000年第2期201-205,共5页Journal of East China University of Science and Technology

摘　　要：从射影几何角度探讨了透视投影的几何本质 ,并对射影几何学中著名的笛沙格定理作了必要的引申 ,从而严格定义了包括空间透射 ( stereohomology)在内的一系列几何变换。这可严格地给这些应用图学中重要的几何变换以理论界定。同时 ,也从理论上给出待求几何变换的解析解成为可能。这项工作填补了长期以来理论图学中一直存在的某些基础理论研究 (即投影理论中的一些基本几何变换 ,如空间透射、空间透视、平行投影、平移变换等 )落后于它的实际应用的一项空白。这不仅对理论图学有十分重要的意义 ,而且对计算机图形学也有一定的指导作用。The geometrical essence of the perspective projection is examined from the viewpoint of projective geometry in this paper,and the famous Desargues theorem in projective geometry is extended too.Therefore a series of geometrical transformations,stereohomology included,are rigorously defined.Thus we can theoretically draw a clear line between these important geometrical transformations in applied graphics.This work also makes it possible to give analytical solutions to the unknown geometrical transformations defined in this paper.The work has filled the gap that some researches in basic theories (namely some basic geometrical transformations in projection theories,such as stereohomology、parallel projection、parallel motion transformation etc) drop behind their practical applications which has existed in theoretical graphics for such a long time.It's significant to theoretical graphics,and also guidance to computer graphics as well.

关 键 词：射影几何 透视投影 笛沙格定理 计算机图形学 

分 类 号：O185.1[理学—数学] TP391.41[理学—基础数学]