透视投影变换的基本问题

Fundamental Problems on Transformation of Perspective Projection

关于透视变换矩阵问题,近10年来有不少文章从不同角度进行了分析和探讨。但是,到目前为止,以下2个基本问题仍未得到完善的解决:1)一个变换矩阵的元素需满足什么条件才能生成一个正确的透视图;2)若变换矩阵满足透视投影要求,那么如何确定透视中心、投影面和物体的相对位置。文中用解析方式回答了上述问题。

The problems on matric of perspective transformation has been discussed in many articles from various angles in last decade.Up to now,however,there is no perfect answer to the following two fundamental problems:1.To produce a correct perspective drawing what conditions must be satisfied for the elements of transformation matric;2.If the matric of transformation can satisfy the requirement of perspective projection,how to determine the relative position of the perspective centre,projection plane and body.Above-mentioned prob- lems are analytically answered in this paper.