重建几何原形的动态逆正投影理论和方法

DYNAMIC CONVERSE ORTHOGRAPHIC PROJECTION THEORY AND METHOD RECONSTRUCTING ORIGINAL GEOMETRY

本文提出了重建几何原形的动态逆正投影理论和方法，提出了动态逆正投影、多面正投影的可逆性、逆正投影线集及实投影、虚投影和复合投影等新概念，论证了直线、平面、柱面和基本形体原形重建定理，并给出了上述重建的图示方法，解决了正投影的可逆性和唯一确定性问题，对组合体进行了划分，并论述了组合体原形重建的方法。对于回转体原形的重建，本文采用了动态逆正投影理论和方法，解决了回转体静态多面正投影不可逆而导致其原形无法重建的问题。

he theory and method of dynamic converse orthographic projection to reconstruct the original geometry is presented. Several new concepts such as dynamic converse orthographic projection, invertibility of polyhedral orthographic projection, set of lines of converse orthographic projection, real projection, virtual projection, and compound projection, etc., are given. The theorems of reconstructing original geometry such as straight lines, cylinders and basic solids, and the methods of reconstructing them are proven. The problems of invertibility and unique determinacy of orthographic projections are solved. Complex solids can be partitioned. The methods to reconstruct complex solids' original geometry are described. The dynamic converse orthographic projection is used to reconstruct the original geometry of the solids of revolution for the static polyhedral orthographic projection is invalid in this case.