三维直线的表示及其约束

The Presentation and Constraints of Lines in 3D Spaces

三维直线的表示是计算机图形学和计算机视觉中最基本的问题之一。在介绍了直线的表示原则以及分析了二维和三维直线的各种表示方法的基础上,选择并提出了适合三维重建的二维和三维直线表示方法:用法线式表示法表示二维直线;基于法线式表示法用垂直相交两平面表示法表示三维直线。提出了二维和三维直线的坐标概念,给出了正轴测投影和透视投影下三维直线之间的一些基本约束关系及其证明。

Based on the given criteria for representing 2D and 3D lines and some representations for comparison,a new method with uniqueness for representing a line in 3D space is proposed.The line in 2D plane is represented by normal parameterization,and the line in 3D space is by two perpendicular and intersecting planes.On the one hand,one of the two planes includes projective center and projection of the 3D line,and the other is perpendicular to and intersects the above plane at the 3D line under perspective projection.On the other hand,one of the two planes contains the projection of the 3D line and is parallel to the projective direction;the other is perpendicular to and intersects the above plane at the 3D line under orthographically axonometric projection.Some constraints between 3D lines are given and proven.