从单幅透视线图建立平面立体的模型

提出了一种基于直线解释平面立体透视投影线图的新方法。采用一种新的方法表示空间直线坐标，根据画出隐藏线的透视线图中隐含的约束条件，建立线性方程组，求解该线性方程组得到平面立体的三维信息。证明了解释平面立体透视投影线图至少有4个自由度。计算和实验结果证明，该方法能很好地恢复平面立体的三维结构，研究成果可用于CAD和计算机视觉系统。

On Making Interpretation of Line Drawing Easier and More Precise in Computer Vision and CAD

Human interpretation of line drawing is different from its computer interpretation. Refs.1, 2, and 3 tried to make computer interpretation of line drawing easier. This paper aims to make such interpretation easier and more precise than that of Refs.1, 2, and 3, particularly easier and more precise than that of Refs.2 and 3. Both Refs.2 and 3 and this paper deal with the problem of constraining relationships between a line and a plane, which is key to the computer interpretation of line drawing. But our way of dealing with the interpretation is different from that of Refs.2 and 3. Section 2 proves that in the interpretation of line drawing of an object under perspective projection, there exist at least four degrees of freedom. Subsection 3.1 discusses the constraining relationship between two intersecting straight lines in space. Subsection 3.2 discusses the constraining relationship between a straight line and a plane containing it. A linear system is established for constructing 3D object from its projection based on above mentioned relationships. Section 4 gives an example; Fig.3 and Fig.5 show preliminarily that our method is indeed better than that of Refs.2 and 3 in making interpretation of line drawing easier and more precise in computer vision and CAD (computer aided design).