从单幅正轴测投影线图建立平面立体的模型

提出了一种从单幅二维正轴测投影线图建立平面立体线框模型的新方法。提出一种新的空间直线坐标表示法，根据正轴测投影线图中隐含的直线与平面之间的从属关系建立约束方程。考虑画出隐藏线的正轴测投影线图，根据线画图中隐含的约束条件，建立一个线性系统，通过求解该线性系统，得到平面立体的三维信息。证明解释平面立体正轴测投影线图至少有4个自由度。

Creating Model of Planar Body from Line Drawing under Orthographically Axonometric Projection

In this paper, a new approach is proposed for reconstruction a three-dimensional planar object from its single line drawing depicting it under orthographically axonometric projection. The line drawing is supposed to be a nidden-drawn one. A new method with uniqueness for representing lines in two-dimensional projective plane and three-dimensional space is introduced. The coordinates relations between a line in three-dimension and its orthographically axonometric projection line in two-dimensional plane are put forward. It is also provided the coordinates relations when two lines are intersecting. On the basis of these coordinates relations, some new constraints about lines and planes have been proposed, and a linear system based on these constraints is eatablished. The three-dimensional information of a planar body can be obtained by solving the linear system from its orthographically axonometric projection. It is proved also that, in the interpretation of line drawing of a planar object under orthographically axonometric projection, there exist at least four degrees of freedom, the three of which are used to determine the location of the planar object, whereas the last one of which is used to determine its pose.