Creating Model of Planar Body from Line Drawing under Orthographically Axonometric Projection
从单幅正轴测投影线图建立平面立体的模型

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.