基于直线解释正轴测投影图

A Method Convenient for Computer Interpretation of Orthographic Axonometric Drawing of “Plane” Body

建立了空间直线与其正投影的坐标关系，给出了空间直线从属于平面时直线坐标与平面坐标的约束关系，以及平行的直线与平面、平面与平面的坐标关系，据此提出了基于直线解释平面立体单幅正轴测投影线图的理论和方法。证明了平面立体正轴测投影线图至少有四个自由度。

In engineering, axonometric drawings usually belong to orthographic type; orthographic axonometric drawings are usually called line drawings for short. In engineering design, many bodies involved have boundary surfaces that are polygons; for convenience, we call these bodies “plane” bodies. Our research formed a part of a project supported by NNSFC (National Natural Science Foundation of China). We found in our research that it was more convenient to use information about lines rather than that about points for computer vision and CAD to interpret line drawings of “plane” body. Our mathematical derivation included many relationships among lines and planes. These relationships, eqs.(6) through(17), we could use to judge whether our interpretation of line drawings of a “plane” body was correct or not. We proved also that, in the interpretation of line drawing of a “plane” body, there existed at least four degrees of freedom.