基于三视图的曲面体重建技术

RECONSTRUCTION OF CURVILINEAR 3D OBJECTS FROM ORTHOGRAPHIC VIEWS

根据空间二次曲线的投影特征 ,首先利用“五点法”分两步来构造投影曲线 ,得到投影二次曲线的几何参数表达式 ,然后应用“点对应匹配法”由各视图相应的投影曲线构造空间二次曲线的坐标式参数方程 ,并同时构造出空间曲线边的支撑平面 ,从而建立与三视图相对应的曲面体线框模型 .最后 ,提取线框模型中的面信息 ,并根据二流形体的性质和莫比乌斯法则 (Moebius rule)以及正投影规律 ,对候选面进行组合判定 ,将实有面进行装配 ,得到重建结果的实体模型 .这种方法将处理对象拓展到了任意投影方位下的二次曲线 .

A method for reconstructing solids with quadric surface from orthographic views is presented. First, the wire-frame model corresponding to the three orthographic views is constructed. In order to generate 3D conic edges in the wire-frame model, a five-point method is firstly utilized to obtain the algebraic representations of all 2D-projection curves in each view, and then all algebraic forms are converted to the corresponding geometric forms analytically. The locus of a 3D conic edge can be derived from the geometric forms of the relevant conic curves in three views, and the relationship between a 3D conic and its orthographic projections is established. In addition, the support plane of each 3D conic edge is created. Finally, all possible faces are searched within the wire-frame model, and all true faces are found to assemble the final solids according to the properties of 2-manifolds, Moebius rule and the characteristics of orthographic projections. The method extends the range of objects to be reconstructed and imposes no restriction on the axis of the quadric surface.