摘要
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.
出处
《计算机研究与发展》
EI
CSCD
北大核心
2002年第11期1423-1428,共6页
Journal of Computer Research and Development
基金
中国科学院"百人计划"项目
中国科学院知识创新工程"数字地球基础理论问题研究"项目基金资助 ( KZCX2 -312 )
