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中文摘要：
平面与二次曲面的截切组合是机械零件常用的设计手段．在分析斜截切二次曲面在三视图中的投影特性的基础上，提出识别和重建这类曲面的算法．首先根据曲面的投影特性在三视图中检索斜截切曲面的投影痕迹；然后以其作为引导，初步判定曲面类型，深度优先搜索进一步识别斜截切二次啮面；再根据投影边的二维信息计算未截切曲面的几何参数，并通过未截切曲面与截平面求交获取截切曲线；最后构造斜截切曲面的拓扑结构，生成三维曲面．该算法可以识别和重建空间任意位置的斜截切二次曲面，拓展了重建算法的形体覆盖域．文中算法目前已运用到形体重建原型系统中，实验结果证明了其有效性．
英文摘要：
Quadric surfaces are commonly adopted in mechanical parts as boundary surfaces and they might be intersected by planes in skew positions. This paper proposes an algorithm to recognize and reconstruct the skewed quadric surfaces based on the analysis of their projection features. The proposed algorithm first detects their intersections with the adjacent planes according to their projection traces on three orthographic views, then retrieves the skewed quadric surfaces and calculates their geometry. The precise intersection lines between the complete quadric surfaces and the adjacent planes are then determined and the topologies of the surfaces are constructed in the 3D object space. The proposed approach could handle the skewed quadric surfaces in arbitrary positions, which extends the domain of shape reconstruction based on engineering drawings. The method has been implemented in a solid reconstruction system, and experimental results demonstrate its usability.
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