曲面实体造型中曲线和曲面交点的求解

求交是曲面实体造型系统中影响拼合算法效率和稳定性的重要因素，而求交算法又是和曲面的几何表示密切相关的。ＮＵＲＢＳ虽然能统一表示所有曲面，但却给二次曲面的求交带来了不必要的复杂性。二次曲面经常在机械零件的设计中被用来描述轴、孔、槽等几何特征，因此它们的求交算法应具有高精度、高效率和高稳定性。为此，对一种实用的二次曲面表示方法——几何法进行了深入研究后，给出了构成二次曲面轮廓的几种二次曲线和空间四次曲线与二次曲面交点的求法。

Research on the Intersection Issue in Solid Modeling Based on Curved Surfaces

The intersecting is an important factor which influences the efficiency and the reliability of Boolean algorithms in solid modeling based on curved surfaces, and the intersecting algorithm is closely related to the geometric representation of curved surfaces. Although curved surfaces can be commonly represented with NURBS, unnecessary complexities are caused for the intersecting of quadric surfaces, which are frequently used to describe geometric features of shafts, holes and grooves etc. in mechanical part designing. Therefore, intersecting algorithms of them are required to have higher accuracy, higher efficiency and higher robustness. For this reason, we introduce a practical representation of quadric surfaces, and on the basis of that, algorithms of intersection points between quadric surfaces and several conics, fourth degree nonplanar space curves constructing their boundaries are developed.