Abstract: Aiming at difficult sorting freeform surfaces,a B-spline surface classification method based on isoparametric curves was presented.By using the invariants of Cartesian coordinate transformation of conic sections and the fitting of plane cubic curves,the types of plane isoparametric curves were identified.For plane cubic and higher order curves,the number of knee point was attached to subdivide curve type.For the plane curve family of surfaces as one of U and V isoparametric curve groups,the spatial positional relationship between plane isoparametric curve families was proposed to determine the generatrix direction of extrusion surface curves and the axis of rotation surface curves,and the spatial curves was identified as extrusion or rotation surface curves.The unidentified rest curves were fitted as cylinder (cone) surface curves by least square method.The parallel,coaxial,cointersection,coplane,public parallel plane,public perpendicular plane,cointersection line,public tangent cylindrical and general spatial relations were used to define the internal geometric relations among the isoparametric curves in one group.Public cointersection point,public direction vector,public intersection axis and general spatial relations were used to define the geometric relations between groups.The sorting,revised and encoding method of isoparametric curve groups were presented,which realized B-spline surface classification.The examples of typical surface codes were given to verify the effectiveness of the proposed method.

Key words: B-spline surface classification, isoparametric curves, similar part retrieval, freeform surfaces

摘要： 针对自由曲面难以分类的问题,提出一种基于等参数线的B样条曲面类型识别方法。利用平面二次曲线存在直角坐标变换下的不变量以及平面三次曲线的拟合识别平面等参数线类型,对于拟合为平面三次及以上的曲线,通过添加拐点数量来细分曲线类型。对于U向和V向等参数线族之一为平面曲线族的空间等参数线族,提出以平面等参数线族的空间位置关系确定柱面曲线的母线方向和回转面曲线的回转轴线,将空间曲线识别为柱面曲线和回转面曲线,通过最小二乘法将还不能识别的空间等参数线进行圆柱(锥)面拟合。以共面、共平行平面、同轴、共垂直平面、共交点、点在线上、共交线、共相切圆柱面和空间一般关系定义等参数线族的内部几何位置关系,以公共交点、公共方向矢量、公共轴线和空间一般关系定义等参数线族之间的几何位置关系,并进一步提出等参数线族的排序、修正和编码方法,通过等参数线结构码实现B样条曲面的类型识别。最后给出了典型编码曲面的实例,通过实例验证了所提方法的有效性。

关键词: B样条曲面类型识别, 等参数线, 相似零件查找, 自由曲面