中文摘要：

将欧氏空间中两非均匀B样条曲线间G1连续条件拓展到曲面空间，提出一种构造网格曲面上两相离曲线光滑过渡曲线的方法。网格曲面上的曲线采用测地B样条表示，具有与欧氏空间中传统B样条相一致的明确数学模型。基于三角网格模型的拓扑邻接关系，提出一种网格曲面上测地线的延长线离散逼近算法，以此为基础，建立两测地B样条曲线间Gl连续条件，将边界连续条件转化为控制顶点的位置约束，从而构建两曲线间的光滑过渡曲线。试验结果表明，所提方法健壮、高效，不依赖于参数化和投影技术，即使对于具有尖锐特征的曲面亦有很强的适应性。

英文摘要：

G1 continuous conditions of two non-uniform B-spline curves in the Euclidean space, were extended to the curved surface space, and then a method, which was the construction of smooth transition curve between nonadja- cent curves on mesh surface, was put forward. The curves on the mesh surface, represented by geodesic B-spline curves, had definite mathematical models consistent with traditional B-spline curves in Euclidean space. Based on the topological adjacency relations of triangular mesh model, a novel discrete approximation algorithm of the extension geodesic line in the mesh surface was proposed, and then G~ continuous conditions of two geodesic B-spline curves were established, at the same time, the boundary continuity conditions were translated into the position constraint of the control vertex, thus smooth transition curve between two curves were formed. Experimental results showed that the proposed method was robust, efficient, and without depending on the parameterization and projection technolo- gy, and also had a strong adaptability even for the surfaces with sharp features.