关键词: 测地B样条, 过渡曲线, 网格曲面, 几何连续, 测地线延长线

Abstract: 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 nonadjacent 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 G1 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 technology, and also had a strong adaptability even for the surfaces with sharp features.

Key words: geodesic B-spline, transition curve, mesh surface, geometric continuity, extension of geodesics