The S-λ model is one of the most useful tools for shape designs and geometric representations in computer-aided geometric design (CAGD), which is due to its good geometric properties such as symmetry, shape adjustable property. With the aim to solve the problem that complex S-λ curves and surfaces cannot be constructed by a single curve and surface, the explicit continuity conditions for G¹ connection of S-λ curves and surfaces are investigated in this paper. On the basis of linear independence and terminal properties of S-λ basis functions, the conditions of G¹ geometric continuity between two adjacent S-λ curves and surfaces are proposed, respectively. Modeling examples imply that the continuity conditions proposed in this paper are easy and effective, which indicate that the S-λ curves and surfaces can be used as a powerful supplement of complex curves and surfaces design in computer aided design/computer aided manufacturing (CAD/CAM) system.

中文翻译：

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S-λ曲线和曲面的G1连接的显式连续性条件

S- λ模型是计算机辅助几何设计（CAGD）中用于形状设计和几何表示的最有用工具之一，这是由于其良好的几何特性（例如对称性，形状可调整性）。为了解决复杂的S- λ曲线和曲面不能由单个曲线和曲面构成的问题，本文研究了S- λ曲线和曲面的G ¹连接的显式连续性条件。根据线性独立性和S- λ基函数的末端性质，两个相邻S- λ之间的G ¹几何连续性条件分别提出了曲线和曲面。建模实例表明，本文提出的连续性条件既简单又有效，这表明S- λ曲线和曲面可以用作计算机辅助设计/计算机辅助制造（CAD / CAM）系统。