| Summary: | The S-<i>λ</i> 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-<i>λ</i> curves and surfaces cannot be constructed by a single curve and surface, the explicit continuity conditions for G<sup>1</sup> connection of S-<i>λ</i> curves and surfaces are investigated in this paper. On the basis of linear independence and terminal properties of S-<i>λ</i> basis functions, the conditions of G<sup>1</sup> geometric continuity between two adjacent S-<i>λ</i> 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-<i>λ</i> 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.
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