This paper presents an approach for smoothly connecting multiple B-spline surfaces with exact G{sup}1 continuity using a finite number of check points along common boundaries. Sufficient and necessary G{sup}1 continuity conditions for connecting two neighbouring B-spline surfaces are first studied. A sufficient condition that needs less number of check points using linear tangent blending is further developed. The selection of the linear tangent blending parameters in case of multiple surfaces is also discussed. Several examples are presented for connecting two neighbouring surfaces, three surfaces meeting at a common corner and multiple surfaces of a computer mouse with exact G{sup}1 continuity conditions.
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