Abstract：In order to achieve high level of smooth blending between the free form curves and surfaces in relatively simple conditions and easy shape adjustment of the curves and surfaces without changing their control vertices, a set of rational trigonometric Bézier basis functions with multiple shape parameters are constructed. Based on these basis functions, the rational trigonometric Bézier curves and surfaces with multiple shape parameters are defined, and the conditions for smooth joining of these curves and surfaces are derived. Following the above conditions of blending, the piecewise composite rational curves and surfaces with multiple shape parameters are defined, which automatically meet with the higher order continuity. The results of numerical examples show the effectiveness of the method.
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2016, Vol. 43 
