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To adjust the shape of the curve conveniently, we exploit a class of shape-controlled planar parametric curve with shape parameters in this paper. The proposed curve inherits the properties of the classic cubic Ferguson curves, what’s more, the shape of the curve can be adjusted as desired by modifying
the shape parameters. A suitable choice of shape parameters can make the quasi-Ferguson curve satisfy C2 continuous. Besides, the most smoothness and the shortest arc length of the quasi- Ferguson curve are obtained by solving the optimal shape parameters.
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