Trigonometric λ-Bézier Curves with Shape Parameter
To handle the lack of local adjustability and low accuracy in expressing conic curves of traditional Bézier curves , a trigonometric λ-Bézier curve with n(n≥2) order shape parameter was constructed. The value range of shape parameters of each order curve remains unchanged to reduce the difficulty. A λ-Bernstein basis function was constructed in trigonometric polynomial space by means of recursion, and the important properties of endpoint and symmetry of this basis function were discussed. Then, the n(n≥2)λ-Bézier curve was defined by this basis function. In addition, the influence of different shape parameters on the shape of the curve and the splicing conditions of the curve were discussed. The curve can achieve G2 splicing under certain conditions. Finally,λ-Bézier surfaces in tensor product form and their properties were given. The example showed that this curve overcame the lack of local adjustability of traditional Bézier curve, and can accurately express conic curves such as circular arc and parabola.
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