The cubic trigonometric Bézier curve with two shape parameters. (English) Zbl 1163.65307

Summary: A cubic trigonometric Bézier curve analogous to the cubic Bézier curve, with two shape parameters, is presented in this work. The shape of the curve can be adjusted by altering the values of shape parameters while the control polygon is kept unchanged. With the shape parameters, the cubic trigonometric Bézier curves can be made close to the cubic Bézier curves or closer to the given control polygon than the cubic Bézier curves. The ellipses can be represented exactly using cubic trigonometric Bézier curves.


65D17 Computer-aided design (modeling of curves and surfaces)
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[1] Hoschek, J.; Lasser, D., Fundamentals of computer aided geometric design, (1993), AK Peters Wellesley, MA, translated by L.L. Schumaker · Zbl 0788.68002
[2] Hong, H.; Schicho, J., Algorithms for trigonometric curves, J. symbolic comput., 26, 279-300, (1998) · Zbl 0926.65018
[3] Han, X., Cubic trigonometric polynomial curves with a shape parameter, Comput aided geom. design, 21, 535-548, (2004) · Zbl 1069.42500
[4] Koch, P.E., Multivariate trigonometric B-splines, J. approx. theory, 54, 162-168, (1988) · Zbl 0671.41006
[5] Koch, P.E.; Lyche, T.; Neamtu, M.; Schumaker, L.L., Control curves and knot insertion for trigonometric splines, Adv. comput. math., 3, 405-424, (1995) · Zbl 0925.65251
[6] Lyche, T.; Winther, R., A stable recurrence relation for trigonometric B-splines, J. approx. theory, 25, 266-279, (1979) · Zbl 0414.41005
[7] Lyche, T.; Schumaker, L.L., Quasi-interpolants based on trigonometric splines, J. approx. theory, 95, 280-309, (1998) · Zbl 0912.41008
[8] Peña, J.M., Shape preserving representations for trigonometric polynomial curves, Comput aided geom. design, 14, 5-11, (1997) · Zbl 0900.68417
[9] Schoenberg, I.J., On trigonometric spline interpolation, J. math. mech., 13, 795-825, (1964) · Zbl 0147.32104
[10] Sáchez-Reyes, J., Harmonic rational Bézier curves, p-Bézier curves and trigonometric polynomials, Comput aided geom. design, 15, 909-923, (1998) · Zbl 0947.68152
[11] Walz, G., Some identities for trigonometric B-splines with application to curve design, Bit, 37, 189-201, (1997) · Zbl 0866.41010
[12] Walz, G., Trigonometric Bézier and Stancu polynomials over intervals and triangles, Comput aided geom. design, 14, 393-397, (1997) · Zbl 0906.68167
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