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Cubic trigonometric polynomial curves with a shape parameter. (English) Zbl 1069.42500

42A05Trigonometric polynomials, inequalities, extremal problems
41A15Spline approximation
42A15Trigonometric interpolation
65D17Computer aided design (modeling of curves and surfaces)
Full Text: DOI
[1] Hoschek, J.; Lasser, D.: Fundamentals of computer aided geometric design. (1993) · Zbl 0788.68002
[2] Han, X.: Quadratic trigonometric polynomial curves with a shape parameter. Computer aided geometric design 19, 503-512 (2002) · Zbl 0998.68187
[3] Han, X.: Piecewise quadratic trigonometric polynomial curves. Math. comp. 72, 1369-1377 (2003) · Zbl 1072.65019
[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. comp. Math. 3, 405-424 (1995) · Zbl 0925.65251
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[7] Lyche, T.; Winther, R.: A stable recurrence relation for trigonometric B-splines. J. approx. Theory 25, 266-279 (1979) · Zbl 0414.41005
[8] Lyche, T.; Schumaker, L. L.: Quasi-interpolants based on trigonometric splines. J. approx. Theory 95, 280-309 (1998) · Zbl 0912.41008
[9] Peña, J. M.: Shape preserving representations for trigonometric polynomial curves. Computer aided geometric design 14, 5-11 (1997) · Zbl 0900.68417
[10] Schoenberg, I. J.: On trigonometric spline interpolation. J. math. Mech. 13, 795-825 (1964) · Zbl 0147.32104
[11] Sánchez-Reyes, J.: Harmonic rational Bézier curves, p-Bézier curves and trigonometric polynomials. Computer aided geometric design 15, 909-923 (1998) · Zbl 0947.68152
[12] Walz, G.: Some identities for trigonometric B-splines with application to curve design. Bit 37, 189-201 (1997) · Zbl 0866.41010
[13] Walz, G.: Trigonometric Bézier and stancu polynomials over intervals and triangles. Computer aided geometric design 14, 393-397 (1997) · Zbl 0906.68167