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


MSC:

42A05 Trigonometric polynomials, inequalities, extremal problems
41A15 Spline approximation
42A15 Trigonometric interpolation
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] 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
[6] Lyche, T, A Newton form for trigonometric Hermite interpolation, Bit, 19, 229-235, (1979) · Zbl 0411.65005
[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
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