Quadratic trigonometric polynomial curves concerning local control. (English) Zbl 1083.65010

Summary: With a nonuniform knot vector and two local shape parameters, a kind of piecewise quadratic trigonometric polynomial curves is presented. The given curves have similar construction and the same continuity as the quadratic nonuniform B-spline curves. Two local parameters serve to local control tension and local control bias, respectively, in the curves. The changes of a local shape parameter will only affect two curve segments. The given curves can approximate the quadratic nonuniform rational B-spline curves and the quadratic rational Bézier curves well for which the relations of the local shape parameters and the weight numbers of the rational curves are described. The trigonometric polynomial curves can yield tight envelopes for the quadratic rational Bézier curves. The given curve also can be decreased to linear trigonometric polynomial curve which is equal to a quadratic rational Bézier curve and represents ellipse curve.


65D17 Computer-aided design (modeling of curves and surfaces)
65D07 Numerical computation using splines
42A05 Trigonometric polynomials, inequalities, extremal problems
Full Text: DOI


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