Quadratic trigonometric polynomial curves concerning local control

With a non-uniform knot vector and two local shape parameters, a kind of piecewise quadratic trigonometric polynomial curves is presented in this paper. The given curves have similar construction and the same continuity as the quadratic non-uniform 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 non-uniform 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.