Computer graphics and geometric modeling using Beta-splines
Computer graphics and geometric modeling using Beta-splines
Multivariate trigonometric B-splines
Journal of Approximation Theory
Multiple-knot and rational cubic beta-splines
ACM Transactions on Graphics (TOG)
ACM Transactions on Graphics (TOG)
A rational cubic spline with tension
Computer Aided Geometric Design
The NURBS book
Trigonometric Be´zier and Stancu polynomials over intervals and triangles
Computer Aided Geometric Design
Shape preserving representations for trigonometric polynomial curves
Computer Aided Geometric Design
Local Control of Bias and Tension in Beta-splines
ACM Transactions on Graphics (TOG)
NURBS for Curve and Surface Design
NURBS for Curve and Surface Design
Quadratic trigonometric polynomial curves with a shape parameter
Computer Aided Geometric Design
Piecewise quadratic trigonometric polynomial curves
Mathematics of Computation
Computer Aided Geometric Design
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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 Bezier 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 Bezier curves. The given curve also can be decreased to linear trigonometric polynomial curve which is equal to a quadratic rational Bezier curve and represents ellipse curve.