Quadratic trigonometric polynomial curves with a shape parameter. (English) Zbl 0998.68187

Summary: Quadratic trigonometric polynomial curves with a shape parameter are presented in this paper. Analogous to the quadratic B-spline curves, the trigonometric polynomial curves are constructed with three consecutive control points for each curve segment and are \(C^{1}\) continuous with a non-uniform knot vector. With the shape parameters, the trigonometric polynomial curves can yield tight envelopes for the quadratic B-spline curves and can be closer to the given control polygon than the quadratic B-spline curves. The trigonometric polynomial curves also can be decreased to linear trigonometric polynomial curves which can represent ellipses.


68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
41A15 Spline approximation
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