Quadratic trigonometric polynomial curves with a shape parameter

Authors:
Xuli Han
Affiliations:
Department of Applied Mathematics and Applied Software, Central South University, Changsha, 410083, PR China
Venue:
Computer Aided Geometric Design
Year:
2002

Citing 6
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Abstract

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 Cl 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.