Cubic trigonometric polynomial curves with a shape parameter

Authors:
Xuli Han
Affiliations:
Department of Applied Mathematics, Central South University, Changsha, 410083, PR China
Venue:
Computer Aided Geometric Design
Year:
2004

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Abstract

Cubic trigonometric polynomial curves with a shape parameter are presented in this paper. The trigonometric polynomial curves are C2 continuous and G3 continuous with a non-uniform knot vector. With a uniform knot vector, the trigonometric polynomial curves are C3 continuous for the shape parameter λ ≠ 1 and C5 continuous for λ = 1. With the shape parameter, the trigonometric polynomial curves can be close to the cubic B-spline curves or closer to the given control polygon than the cubic B-spline curves. The trigonometric polynomial curves also can be decreased to quadratic trigonometric polynomial curves which can represent ellipses. The trigonometric Bézier curve and trigonometric polynomial interpolation are also discussed.