Abstract
Cubic trigonometric polynomial curves with a shape parameter are presented in this paper. The trigonometric polynomial curves are C 2 continuous and G 3 continuous with a non-uniform knot vector. With a uniform knot vector, the trigonometric polynomial curves are C 3 continuous for the shape parameter λ≠1 and C 5 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.
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