Cubic trigonometric polynomial curves with a shape parameter Original Research Article

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.