Quadratic Trigonometric Spline Curves with Multiple Shape Parameters

Quadratic trigonometric spline curves with multiple shape parameters are presented in this paper. Analogous to the cubic B-spline curves, each trigonometric spline curve segment is generated by four consecutive control points. The trigonometric spline curves with a non-uniform knot vector are C¹ continuous. With a uniform knot vector, the trigonometric spline curves are C continuous when all shape parameter lambda_i =1. Taking different values of the shape parameters, one can globally or locally adjust the shapes of the curves, so that the trigonometric spline 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 spline curves also can represent ellipse and generate a family of ellipse with the same control points. A quadratic trigonometric Bezier curves are also introduced as a special case of the given trigonometric spline curves.