Four Kinds of Trigonometric Spline Curves with Shape Parameter

Four kinds of trigonometric spline curves with shape parameter are presented in this paper. The trigonometric spline curves are constructed with three consecutive control points for each curve segment. The given curves posses many properties of the quadratic B-spline. Meanwhile, they have many better properties than the quadratic B-spline curve. The given curves have continuity with equidistant knot vector, and they have continuity when choosing special parameters. The shape parameter can adjust the given curvespsila shape with the same control polygon. With the increase of the shape parameter, the trigonometric spline curves approximate to the control polygon. The given curves can be closer to the control polygon than the quadratic B-spline curve.