Two Kinds of Trigonometric Spline Curves with Shape Parameter

Two 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 curve. Meanwhile, they have many better properties than the quadratic B-spline curve. The first kind of curve is continuous with equidistant knot vector, and it is continuous with special shape parameter. The second kind of curve is continuous with equidistant knot vector. The shape parameter can adjust the given curves´ 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. In the last, the trigonometric spline surfaces with shape parameter are also constructed and they have most properties of the corresponding trigonometric spline curves.