Three Kinds of Curves That Shape Can Adjust

Three kinds of trigonometric bases are constructed in this paper. Based on these bases, three kinds of trigonometric spline curves with shape parameter are defined. As each piece of the curves is generated by three consecutive control points, they retain many properties of the quadratic B-spline curves, but they have higher order continuity than the quadratic B-spline curves. For equidistant knots, they have C² continuity under normal conditions, and they have C³ continuity under special conditions. Besides, the curves are closer to the control polygon than the quadratic B-spline curves when the shape parameters under special conditions. In the last, the trigonometric spline surfaces with shape parameter are constructed. They have most properties of the corresponding trigonometric spline curves.