Two Kinds of B-Spline-Type Trigonometric Curves

Two kinds of trigonometric spline bases are constructed in this paper. Based on these bases, two kinds of trigonometric spline curves are defined. As each piece of these trigonometric spline curves are generated by three consecutive control points, these curves retain many properties of the quadratic B-spline curves, but they have better continuity than the quadratic B-spline curves. For equidistant knots, they have C³ continuity under normal conditions, and the second kind of curve has C⁵ continuity under special conditions. Besides, these trigonometric spline 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 parameters are also constructed and they have most properties of the corresponding trigonometric spline curves.