Two Kinds of Curves with Shape Parameters

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 curve,but they have a higher order of continuity than the quadratic B-spline curve.For equidistant knots,these curves are C3continuous,and they are C5 continuous under special conditions.The shape parameters of the curves have an explicit geometric meaning.The curves approach the control polygon as the parameter increases.Besides,these curves are closer to the control polygon than the quadratic B-spline curve when the shape parameters are under special conditions.By using the tensor product method,the two kinds of curves can be extended to surfaces.The surfaces have a higher order of continuity than the bi-quadratic B-spline surfaces.