| The shape of cubic B-spline curve is fixed to its control polygon.In addition,it cannot describe the conic section besides the parabola.In order to overcome disadvantages,a set of algebraic-trigonometric blending spline basis,which enjoys many nice properties,was constructed. A kind of new curve,which structure was similar to the classical cubic B-spline curve,was defined.The new curve not only inherited the major advantages of the cubic B-spline curve,but also enjoyed shape adjustability,and it exactly expressed circle,ellipse, parabola,sine curve,cosine curve,cycloid and cylinder helix.For equidistant knots,the new curve was C2continuous,and it achieved C3 continuity when taking special shape parameter.In addition,how to choose control points to make the new curve tangent to a given control polygon was discussed. |
