一类带两个形状参数的类四次三角Bézier曲线

A Class of Quasi-quartic Trigonometric Polynomial Bézier Curves with Two Shape Parameters

给出了带两个形状参数λ1,λ2的类四次三角多项式Bézier曲线。该曲线不仅具有与四次Bézier曲线类似的性质,而且无需有理形式即可精确表示圆、椭圆、抛物线等二次曲线弧以及高精度近似表示圆柱螺线等超越曲线。利用两个参数的不同取值能够局部或整体调控曲线的形状,并且可以从两侧逼近控制多边形。讨论了两段曲线G2和C4连续的拼接条件。实例表明,该曲线在造型设计方面具有较高的应用价值。

A class of quasi-quartic trigonometric polynomial Bézier curves with two shape parameters of λ1 and λ2 is presented.The trigonometric polynomial curves have the same featurs with traditional quartic Bézier curves,and it can represent exactly some quadratic curves such as the arc of a circle,an ellipse,or a parabola and some transcendental curves such as circular helix without using rational form.Its shape can be adjusted locally or totally through changing the value of the two parameters,and it can approach to the given control polygon from both sides.The G2 and C4 continuity condition of two pieces of curves is discussed.Examples are given to illustrate the new curve in model design.