一类二次TC-Bézier曲线的研究

Study on a class of quadratic TC-Bézier curve

定义了一组带有两个形状参数的三角基函数,并基于四点定义了一类二次TC-Bézier曲线,分析了基函数及曲线的性质。在-1≤λ1,λ2≤1范围内,通过参数变化可以很方便的调控曲线的形状,并且可以精确表示直线段、椭圆(圆)弧及抛物线。最后讨论了曲线在C1连续下的拼接及其应用,实例表明,定义的曲线更有利于曲线设计。

A class of trigonometric basis functions with two shape control parameters is presented, and the corresponding trigonometric curve with two shape parameters is defined, the property of basis functions and TC-Bézier curve is also analyzed. When -1≤λ1,λ2≤1, the shape of curve can be controlled easily by changing with parameters. The straight line segment, ellipse （circular） and parabola are can be represented exactly by TC-Bézier curve. At last, the C^1 continuous joint of curve pieces is discussed and the example illustrates the TC-Bézier curve is useful in curve design.