摘要
本文给出了带形状参数的类四次三角多项式Bézier曲线。由五个控制顶点生成的曲线不仅具有类似于四次Bézier曲线的诸多性质,而且其形状可由一个参数进行调节,使得该曲线具有更强的表现能力。参数有明确的几何意义:参数越大,曲线越逼近控制多边形,具有比四次Bézier曲线更好的逼近性。曲线无需有理形式即可精确表示圆、椭圆、抛物线等二次曲线弧。为便于自由曲线的设计,还讨论了两段曲线的拼接性,并给出了曲线G2和C3连续的拼接条件。应用实例表明,该曲线在计算机辅助几何设计中具有较高的应用价值。
A class of quasi-quartic trigonometric polynomial Bezier curves with a shape parameter is presented. The curve is controlled by five points, and it has a lot of similar characteristics with the traditional quartic Bezier curve, and its shape can be adjusted by a parameter, which makes the curve feature more powerful expression ability. The shape parameter affects the property of geometry, the larger is the parameter, and the more of the curve approaches the control polygon, therefore, the trigonometric polynomial curve with the shape parameter can be close to the given control polygon than the quartic Bezier curve. The new curve can represent exactly the arc of circle, arc of ellipse, arc of parabola and other quadratic curves without using a rational form. For designing free curves, the G2 and C3 continuity condition of two-piece curves are also discussed. The modeling examples illustrate that the new curve has a high application value for computer aided geometric design.
出处
《计算机工程与科学》
CSCD
北大核心
2011年第3期77-81,共5页
Computer Engineering & Science
基金
湖南人文科技学院青年基金项目(2010QN09)
