带弧长约束条件的细分曲线设计

Subdivision Gurve Design with Arc Length Constraint

为了精确表示目标物体的形状信息,满足弧长、面积和体积等条件的带几何约束的曲线曲面设计成为CAD中常见的问题。用细分方法解决带弧长约束条件的曲线设计问题,通过调整细分中的自由参数来控制细分控制多边形的累加弦长(极限情况下为曲线的弧长)。给出了该问题的解存在的一个充分条件,讨论了弧长的若干性质。同时在弧长约束下,给出了一种生成精确圆周的算法,并且讨论了参数的变化情况。数值试验结果表明了算法的有效性。

Curves and surfaces design with geometric constraint such as arc length, area and volume is a common problem in CAD to precisely represent the shape of objects. In this paper the problem of curve design with arc length constraint by 4-point interpolatory subdivision is discussed by adjusting the free parameter of the 4-point interpolatory subdivision. A sufficient condition for the feasibility of this problem is given, some properties of arc length are discussed. With the arc length constraint, an algorithm of generating accurate circle is given, and discussion about the parameter is also given in this paper. Numerical tests illustrate the efficiency of our algorithms.