工程中同坡曲面的计算机辅助几何设计

• 作 者: 李军成 宋来忠
• 机 构: 湖南人文科技学院数学系,湖南娄底,417000;三峡大学理学院,湖北,宜昌,443002
• 出 处: 武汉大学学报（工学版）
• 发表日期: 2010年1期
• 关键词: identical slope gradient surface cubic parametric curve interpolation envelope s

当同坡曲面的导线方程有准确表达式时,可以很方便地建立该曲面的参数方程,但在实际工程中,导线方程的准确表达式是很难得到的,往往只知道导线通过一列测量数据点.针对这个问题,给出了一种构造实际工程中同坡曲面的方法,该法首先利用三次参数曲线插值原理,根据测量所得的数据点构造出满足二阶连续的插值曲线,并将该插值曲线近似作为同坡曲面的导线,然后再从同坡曲面的形成原理人手,建立了该类坡面的参数方程,为同坡曲面的计算机几何设计奠定了理论基础.最后通过实例表明,该方法可行且效果较好,符合实际工程的要求,“,”The equation of identical slope gradient surface could be constructed expediently when the exact expression of lead curve is known. But in practical engineering, the exact expression of lead curve is hard to obtain; and only some measured data points are given. For solving that problem, a method of constructing the identical slope gradient surface in engineering is presented. Firstly, cubic parametric interpolation curve with second order continuous is constructed according as the measured data points, which is regarded as the lead curve. Then, the parametric equation of identical slope gradient surface is constructed based on the forming principle of that surface, which forms the basis for computer aided geometric design of identical slope gradient surface. Lastly, some examples are given to show that the method is feasible and effectual, which accord with the practical engineering.