基于能量法光顺的自由曲线快速算法

Rapid Algorithm Based on Energy of Curve Segments Passing through Given Data Points

大多过型值点的曲线造型都是采用反求算法。当型值点数增加或实时设计时,随着型值点的增加,会导致反求方程组的阶数增加,当增加到一定程度,产生的计算量会太大。根据能量法光顺原理,提出了一种曲线形式作为曲线造型的基础,曲线过型值点,达到G2光滑,光顺性也很好,并且无须进行反求运算,有计算量少、速度快的特点。

The construction of curve segments passing through the given data points is very important in CAD. In most ACD software the construction of curve segments passing through the given data points is constructed with converse computing. In this paper a new function of curve segments is presented to construct piecewise curve segments passing through the given data points in real-time, maintaining G^2 continuity and satisfying fairness criterion, And an algorithm based on energy need not converse the control points also he presented.