具有精确等距线的Bézier曲线

Bezier Curve With Rational Offset

等距线（面）问题是武器装备先进制造技术的关键技术之一。通过引入数论中的Pythagorean方法，得到了一类具有精确等距线的Bézier曲线，即速端曲线满足Pythagorean条件的Bézier曲线，称之为Pythagorean Bézier速端曲线 (PB曲线)。建立了显示表示结构，并分析了它的自由度。对于n次(n为奇数)PB曲线，得到了以(2n-1)次有理曲线精确表示的等距线和多项式形式的弧长表达式。算例表明,PB曲线能够广泛的应用于武器装备先进制造技术的几何造型中。

Offset technique is key technique in advanced manufacture of weapon equipment. A family Bézier curves with rational offset is obtained by Pythagorean method, i.e. Pythagorean Bézier hodograph curves. An explicit representation of PB curves is established and its degree of freedom is analyzed. For n (n is odd) degree PB curve, its offset curve is represented by rational Bézier curve with (2n-1) degree and arc length by polynomial. The examples illustrate PB curve is an effective method for geometric modeling in advanced manufacture of weapon equipment.