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1.引言 工业领域里的许多CAD/CAM系统,往往需要建立有关几何模型的连续、自动的数控刀具轨迹.例如,数控加工机床的刀具中心轨迹的计算,在纺织和制鞋业中,缝纫机械和自动化工业中铣床的数据控制,以及汽车外形设计,机器人的运动轨迹等都涉及到等距线和等距面的有效设计和计算[1,3,4,10] 一般地,具有给定函数类形式的曲线(面)的等距线(面),常常不能被精确地表示为同类函数形式.例如,有理函数形式的参数曲线(面)的等距线(面)通常不再是有理的曲线(面),而是参数 t的无理向量函数形式[3,4,10]… 相似文献
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Pythagorean Bézier速端曲线及其等距线 总被引:2,自引:0,他引:2
The Pythagorean Bézier hodograph curves are Bézier curves {x(t), y(t)}, whose hodograph (first-order parametric derivative) components satisfy the Phythagorean condition x'2(t) +y'2(t) = σ'(t) for some polynomial σ(t). For nth degree PB curve (n is odd), its offset curve is represented by rational Bézier curve with (2n - 1)th degree and arc length by polynomial. Specially, the properties of cubic PB curve are studied, its geometric features are discussed and its quasi-Hermite interpolating curve and GC1 composite cubic PB curve are also constructed. 相似文献
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