Planar G2 transition between two circles with a fair cubic Bezier curve
Planar G2 transition between two circles with a fair cubic Bezier curve
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DOI：
10.1016/s0010-4485(99)00073-1
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发表时间：
1999-12-01
影响因子：
4.3
通讯作者：
Meek, DS
中科院分区：
文献类型：
--
作者：
Walton, DJ;Meek, DS
消费产品，如乒乓球拍，可以通过混合圆圈来设计。为了在视觉上令人满意，希望混合物的曲率是连续的，而不是无关的曲率极值。圆与圆之间曲率逐渐增大或减小的缓和曲线在公路和铁路设计中也起着重要作用。最近发展了平面三次和毕达哥拉斯速度图五次螺线段，并演示了如何将这些段两两组合形成适合G(2)混合的过渡曲线。现在表明，一条三次曲线可以用于混合或作为过渡曲线，并保证曲率连续性和光顺性。使用一条曲线而不是两个线段的好处是，设计者和实施者需要关心的实体更少。(C)2000爱思唯尔科学有限公司。保留所有权利。
Consumer products such as ping-pong paddles, can be designed by blending circles. To be visually pleasing it is desirable that the blend be curvature continuous without extraneous curvature extrema. Transition curves of gradually increasing or decreasing curvature between circles also play an important role in the design of highways and railways. Recently planar cubic and Pythagorean hodograph quintic spiral segments were developed and it was demonstrated how these segments can be composed pairwise to form transition curves that are suitable for G(2) blending. It is now shown that a single cubic curve can be used for blending or as a transition curve with the guarantee of curvature continuity and fairness. Use of a single curve rather than two segments has the benefit that designers and implementers have fewer entities to be concerned with. (C) 2000 Elsevier Science Ltd. All rights reserved.