Developable Bezier-like surfaces with multiple shape parameters and its continuity conditions
Developable Bezier-like surfaces with multiple shape parameters and its continuity conditions
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具有多个形状参数的可展贝塞尔曲面及其连续性条件
DOI：
10.1016/j.apm.2017.01.043
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发表时间：
2017-05-01
影响因子：
5
通讯作者：
Wei, Guo
中科院分区：
文献类型：
--
作者：
Hu, Gang;Cao, Huanxin;Wei, Guo
为了解决可展曲面的形状调整和形状控制问题，提出了两种多形状参数类Bezier可展曲面计算机辅助设计的直接显式方法.首先，以构造多形状参数的Bezier型曲线为目的，提出了一类新的Bernstein型基函数，它是经典伯恩斯坦基函数的推广.然后，根据三维射影空间中点平面对偶的重要思想，利用Bernstein型基函数的控制平面设计了具有多个形状参数的可展Bezier型曲面。可展类Bezier曲面的形状可以通过改变其三个形状参数来调整。当形状参数取不同的值时，可以构造出一族可展的类Bezier曲面，它们保持了Bezier曲面的特征。最后，针对工程中大多数复杂可展曲面往往不能用单个可展曲面构造的问题，给出了相邻可展类Bezier曲面间G（1）连续、Farin-Boehm G（2）连续和G（2）Beta连续的充要条件.此外，还讨论了可展类Bezier曲面的一些性质及其应用。建模实例表明，该方法简单有效，通过调整可展曲面的位置和形状，极大地提高了工程外观设计中的问题求解能力。(C)2017爱思唯尔公司All rights reserved.
To solve the problems of shape adjustment and shape control of developable surfaces, we propose two direct explicit methods for the computer-aided design of developable Bezier-like surfaces with multiple shape parameters. Firstly, with the aim of constructing Bezier-like curves with multiple shape parameters, we present a class of novel Bernstein-like basis functions, which is an extension of classical Bernstein basis functions. Then, according to the important idea of duality between points and planes in 3D projective space, we design the developable Bezier-like surfaces with multiple shape parameters by using control planes with Bernstein-like basis functions. The shape of the developable Bezier-like surfaces can be adjusted by changing their three shape parameters. When the shape parameters take different values, a family of developable Bezier-like surfaces can be constructed and they retain the characteristics of Bezier surfaces. Finally, in order to tackle the problem that most complex developable surfaces in engineering often cannot be constructed by using a single developable surface, we derive the necessary and sufficient conditions for G(1) continuity, Farin-Boehm G(2) continuity and G(2) Beta continuity between two adjacent developable Bezier-like surfaces. In addition, some properties and applications of the developable Bezier-like surfaces are discussed. The modeling examples show that the proposed methods are effective and easy to implement, which greatly improve the problem-solving abilities in engineering appearance design by adjusting the position and shape of developable surfaces. (C) 2017 Elsevier Inc. All rights reserved.