广义对数曲线的G逼近

IF 0.7 Q2 MATHEMATICS
Diya’ J. Albayari, R. Gobithaasan, K. Miura
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引用次数: 0

摘要

在计算机辅助设计(CAD)中,对曲线的要求之一是具有单调曲率轮廓的曲线。广义对数美观曲线(GLACs)是一类具有单调曲率轮廓的美观曲线。然而,我们不能直接在CAD系统中实现GLAC,因为它是一种超越形式的形式。在本文中,我们使用具有两个形状参数的三次三角bsamzier (t - bsamzier)曲线来近似具有G2连续性的GLAC。最后的近似公式继承了GLAC的形状参数,而t - bsamzier的形状参数被用来满足G2约束。数值结果表明,该算法能够在(至少)两次迭代中在给定公差范围内逼近GLAC。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Approximation of Generalized Log-Aesthetic Curves with G
One of the requirements of curves in computer-aided design (CAD) is a curve with monotonic curvature profiles. Generalized log-aesthetic curves (GLACs) comprise a family of aesthetic curves which possesses a monotonic curvature profile. However, we cannot directly implement GLAC in CAD systems since it is in the form of a transcendental form. In this paper, we used cubic trigonometric Bézier (T-Bézier) curves with two shape parameters to approximate GLAC with G2 continuity. The final approximation formula inherits the shape parameters of GLAC whereas T-Béziers’ shape parameters are utilized to satisfy G2 constraints. Numerical results indicate that the proposed algorithm is capable of approximating GLAC within the given tolerance in (at least) two iterations.
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