The Approximation of Generalized Log-Aesthetic Curves with G

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

Abstract

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.
广义对数曲线的G逼近
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。
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