Lines of Curvature for Log Aesthetic Surfaces Characteristics Investigation

Gobithaasan, R. U.; Teh, Yee Meng; Miura, Kenjiro T.; Ong, Wen Eng

doi:10.3390/math9212699

Cited by 2 publications

(1 citation statement)

References 26 publications

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“…LASCs are widely applied in many fields, such as industrial design [26,27] and artistic aesthetics [28,29]. Each LASC has a linear, logarithmic curvature graph (LCG) and a linear, logarithmic torsion graph (LTG), as represented by Equations ( 1) and (2) [30].…”

Section: Log-aesthetic Space Curvesmentioning

confidence: 99%

Multi-Constrained Geometric Guidance Law with a Data-Driven Method

Yan,

Tang,

et al. 2023

Drones

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A data-driven geometric guidance method is proposed for the multi-constrained guidance problem of variable-velocity unmanned aerial vehicles (UAVs). Firstly, a two-phase flight trajectory based on a log-aesthetic space curve (LASC) is designed. The impact angle is satisfied by a specified straight-line segment. The impact time is controlled by adjusting the phase switching point. Secondly, a deep neural network is trained offline to establish the mapping relationship between the initial conditions and desired trajectory parameters. Based on this mapping network, the desired flight trajectory can be generated rapidly and precisely. Finally, the pure pursuit and line-of-sight (PLOS) algorithm is employed to generate guidance commands. The numerical simulation results validate the effectiveness and superiority of the proposed method in terms of impact time and angle control under time-varying velocity.

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Section: Log-aesthetic Space Curvesmentioning

confidence: 99%

Multi-Constrained Geometric Guidance Law with a Data-Driven Method

Yan,

Tang,

et al. 2023

Drones

View full text Add to dashboard Cite

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The Development of Log Aesthetic Patch and Its Projection onto the Plane

et al. 2022

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In this work, we introduce a new type of surface called the Log Aesthetic Patch (LAP). This surface is an extension of the Coons surface patch, in which the four boundary curves are either planar or spatial Log Aesthetic Curves (LACs). To identify its versatility, we approximated the hyperbolic paraboloid to LAP using the information of lines of curvature (LoC). The outer part of the LoCs, which play a role as the boundary of the hyperbolic paraboloid, is replaced with LACs before constructing the LAP. Since LoCs are essential in shipbuilding for hot and cold bending processes, we investigated the LAP in terms of the LoC’s curvature, derivative of curvature, torsion, and Logarithmic Curvature Graph (LCG). The numerical results indicate that the LoCs for both surfaces possess monotonic curvatures. An advantage of LAP approximation over its original hyperbolic paraboloid is that the LoCs of LAP can be approximated to LACs, and hence the first derivative of curvatures for LoCs are monotonic, whereas they are non-monotonic for the hyperbolic paraboloid. This confirms that the LAP produced is indeed of high quality. Lastly, we project the LAP onto a plane using geodesic curvature to create strips that can be pasted together, mimicking hot and cold bending processes in the shipbuilding industry.

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Lines of Curvature for Log Aesthetic Surfaces Characteristics Investigation

Cited by 2 publications

References 26 publications

Multi-Constrained Geometric Guidance Law with a Data-Driven Method

Multi-Constrained Geometric Guidance Law with a Data-Driven Method

The Development of Log Aesthetic Patch and Its Projection onto the Plane

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