Lines of Curvature for Log Aesthetic Surfaces Characteristics Investigation

Lines of curvatures (LoCs) are curves on a surface that are derived from the first and second fundamental forms, and have been used for shaping various types of surface. In this paper, we investigated the LoCs of two types of log aesthetic (LA) surfaces; i.e., LA surfaces of revolution and LA swept...

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Main Authors:	R.U. Gobithaasan, Yee Meng Teh, Kenjiro T. Miura, Wen Eng Ong
Format:	article
Language:	EN
Published:	MDPI AG 2021
Subjects:	log aesthetic curves log aesthetic surface LoC GPU CUDA Mathematics QA1-939
Online Access:	https://doaj.org/article/bd08d0f4f48643e6b11d3001679a4a2d
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spelling	oai:doaj.org-article:bd08d0f4f48643e6b11d3001679a4a2d2021-11-11T18:15:44ZLines of Curvature for Log Aesthetic Surfaces Characteristics Investigation10.3390/math92126992227-7390https://doaj.org/article/bd08d0f4f48643e6b11d3001679a4a2d2021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2699https://doaj.org/toc/2227-7390Lines of curvatures (LoCs) are curves on a surface that are derived from the first and second fundamental forms, and have been used for shaping various types of surface. In this paper, we investigated the LoCs of two types of log aesthetic (LA) surfaces; i.e., LA surfaces of revolution and LA swept surfaces. These surfaces are generated with log aesthetic curves (LAC) which comprise various families of curves governed by <i>α</i>. First, since it is impossible to derive the LoCs analytically, we have implemented the LoC computation numerically using the Central Processing Unit (CPU) and General Processing Unit (GPU). The results showed a significant speed up with the latter. Next, we investigated the curvature distributions of the derived LoCs using a Logarithmic Curvature Graph (LCG). In conclusion, the LoCs of LA surface of revolutions are indeed the duplicates of their original profile curves. However, the LoCs of LA swept surfaces are LACs of different shapes. The exception to this is when this type of surface possesses LoCs in the form of circle involutes.R.U. GobithaasanYee Meng TehKenjiro T. MiuraWen Eng OngMDPI AGarticlelog aesthetic curveslog aesthetic surfaceLoCGPUCUDAMathematicsQA1-939ENMathematics, Vol 9, Iss 2699, p 2699 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	log aesthetic curves log aesthetic surface LoC GPU CUDA Mathematics QA1-939
spellingShingle	log aesthetic curves log aesthetic surface LoC GPU CUDA Mathematics QA1-939 R.U. Gobithaasan Yee Meng Teh Kenjiro T. Miura Wen Eng Ong Lines of Curvature for Log Aesthetic Surfaces Characteristics Investigation
description	Lines of curvatures (LoCs) are curves on a surface that are derived from the first and second fundamental forms, and have been used for shaping various types of surface. In this paper, we investigated the LoCs of two types of log aesthetic (LA) surfaces; i.e., LA surfaces of revolution and LA swept surfaces. These surfaces are generated with log aesthetic curves (LAC) which comprise various families of curves governed by <i>α</i>. First, since it is impossible to derive the LoCs analytically, we have implemented the LoC computation numerically using the Central Processing Unit (CPU) and General Processing Unit (GPU). The results showed a significant speed up with the latter. Next, we investigated the curvature distributions of the derived LoCs using a Logarithmic Curvature Graph (LCG). In conclusion, the LoCs of LA surface of revolutions are indeed the duplicates of their original profile curves. However, the LoCs of LA swept surfaces are LACs of different shapes. The exception to this is when this type of surface possesses LoCs in the form of circle involutes.
format	article
author	R.U. Gobithaasan Yee Meng Teh Kenjiro T. Miura Wen Eng Ong
author_facet	R.U. Gobithaasan Yee Meng Teh Kenjiro T. Miura Wen Eng Ong
author_sort	R.U. Gobithaasan
title	Lines of Curvature for Log Aesthetic Surfaces Characteristics Investigation
title_short	Lines of Curvature for Log Aesthetic Surfaces Characteristics Investigation
title_full	Lines of Curvature for Log Aesthetic Surfaces Characteristics Investigation
title_fullStr	Lines of Curvature for Log Aesthetic Surfaces Characteristics Investigation
title_full_unstemmed	Lines of Curvature for Log Aesthetic Surfaces Characteristics Investigation
title_sort	lines of curvature for log aesthetic surfaces characteristics investigation
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/bd08d0f4f48643e6b11d3001679a4a2d
work_keys_str_mv	AT rugobithaasan linesofcurvatureforlogaestheticsurfacescharacteristicsinvestigation AT yeemengteh linesofcurvatureforlogaestheticsurfacescharacteristicsinvestigation AT kenjirotmiura linesofcurvatureforlogaestheticsurfacescharacteristicsinvestigation AT wenengong linesofcurvatureforlogaestheticsurfacescharacteristicsinvestigation
_version_	1718431908205953024

Lines of Curvature for Log Aesthetic Surfaces Characteristics Investigation

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