Lines of Curvature for Log Aesthetic Surfaces Characteristics Investigation

R.U. Gobithaasan, Yee Meng Teh, Kenjiro T. Miura and Wen Eng Ong
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R.U. Gobithaasan: Special Interest Group on Modelling & Data Analytics, Faculty of Ocean Engineering Technology and Informatics, University Malaysia Terengganu, Kuala Nerus 21030, Malaysia
Yee Meng Teh: School of Mathematical Sciences, Universiti Sains Malaysia, Minden 11800, Malaysia
Kenjiro T. Miura: Graduate School of Science & Technology, Shizuoka University, Hamamatsu, Shizuoka 432-8561, Japan
Wen Eng Ong: School of Mathematical Sciences, Universiti Sains Malaysia, Minden 11800, Malaysia

Mathematics, 2021, vol. 9, issue 21, 1-14

Abstract: 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 ? . 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.

Keywords: log aesthetic curves; log aesthetic surface; LoC; GPU; CUDA (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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