Drawable Region of the Generalized Log Aesthetic Curves
The main characteristic of visually pleasing curves used for product design is a monotonic curvature profile. Recently, a planar curve called Generalized Log Aesthetic Curve (GLAC) has been extended from the Log Aesthetic Curve (LAC), and it has an additional shape parameter, ν. This curve preserves...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/732457 |
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| _version_ | 1832556119208230912 |
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| author | R. U. Gobithaasan R. Karpagavalli Kenjiro T. Miura |
| author_facet | R. U. Gobithaasan R. Karpagavalli Kenjiro T. Miura |
| author_sort | R. U. Gobithaasan |
| collection | DOAJ |
| description | The main characteristic of visually pleasing curves used for product design is a monotonic curvature profile. Recently, a planar curve called Generalized Log Aesthetic Curve (GLAC) has been extended from the Log Aesthetic Curve (LAC), and it has an additional shape parameter, ν. This curve preserves the monotonicity of curvature and is said to produce visually pleasing curves. This paper delves on the drawable region of the GLAC segment which indicates the probable solutions of shape parameters from given interpolating points and the direction of travel at those points. The first section reviews the formulation of GLAC and its related bounds. The section describes the algorithm for identifying the drawable region. It is followed by the section describing how small changes of ν widen the drawable boundaries. The final section discusses the superiority of GLAC compared to LAC for use in industrial product design. |
| format | Article |
| id | doaj-art-991029904abd401da8f89fa5de70d996 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-991029904abd401da8f89fa5de70d9962025-02-03T05:46:20ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/732457732457Drawable Region of the Generalized Log Aesthetic CurvesR. U. Gobithaasan0R. Karpagavalli1Kenjiro T. Miura2Department of Mathematics, FST, Universiti Malaysia Terengganu, 21030 Kuala Terengganu, MalaysiaDepartment of Mathematics, FST, Universiti Malaysia Terengganu, 21030 Kuala Terengganu, MalaysiaGraduate School of Science & Technology, Shizuoka University, Shizuoka 432-8561, JapanThe main characteristic of visually pleasing curves used for product design is a monotonic curvature profile. Recently, a planar curve called Generalized Log Aesthetic Curve (GLAC) has been extended from the Log Aesthetic Curve (LAC), and it has an additional shape parameter, ν. This curve preserves the monotonicity of curvature and is said to produce visually pleasing curves. This paper delves on the drawable region of the GLAC segment which indicates the probable solutions of shape parameters from given interpolating points and the direction of travel at those points. The first section reviews the formulation of GLAC and its related bounds. The section describes the algorithm for identifying the drawable region. It is followed by the section describing how small changes of ν widen the drawable boundaries. The final section discusses the superiority of GLAC compared to LAC for use in industrial product design.http://dx.doi.org/10.1155/2013/732457 |
| spellingShingle | R. U. Gobithaasan R. Karpagavalli Kenjiro T. Miura Drawable Region of the Generalized Log Aesthetic Curves Journal of Applied Mathematics |
| title | Drawable Region of the Generalized Log Aesthetic Curves |
| title_full | Drawable Region of the Generalized Log Aesthetic Curves |
| title_fullStr | Drawable Region of the Generalized Log Aesthetic Curves |
| title_full_unstemmed | Drawable Region of the Generalized Log Aesthetic Curves |
| title_short | Drawable Region of the Generalized Log Aesthetic Curves |
| title_sort | drawable region of the generalized log aesthetic curves |
| url | http://dx.doi.org/10.1155/2013/732457 |
| work_keys_str_mv | AT rugobithaasan drawableregionofthegeneralizedlogaestheticcurves AT rkarpagavalli drawableregionofthegeneralizedlogaestheticcurves AT kenjirotmiura drawableregionofthegeneralizedlogaestheticcurves |