Sains Malaysiana 40(11)(2011): 1301–1305

Aesthetic Spiral for Design

(Lingkaran Estetik untuk Reka Bentuk)

R.U. Gobithaasan

Dept. of Mathematics, Faculty of Science and Technologi, University Malaysia Terengganu,

21030 Kuala Terengganu, Malaysia

Kenjiro T. Miura

Graduate School of Science & Technology, Shizuoka University, Shizuoka 432-8561,

Japan

Received: 15 March 2010 / Accepted: 9 March 2011

ABSTRACT

A planar spiral called Generalized Log Aesthetic Curve segment (GLAC) has been proposed using the curve synthesis process with two types of formulation; ρ-shift and κ-shift. Both methods were carried out by extending the formulation of Generalized Cornu Spiral (GCS) in a similar manner to the Log Aesthetic Curve (LAC). The family of GLAC comprises of planar curves of high quality such as GCS, LAC, clothoid, logarithmic spiral and circle involute. The GLAC segment has an additional parameter to determine its shape as compared to GCS and LAC segment, hence an extra constraint can be satisfied when shaping the GLAC segment. The last section of the paper shows a numerical example.

Keywords: Curve synthesis; spiral; high quality curves; monotonic curvature curves

ABSTRAK

Satu lingkaran segmen 2D bernama Lengkung Astetik Log Umum (GLAC) telah dibentuk dengan menggunakan proses sintesis lengkung melalui dua jenis rumusan; ρ-shift dan κ-shift. Kedua-dua perumusan ini dikembangkan dengan menggunakan rumus Lingkaran Cornu Umum (GCS) yang mirip dengan pembentukkan rumus Lengkung Astestik Log (LAC). Ahli keluarga GLAC ini terdiri daripada lengkung-lengkung yang berkualiti tinggi contohnya seperti GCS, LAC, lingkaran klotoid, lingkaran logarithma, bulatan involut dan sebagainya. Segmen GLAC ini juga mempunyai satu parameter tambahan untuk menentukan bentuknya berbanding dengan segmen GCS dan LAC, maka satu kekangan tambahan dapat dipenuhidalam pembentukan segmen GLAC. Bahagian akhir menunjukkan satu contoh berangka.

Kata kunci: Lengkung berkualiti tinggi; lengkung berkelengkungan monotonic; lingkaran; sintesis lengkung

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*Corresponding author; email : gr@umt.edu.my or gobithaasan@gmail.com