Pembinaan lengkungan peralihan berbentuk C yang memuaskan Data Interpolasi Hermite G2

Constructing C-shape transition curve that satisfy G2 Hermite Interpolation Data

Authors

  • Azhar Ahmad Department of Mathematics, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, 35900 Tanjong Malim, Perak, Malaysia

DOI:

https://doi.org/10.37134/jsml.vol8.2.6.2020

Keywords:

Lengkungan peralihan, kuadratik nisbah Bezier, keselanjaran geometri

Abstract

Makalah ini membincangkan satu kaedah pembinaan lengkungan peralihan berbentuk C yang memenuhi syarat-syarat data interpolasi Hermite Lengkungan peralihan ini dibina berasaskan gabungan dua pilin kuadratik nisbah Bezier atau gabungan bersama satu segmen garis lurus bagi mencapai keselanjaran  pada keseluruhan binaan. Kaedah analisis geometri bersama syarat kemonotonan suatu lengkungan kuadratik nisbah Bezier telah digunakan bagi mencapai objektif kajian. Hasil kajian yang dicapai adalah satu teknik pembinaan yang membolehkan kita memperolehi lengkungan peralihan secara terus, mudah diaplikasikan serta tanpa perlu menggunakan sebarang prosedur tranformasi affin. Syarat untuk lengkungan peralihan ini terhasil ditentukan oleh data Hermite yang diberi dan kepelbagaiannya pula dikawal oleh panjang segmen garis lurus yang menghubungkan kedua-dua pilin berkenaan. Keupayaan memenuhi sifat-sifat interpolasi ini memberi banyak kelebihan dan amat sesuai untuk aplikasi tertentu di dalam CAGD (Computer Aided Geometric Design), umpamanya rekabentuk produk industri, trajektori robot non-holonomic, serta rekabentuk mendatar landasan keretapi dan lebuhraya. Oleh kerana kuadratik nisbah Bezier merupakan sebahagian daripada perwakilan NURBS (Nonuniform Rational B-splines) maka adalah mudah bagi kita mengabungjalinkan formulasi lengkungan peralihan yang dicadangkan ini ke dalam kebanyakan sistem pengaturcara CAD (Computer Aided Design).

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Published

2020-04-07

How to Cite

Ahmad, A. (2020). Pembinaan lengkungan peralihan berbentuk C yang memuaskan Data Interpolasi Hermite G2: Constructing C-shape transition curve that satisfy G2 Hermite Interpolation Data. Journal of Science and Mathematics Letters, 8(2), 39–50. https://doi.org/10.37134/jsml.vol8.2.6.2020