Gray Wolf Optimizer for Knot Placement in B-Spline Curve Fitting

Yıl 2017, Cilt: 6 Sayı: 2, 97 - 109, 31.08.2017

Özkan İnik , İsmail Koç

Öz

Gerçek bir nesnenin dijital ortama
aktarılmasıyla gerçekçi bir temsilinin oluşturulması yüzey modellemenin ana
temasıdır. Bu aktarım işlemi öncelikle bu nesnelerin taranması daha sonra elde
edilen veri noktalarından nesneyi temsil edecek verileri uydurarak eğri ve
yüzey modelleri elde edilmesidir. Veri
uydurma problemi geometrik modelleme, bilgisayarlı tasarım(CAD), bilgisayarlı
modelleme(CAM) ve bilgisayarlı üretim alanlarındaki araştırma konuları
içerisinde önemli bir yer tutmaktadır. Veri
noktalarından eğri ve yüzey modellerinin elde etmek için tersine mühendislik
kullanılmaktadır. B-Spline eğrileri özellikle yüzey modelleme ve eğri oluşturma
için kullanımı çok esnek eğrilerdir. B-Spline eğri tahmini için literatürde
birden fazla optimizasyon algoritmaları kullanmıştır.  Bu çalışmada, Gri Kurt Optimizasyon(GWO) Algoritması
ile B-Spline eğri tahmini yapılmıştır.  GWO
yöntemi ile yapılan eğri tahmininde düğüm yerlerinin tespiti ve düğüm sayısı
gelişigüzel seçilerek en küçük hata ile eğri tahmini hedeflenmiştir. Eğri
tahmini için literatürde sıklıkla kullanılan 6 farklı fonksiyonu kullanılmıştır.
GWO ile birden fazla fonksiyon düşük hata oranı ile başarılı bir şekilde elde
edilmiştir.  

Anahtar Kelimeler

B-Spline eğri uydurma, gri kurt optimizasyon(GWO), düğüm yerleştirme, optimizasyon, ters mühendislik

Gray Wolf Optimizer for Knot Placement in B-Spline Curve Fitting

Öz

The formation of
a realistic representation constitutes the main theme of the surface modeling
by the transfer of a real object to digital media. This transfer process is
performed by first scanning the objects and then obtaining curve and surface
models by fitting the data representing the object from the data points
obtained later. The data fitting for curve problem has an important area in
research topics in geometric modeling, computer-aided design (CAD),
computer-aided manufacturing (CAM), and computerized production. Reverse
engineering is used to obtain curve and surface models from data points. B-Spline curves are very flexible curves, especially for
surface modeling.  Several optimization
algorithms have been used in the literature for B-Spline curve fitting. In this
study, B-Spline curve fitting is carried out by Gray Wolf Optimizer (GWO). The
estimation of the knot locations and the number of knots are randomly selected
in the curve estimation by the GWO method and the curve estimation with the
smallest error is aimed. For the curve fitting, six different functions are
used which are frequently used in the literature.  The experimental studies show that the
proposed algorithm obtains the results with low error rates for more than one
functions.

Anahtar Kelimeler

B-Spline Curve Fitting, Gray Wolf Optimizer (GWO), Knot placement, Optimization, Reverse Engineering

Kaynakça

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