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

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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