Düzlemsel Bezier Eğrilerinin S(2) Denklik Şartları

Yıl 2017, Cilt: 5 Sayı: 2, 471 - 477, 01.12.2017

Muhsin İncesu , Osman Gürsoy

Öz

Bu çalışmada R2 de  vektörlerden oluşan iki sistemin, yine R2 de tüm benzerlik dönüşümlerinin grubu olan  G=S(2) grubuna göre denklik şartlarının; bu vektörlerin G-invaryant  rasyonel fonksiyonlar  cismi olan R(x1,x2,…,xk)S(2)   cisminin üreteçleri cinsinden ifade edilmesi çalışılmıştır. Böylece R2 de verilen düzlemsel Bezier eğrilerinin  S(2) grubuna göre denklik şartları da ifade edilmiştir. 

Anahtar Kelimeler

Benzerlik dönüşümleri, invaryantlar, üreteçler, denklik koşulları, Bezier Eğrileri

The S(2) equivalence Conditions of Planar Bezier Curves

Öz

In this paper it is studied that the equivalence conditions of two systems consisted of vectors according to the group G=S(2) of similarity transformations in R2 in terms of the generator invariants of the field G-invariant rational functions R(x1,x2,…,xk)S(2).  So the equivalence conditions of two splanar Bezier curves are expressed. 

Anahtar Kelimeler

Similarity transformations, invariants, generators, equivalence conditions

Kaynakça

• Kurşun H.ve Kalkan Y., İstanbul’ da Farklı Tarihlerde Yapılmış Doğalgaz Alt Yapı Haritalarının Doğruluk Yönünden bir Karşılaştırılması, 2. Mühendislik Ölçmeleri Sempozyumu, 23-25 Kasım 2005, İTÜ, İstanbul
• Yaprak S ve Yaprak H., Comparison of GPS Stop and Go Method and Electronic Tachometry Technique in Map Production, Gazi Üniversitesi Journal of Science ,18,4 (2005) 627-637.
• Özer S., Kortewed –de Vries Denklemlerinin Nümerik Çözümü, Doktora Tezi, İnönü Üniversitesi Fen bilimleri Enstitüsü, 1995.
• Kai- Tai Fang, et all, Critical value determination on similarity of Fingerprints, Chemometrics and Intelligent Laboratory Systems, 82, 1 (2006) 236-240.
• Wang L.X., et all, Vectorial angle method for evaluating the similarity between two chromatographic fingerprints of chinese herb, Acta Pharmaceutica Sinica, 37, 9 (2002) 713-717.
• Dresner Martin, Leisure versus business passengers: Similarities, differences, and implications, Journal of Air Transport Menagement, 12 (2006) 28-32.
• Yo Horikawa, Bispectrum – based feature of 2D and 3D images invariant to similarity Transformations, Proc. IEEE, (2000) 511-514.
• Yo Horikawa, Pattern recognition with invariance to similarity transformations based on the third- order correlation, Proc. 13th. International Conference on Pattern Recognition (ICPR’96) , 2 (1996) 200-204.
• Weyl H., The Classical Groups, Their Invariants and Representations, 2nd ed., with suppl.. Princeton, Princeton University Press, 1946
• Khadjiev Dj., An Application of the Invariant Theory to the Differential Geometry of Curves, Fan, Tashkent, 1988. ( in Russian )
• İdris Oren, Invariants of Points fort he orthogonal groups O(3,1), PhD. Thesis, Karadeniz Technical University, 2007.
• Yasemin Sağıroğlu, Affine Differential Invariants of parametric curves, Ph D. Thesis, Karadeniz Technical University, 2002.
• Alexander Schrijver, Tensor subalgebras and first fundamental theorems in invariant theory, journal of Algebra, 319, (2008), 1305-1319.
• Muhsin Incesu, Osman Gursoy, On Similarity Invarant Rational Function fot k vector variables and their genarators in R2, Modelling and Application Theory, V.1 issue 1 , (2016) ,37-53.
• Muhsin Incesu, Osman Gursoy, LS(2)-Equivalence Conditions of Control Points and Application to Planar Bezier Curves” New Trends in Mathematical Science, V.5, No. 3, (2017) 70-84.
• Greub W. H., Linear algebra, 3rd. Ed., Springer- Verlag Berlin Heidelberg, Netherland, 1967.
• Marsh D., Applied Geometry for Computer Graphics and CAD, Springer-Verlag London Berlin Heidelberg, London, 1999.