Düzlemsel Bezier Eğrilerinin S(2) Denklik Şartları

Year 2017, Volume: 5 Issue: 2, 471 - 477, 01.12.2017

Muhsin İncesu , Osman Gürsoy

Abstract

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. 

Keywords

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

The S(2) equivalence Conditions of Planar Bezier Curves

Abstract

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. 

Keywords

Similarity transformations, invariants, generators, equivalence conditions

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