Eğri ve yüzey tasarımları
Küçük Resim Yok
Tarih
1992
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Ege Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
SUMMARY In the introduction part of this thesis, the subject and purpose of this study is introduced. In the first part: By studying certain kinds of curves and surface patches such as, Ferguson Parametric Curves and Patches, Bezier Unisurf Curves and Patches, Bernstein- Bezier Polinomial Curves. Rational Parametric Curves and Surfaces, the use of parametric equations in curve and surface design are examined. These curves and surfaces establish a base for Computer Aided Geometric Design (CAGD). Furthermore, some knowledge about the Characteristic Polygon of a curve, which has applications in the geometric design and a very useful property Convex Hull Property is given. In the second part, the use of Polinomial Splines and B-Sp lines in the fitting of plane curves, are considered. Also, positional, tangent and curvature continuity necessary in the construction of Composite Curves and Surfaces and kinds of parametrization necessary to satisfy them is examined. Besides this, it's given some knowledge about Parametric Splines. Chord Length Parametrization and error bounds. Moreover, it's shown that splines also have Convex Hull Property and a technique for interpolation with 94ÖZET Bu tezin giriş kısmında tez konusu ve amacı belirtildi. Birinci böl Umde. Bilgi sayar Destekli Tasarımda (BDT) baz teşkil eden Ferguson Parametrik Eğri ve Yamaları, Berstein-bezier Eğri ve Yamaları, Berstein-Bezier Polinom Eğrileri, Rasyonel Parametrik Eğri ve Yüzeyler ele alınarak, eğri ve yüzey tasarımında parametrik denklemlerin kullanılışı incelendi. Ayrıca, geometrik tasarımda önemli uygulamaları olan» bir eğrinin Karakteristik Çokgeni incelendi ve çok kullanışlı bir özellik olan Dışbükey Tekne özelliği hakkında bilgi verildi. İkinci bölümde, düzlem eğrilerin uyarlanmasında Splayn Polinomlarının ve B-Splayn Eğrilerinin kullanımı araştırılarak. Birleşik Eğri ve Yüzeylerin oluşturulmasında gerekli olan pozisyon, teğet ve eğrilik süreklilikleri ve bunların sağlanması için gereken parametrizasyon çeşitleri incelendi. Bu arada, Parametrik Splaynlar ve kiriş uzunluğu parametrizasyonundan bahsedilerek, hata oranları hakkında bilgi verildi. Ayrıca, splayn lar in da Dışbükey Tekne özelliğine sahip olduğu gösterildi ve splaynlar ile interpolasyon için hangi tarz bir interpolasyon tekniğine ihtiyaç duyulduğu araştırılarak, parçalı tarzdaki bir interpolasyonun ve 92
SUMMARY In the introduction part of this thesis, the subject and purpose of this study is introduced. In the first part: By studying certain kinds of curves and surface patches such as, Ferguson Parametric Curves and Patches, Bezier Unisurf Curves and Patches, Bernstein- Bezier Polinomial Curves. Rational Parametric Curves and Surfaces, the use of parametric equations in curve and surface design are examined. These curves and surfaces establish a base for Computer Aided Geometric Design (CAGD). Furthermore, some knowledge about the Characteristic Polygon of a curve, which has applications in the geometric design and a very useful property Convex Hull Property is given. In the second part, the use of Polinomial Splines and B-Sp lines in the fitting of plane curves, are considered. Also, positional, tangent and curvature continuity necessary in the construction of Composite Curves and Surfaces and kinds of parametrization necessary to satisfy them is examined. Besides this, it's given some knowledge about Parametric Splines. Chord Length Parametrization and error bounds. Moreover, it's shown that splines also have Convex Hull Property and a technique for interpolation with 94splines is searched. It's found that. a Piecewise Interpolation, especially Piecewise Hermite Interpolation is convinient for many types of curves and surfaces. 95
SUMMARY In the introduction part of this thesis, the subject and purpose of this study is introduced. In the first part: By studying certain kinds of curves and surface patches such as, Ferguson Parametric Curves and Patches, Bezier Unisurf Curves and Patches, Bernstein- Bezier Polinomial Curves. Rational Parametric Curves and Surfaces, the use of parametric equations in curve and surface design are examined. These curves and surfaces establish a base for Computer Aided Geometric Design (CAGD). Furthermore, some knowledge about the Characteristic Polygon of a curve, which has applications in the geometric design and a very useful property Convex Hull Property is given. In the second part, the use of Polinomial Splines and B-Sp lines in the fitting of plane curves, are considered. Also, positional, tangent and curvature continuity necessary in the construction of Composite Curves and Surfaces and kinds of parametrization necessary to satisfy them is examined. Besides this, it's given some knowledge about Parametric Splines. Chord Length Parametrization and error bounds. Moreover, it's shown that splines also have Convex Hull Property and a technique for interpolation with 94splines is searched. It's found that. a Piecewise Interpolation, especially Piecewise Hermite Interpolation is convinient for many types of curves and surfaces. 95
Açıklama
Anahtar Kelimeler
Matematik, Mathematics, Eğriler, Curves, Geometri, Geometry, Tasarım, Design, Yüzeyler, Surfaces
