On The Some Special Biquadratic Bezier Surfaces in E^3

Year 2025, Volume: 15 Issue: 3, 1110 - 1123, 01.09.2025

Şeyda Kılıçoglu , Semra Yurttançıkmaz

https://doi.org/10.21597/jist.1643500

Abstract

In this study, biquadratic Bezier surfaces were investigated. These surfaces have a very important place in the scientific world. The importance of biquadratic Bézier surfaces lies in their ability to provide a smooth, flexible, and computationally efficient method for modeling surfaces. They fill the gap between simpler bilinear surfaces and more complex bicubic surfaces, offering a great solution in areas where both simplicity and precision are needed. While not as commonly used in high-end 3D modeling as their higher-order counterparts, they remain a useful tool for surface design, particularly when the trade-off between quality and computational efficiency is critical. In this study, firstly the matrix representations of biquadratic Bezier surfaces are given. Then, it is stated how to find the control points of some special surface types given as biquadratic Bezier surfaces, and the control points of parabolic cylinder, elliptic paraboloid and hyperbolic paraboloid surfaces are calculated.

Keywords

Biquadratic bezier Surfaces , Elliptic paraboloid , Hyperbolic Paraboloid , Parabolic cylinder

E^3'te Bazı Özel Bikuadratik Bezier Yüzeyleri Üzerine

Abstract

Bu çalışmada bikuadratik Bezier yüzeyleri incelenmiştir. Bu yüzeyler bilim dünyasında çok önemli bir yere sahiptir. Bikuadratik Bézier yüzeylerinin önemi, yüzeyleri modellemek için düzgün, esnek ve hesaplama açısından verimli bir yöntem sağlama yeteneklerinde yatmaktadır. Daha basit bilineer yüzeyler ile daha karmaşık bikübik yüzeyler arasındaki boşluğu doldururlar ve hem basitliğin hem de hassasiyetin gerekli olduğu alanlarda harika bir çözüm sunarlar. Üst düzey 3B modellemede yüksek mertebeden benzerleri kadar yaygın olarak kullanılmasalar da, özellikle kalite ve hesaplama verimliliği arasındaki denge kritik olduğunda, yüzey tasarımı için yararlı bir araç olmaya devam etmektedirler. Bu çalışmada, öncelikle bikuadratik Bezier yüzeylerinin matris gösterimleri verilmiştir. Daha sonra, bikuadratik Bezier yüzeyleri olarak verilen bazı özel yüzey tiplerinin kontrol noktalarının nasıl bulunacağı belirtilmiş ve parabolik silindir, eliptik paraboloid ve hiperbolik paraboloid yüzeylerinin kontrol noktalarının nasıl hesaplandığı açıklanmıştır.

Keywords

Bikuadratik Bezier Yüzeyler , Eliptik Paraboloid , Hiperbolik Paraboloid , Parabolik Silindir

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