Rotational Surfaces Generated by Cubic Hermitian and Cubic Bezier Curves

Abstract

Dönel yüzeylerin şekillerinin ayarlanmasında geometrik tasarımın istenilen şekilde olması için, ilk olarak iki yerel şekil parametreli kübik Hermityan ve kübik Bezier eğrileri kullanılarak dönel yüzeyler oluşturuldu. Oluşturulan bu yeni dönel yüzeylerin, yerel şekil parametrelerinin değiştirilmesi ile yüzeylerin şekillerinin ayarlanması konusunda iyi bir performansa sahip olduğu görüldü. Ayrıca, kübik Hermityan ve kübik Bezier eğrileri tarafından oluşturulan dönel yüzeyler, ilgi çekici yüzeylerin tasarımı için değerli bir yol sağlamaktadır. Bu bağlamda, bu dönel yüzeylerin ortalama ve Gauss eğrilikleri elde edilerek, bu yüzeyler için bazı karakterizasyonlar verildi.

T-Bezier Eğrilerin Yüzey Uygulamaları

“…To compute 𝐾 and 𝐻, we use the first and second fundamental forms of the surface: 𝐸𝑑𝑢 2 + 2𝐹𝑑𝑢𝑑𝑣 + 𝐺𝑑𝑣 2 and 𝐿𝑑𝑢 2 + 2𝑀𝑑𝑢𝑑𝑣 + 𝑁𝑑𝑣 2 with the matrix form…”

“…There are lots of curves used in surface design and the Bezier curve is one of the most important of these curves which is named by French engineer Pierre Bézier , who used the Bezier curve in the 1960s for designing curves for bodywork of Renault cars. De Casteljau's algorithm is a recursive method and has an important role to evaluate polynomials in Bernstein form or (for application and analysis about this curve, (see [2], [3], [4], [5], [8], [9]). Bezier curves are studied in different areas.…”

“…In addition, useful studies have been made in industrial field and examples have been made on the basis of curves (see [22]). Surface geometry is an application of curves for engineering and industrial designs such as, rotational surfaces (see [1], [2]), tensor product surfaces (see [16]), rational Bezier surfaces, B-spline surfaces (see [11]), NURBS surfaces and etc (see [17], [18]). These surfaces have been studied by geometers and engineers generally in Euclidean space, Minkowski space (see [21]), Galilean space, pseudo-Galilean space and etc (see [1][2][3][4][5][6][7][8], [10][11][12]).…”

“…Surface geometry is an application of curves for engineering and industrial designs such as, rotational surfaces (see [1], [2]), tensor product surfaces (see [16]), rational Bezier surfaces, B-spline surfaces (see [11]), NURBS surfaces and etc (see [17], [18]). These surfaces have been studied by geometers and engineers generally in Euclidean space, Minkowski space (see [21]), Galilean space, pseudo-Galilean space and etc (see [1][2][3][4][5][6][7][8], [10][11][12]). For example, Xi-An Hana, YiChen Maa, XiLi Huangc have used T-basis functions with two shape parameters in their paper which is the specific type of generalized trigonometric Bezier (i.e.…”

The Analysis of Some Spherical Mechanism Movements and Joint Designs by The New SLERP Interpolations

“…Jafari et al 2014) analyzed the Bezier curves by utilizing the spherical linear interpolation [12]. In addition, Kuşak Samancı et al(2015), Karadağ et al(2019), Incesu (2021) obtained some properties of the Bezier curves [13][14][15]. On the other hand, the mechanisms and machines theory was firstly launched into analyzing in Russia in 1800 and then spread around the world.…”