2021 # The new characterization of ruled surfaces corresponding dual Bézier curves

**Abstract:** Let
be a Bézier curve in D3, that is, the control points of
are the vectors in D3 = {u = (u1, u2, u3) : ui ∈ D,i = 1,2,3} which is the set of dual vectors whose each coordinate components are dual numbers defined as a+εa* : a,a* ∈ R,ε ≠ 0; ε2 = 0. So the spherical projection of
is a spherical curve denoted by
on the unit sphere in D3 and every point of
corresponds to a directed line in real space R3 by Study transformation. In this study, the ruled surface X(t, ν) corresponding to this projection cur…

Help me understand this report

Search citation statements

Paper Sections

Select...

1

1

Citation Types

0

2

0

Year Published

2022

2023

Publication Types

Select...

3

Relationship

0

3

Authors

Journals

(2 citation statements)

0

2

0

“…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.…”

confidence: 99%

“…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.…”

confidence: 99%

“…6 On the other hand, ruled surfaces are constructed by a one-parameter family of lines and have been studied extensively in differential geometry. [7][8][9][10][11][12] Since they are simply generated, these surfaces find application in a variety of fields such as computer aided design, architectural design, electric discharge machining, and simulation of rigid bodies.…”

confidence: 99%