LS(2)-Equivalence conditions of control points and application to planar Bezier curves

İncesu, Muhsin; Gürsoy, Osman

doi:10.20852/ntmsci.2017.186

Cited by 10 publications

(12 citation statements)

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“…can be written. After this the proof can be completed as the proof of theorem 19 in [22]. So, = (4) is obtained.…”

Section: The G-equivalence Conditions Of Points Systems For G= S(3) Amentioning

confidence: 95%

“…ii) if k>3 then the system 〈 , 〉; i,j =1,2,3; ≤ 〈 , 〉; i,j =1,2,3; p = 4,5,…,k generate the O(3)-invariant rational functions. [22]. iii) if k>4 then the system, ii) if 2 ≤ < 4 then the system ; i<j<k…”

Section: The Generator Invariants Of Points By the Group G = S(3) Andmentioning

confidence: 99%

“…Khadjiev and R. Aripov generalized this invariants to all Euclidean motions in [9,10]. Recently Sagiroglu [11][12][13], Oren [14][15][16]21] Peksen [13,16], Incesu and Gursoy [17][18][19][20][21][22][23] are some contributors in this area. The best examples of points systems are Bézier curves and Bézier surfaces.…”

Section: Introductionmentioning

confidence: 99%

“…The best examples of points systems are Bézier curves and Bézier surfaces. The invariants of these curves and surfaces under an affine transformation have the same meaning as the invariants of the control points of these curves and surfaces [22]. Bézier and B-Spline curves has been studied in many different are of CAD and CAM system.…”

Section: Introductionmentioning

confidence: 99%

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On the G-Similarities of two open B-spline curves in R3

İncesu

Gürsoy

2020

Muş Alparslan Üniversitesi Fen Bilimleri Dergisi

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Let G be a transformation group in R3. Any two vectors x and y in R3 are called G-equivalence vectors if there exist a transformation g G such that y = gx satisfies. In this paper the transformation group G will be considered as similarity transformations group or its any subgroup. So if given two vectors x and y in R3 are G-equivalence vectors then these vectors x and y are called G-similar. i.e. rotational, reflectional, translational or scaling similarity. B-spline curves are used basically in Computer Aided Design (CAD), Computer Aided Geometric Design (CAGD), Computer Aided Modeling (CAM). In determining the invariants of spline curves and surfaces at any point, it is necessary to find the analytical equation of each curve and surface and calculate its invariants such as curvature, torsion, principal curvatures, mean and Gaussian curvatures at the desired point. However, it can be very difficult to find the curve or surface to be designed analytically. For example, when a car is designed, the aerodynamic curves in the car will be different from the known surface equation of the car. It is very difficult to write this equation exactly. For these curves and surfaces we designed, the way to overcome this difficulty is to design them with spline curves and surfaces. In this paper the G- equivalence conditions of given two open B-spline curves are studied in case G is similarity transformations group or its any subgroup.

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“…can be written. After this the proof can be completed as the proof of theorem 19 in [22]. So, = (4) is obtained.…”

Section: The G-equivalence Conditions Of Points Systems For G= S(3) Amentioning

confidence: 95%

Section: The Generator Invariants Of Points By the Group G = S(3) Andmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the G-Similarities of two open B-spline curves in R3

İncesu

Gürsoy

2020

Muş Alparslan Üniversitesi Fen Bilimleri Dergisi

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show abstract

“…Öklid geometrisi dışındaki geometrilerde de eğrilerin denklik probleminin araştırılması yapılmaktadır. Afin geometride ve alt gruplarının bazılarında bu problem araştırılmıştır (Giblin ve Sano, 2012;Sağıroğlu ve Pekşen, 2010;İncesu ve Gürsoy, 2017;.…”

Section: Introductionunclassified