Defining a curve as a Bezier curve

Baydaş, Şenay; Karakaş, Bülent

doi:10.1080/16583655.2019.1601913

Cited by 36 publications

(20 citation statements)

References 7 publications

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“…In such cases, the Bézier curve is frequently chosen to form smooth paths [9][10][11]. The Bézier curve, which is mathematically defined as Bernstein polynomials, can smoothly connect two endpoints with specific direction requirements, and the curve's shape can be easily adjusted by modifying its control points [12].…”

Section: Introductionmentioning

confidence: 99%

Obstacle Avoidance Path Planning for Worm-like Robot Using Bézier Curve

et al. 2021

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Worm-like robots have demonstrated great potential in navigating through environments requiring body shape deformation. Some examples include navigating within a network of pipes, crawling through rubble for search and rescue operations, and medical applications such as endoscopy and colonoscopy. In this work, we developed path planning optimization techniques and obstacle avoidance algorithms for the peristaltic method of locomotion of worm-like robots. Based on our previous path generation study using a modified rapidly exploring random tree (RRT), we have further introduced the Bézier curve to allow more path optimization flexibility. Using Bézier curves, the path planner can explore more areas and gain more flexibility to make the path smoother. We have calculated the obstacle avoidance limitations during turning tests for a six-segment robot with the developed path planning algorithm. Based on the results of our robot simulation, we determined a safe turning clearance distance with a six-body diameter between the robot and the obstacles. When the clearance is less than this value, additional methods such as backward locomotion may need to be applied for paths with high obstacle offset. Furthermore, for a worm-like robot, the paths of subsequent segments will be slightly different than the path of the head segment. Here, we show that as the number of segments increases, the differences between the head path and tail path increase, necessitating greater lateral clearance margins.

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Section: Introductionmentioning

confidence: 99%

Obstacle Avoidance Path Planning for Worm-like Robot Using Bézier Curve

et al. 2021

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“…Some of these studies by G. Farin [24], R. Farouki [25,26], J. Hoschek [27], W. Tiller [28], H. Potmann [29], Incesu and Gursoy [30,34], Samancı et al [31,33,36,37], Bulut and Caliskan [32], Erkan and Yuce [35], Baydas and Karakas [38] can be given exemplarily.…”

Section: Introductionmentioning

confidence: 99%

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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“…In a recent article published in this journal, Baydas and Karakas [1] show how to compute the Bézier representation of a curve given in power form. We note that this straightforward exercise is already solved in textbooks on CAGD.…”

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confidence: 99%

“…• The so-called creator matrix A (Definition 3.1 in [1]) is simply the transformation matrix [2][3][4][5][6][7][8][9][10] from Bézier to power form. Indeed, let T = {t i } n i=0 denote the set of power functions up to degree n, and P = {P 0 , .…”

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confidence: 99%

“…Finally, computing the derivative or integral of a curve in Bézier form also amounts to simple formulae, found in any of the aforementioned textbooks. Transforming the curve to power form for these computations, as Baydas and Karakas [1] propose, is not advisable for high values of n, because the conversion matrices between the power and Bernstein bases suffer from ill-conditioning [4][5][6][7][8]. For CAGD purposes, always use the Bernstein basis ab initio and at all stages.…”

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confidence: 99%

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