Computer Realizations of the Cubic Parametric Spline Curve of Bèzier Type

Stelia, Oleg; Potapenko, Leonid; Sirenko, I.

doi:10.47839/ijc.18.4.1612

Cited by 3 publications

(1 citation statement)

References 24 publications

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“…The most comprehensive information on Bézier curves and geometries is available in Gerald Farin's book "Curves and Surfaces for CAGD" [2]. Bézier curves have a wide range of uses, such as computer graphics, CAD, CAM, font design, vector drawing and 3D modeling [12]. In general, the Bézier curve is directly related to the vertices of the polygon that will define the curve shape.…”

Section: Bézier Curvesmentioning

confidence: 99%

A Novel Contour Tracing Algorithm for Object Shape Reconstruction Using Parametric Curves

Arslan¹,

Gurkahraman²

2023

Computers, Materials &Amp; Continua

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Parametric curves such as Bézier and B-splines, originally developed for the design of automobile bodies, are now also used in image processing and computer vision. For example, reconstructing an object shape in an image, including different translations, scales, and orientations, can be performed using these parametric curves. For this, Bézier and B-spline curves can be generated using a point set that belongs to the outer boundary of the object. The resulting object shape can be used in computer vision fields, such as searching and segmentation methods and training machine learning algorithms. The prerequisite for reconstructing the shape with parametric curves is to obtain sequentially the points in the point set. In this study, a novel algorithm has been developed that sequentially obtains the pixel locations constituting the outer boundary of the object. The proposed algorithm, unlike the methods in the literature, is implemented using a filter containing weights and an outer circle surrounding the object. In a binary format image, the starting point of the tracing is determined using the outer circle, and the next tracing movement and the pixel to be labeled as the boundary point is found by the filter weights. Then, control points that define the curve shape are selected by reducing the number of sequential points. Thus, the Bézier and B-spline curve equations describing the shape are obtained using these points. In addition, different translations, scales, and rotations of the object shape are easily provided by changing the positions of the control points. It has also been shown that the missing part of the object can be completed thanks to the parametric curves.

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Section: Bézier Curvesmentioning

confidence: 99%

A Novel Contour Tracing Algorithm for Object Shape Reconstruction Using Parametric Curves

Arslan¹,

Gurkahraman²

2023

Computers, Materials &Amp; Continua

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The Rain Prediction in Australia Based Big Data Analysis and Machine Learning Technology

Polishchuk

Berko

Chyrun

et al. 2021

2021 IEEE 16th International Conference on Computer Sciences and Information Technologies (CSIT)

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Realization of the smoothness of spline trajectory configuration for avoidance of nogo areas in due time

Yuyukin

2024

jour

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The configuration of the spline trajectory with the integration of the sleekness criterion into the optimization of the path when moving a marine mobile object in a given direction, taking into account restrictive navigational obstacles, is considered. The smoothness of the trajectory is investigated as the use of the possibility of avoidance of nogo area due to the organization of variable flexibility of the spline structure as the realization of the possibility of rapid dynamic redevelopment in case of unavailability of the initially chosen path. The understanding of intelligent path planning as effective routing is argued with the strategic compliance of the condition for the fastest possible achievement of the goal of the shortest movement in a conflict navigation environment. The phenomenon of cubic B-spline approximation is substantiated as a rational means of synthesizing a path line, since the planned trajectory can be generated in a segmented manner for different variations of the curvature of an algebraic curve based on a balanced combination of isogeometric constraints with optimal arrangement of nodes. The variable generation of the spline shape is performed by coordinating grid points with finite functions while interactive implementing the smoothing effect. It is concluded that heuristic variation of smoothing parameters makes it possible to obtain B-splines of various geometric evolution with the possibility of transforming the multi-link structure of the ship motion line without the need to form a fundamentally new route. The hypothesis of spline structures stability due to the piecewise architecture of the spline, when local violations of mathematical composition do not critically affect the overall task of modeling the trajectory configuration is put forward. The expediency of using variable simulation of a maneuverable trajectory in real time for path planning due to the operational bending of cubic B-splines in order to avoid any collisions is noted. As a demonstration of the practical applicability of constructing the optimal configuration of the spline trajectory, two different variants of the spline route in real time are designed in the form of sequential computer screenshots. The issue of providing automated route formation with synchronous representation of geometric computer support of a safe way line to the watch assistant, stimulating the possibility of intellectual assistance to the navigator in using the strategy of instantaneous adoption of an agreed decision on ship management by providing situational awareness, is actualized. The developed algorithm has been tested as a harmonized support for the navigation staff in the organization of effective routing. A hypothetical use of a planned approach for calculating the trajectory of a marine autonomous surface vessel in order to practically form the concept of unmanned navigation is proposed.

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Computer Realizations of the Cubic Parametric Spline Curve of Bèzier Type

Cited by 3 publications

References 24 publications

A Novel Contour Tracing Algorithm for Object Shape Reconstruction Using Parametric Curves

A Novel Contour Tracing Algorithm for Object Shape Reconstruction Using Parametric Curves

The Rain Prediction in Australia Based Big Data Analysis and Machine Learning Technology

Realization of the smoothness of spline trajectory configuration for avoidance of nogo areas in due time

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