An Improved Algorithm for the Approximation of a Cubic Bezier Curve and its Application for Approximating Quadratic Bezier Curve

Riškus, Aleksas; Liutkus, Giedrius

doi:10.5755/j01.itc.42.4.1707

Cited by 5 publications

(4 citation statements)

References 12 publications

(28 reference statements)

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“…For each component element, the data points detected directly by the ACE/SIS [STEREO-A/LET] in the original spectrum are relatively sparse. To obtain an extensive spectrum with denser data points, the interpolation with the Bezier Curves method ( 50 ) is applied to the original spectrum of each component element. However, only the nominal values of differential fluxes for these interpolated data points can be acquired based on this method.…”

Section: Resultsmentioning

confidence: 99%

First measurements of low-energy cosmic rays on the surface of the lunar farside from Chang’E-4 mission

Luo

Zhang

et al. 2022

Sci. Adv.

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Section: Resultsmentioning

confidence: 99%

First measurements of low-energy cosmic rays on the surface of the lunar farside from Chang’E-4 mission

Luo

Zhang

et al. 2022

Sci. Adv.

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“…Tables (2) and (3) show the four selected control points for both statements university of technology and computer sciences department in a consecutive manner, whilst figure (2) shows 2D virtual image using Bezier curves for those same statements. 6) and (7) show four selected control points for both university and department of electromechanical engineering statements followed by figure (4) representing 2D virtual image for the same statements. Finally, tables (8) and (9) show four selected control points for both university and department of chemical engineering statements followed by figure (5) representing 2D virtual image for the same statements.…”

Section: Resultsmentioning

confidence: 99%

2D Virtual Image Generation for Document Security Using Bezier Cubic Splines

Mohammed¹

2014

ETJ

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This paper presents suggested algorithm to draw or generate a 2D virtual secure image from Arabic text in any document to make it a secure document and avoid any fraud operations which can be done on that document. Bezier curves had been used to generate this image depending on some computed values which is defined and evaluated from the read text in the document. Those defined values have a great effect on secure image generation where those values represent the control points which they are used in Bezier cubic function. Bezier cubic had been used to implement the secure image. Many segments written had been taken as samples to test the suggested algorithm.

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“…In curve comparison or image matching, for example pattern recognition, curvature [17] is generally used as a feature for characterizing shapes. The curvature at any point of curve can be defined by the inverse of the radius of its osculating circle.…”

Section: Introductionmentioning

confidence: 99%

An Approximation of Bézier Curves by a Sequence of Circular Arcs

Nuntawisuttiwong

Dejdumrong

2021

ITC

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Some researches have investigated that a Bézier curve can be treated as circular arcs. This work is to proposea new scheme for approximating an arbitrary degree Bézier curve by a sequence of circular arcs. The sequenceof circular arcs represents the shape of the given Bézier curve which cannot be expressed using any other algebraicapproximation schemes. The technique used for segmentation is to simply investigate the inner anglesand the tangent vectors along the corresponding circles. It is obvious that a Bézier curve can be subdivided intothe form of subcurves. Hence, a given Bézier curve can be expressed by a sequence of calculated points on thecurve corresponding to a parametric variable t. Although the resulting points can be used in the circular arcconstruction, some duplicate and irrelevant vertices should be removed. Then, the sequence of inner angles arecalculated and clustered from a sequence of consecutive pixels. As a result, the output dots are now appropriateto determine the optimal circular path. Finally, a sequence of circular segments of a Bézier curve can be approximatedwith the pre-defined resolution satisfaction. Furthermore, the result of the circular arc representationis not exceeding a user-specified tolerance. Examples of approximated nth-degree Bézier curves by circular arcsare shown to illustrate efficiency of the new method.

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An Improved Algorithm for the Approximation of a Cubic Bezier Curve and its Application for Approximating Quadratic Bezier Curve

Cited by 5 publications

References 12 publications

First measurements of low-energy cosmic rays on the surface of the lunar farside from Chang’E-4 mission

First measurements of low-energy cosmic rays on the surface of the lunar farside from Chang’E-4 mission

2D Virtual Image Generation for Document Security Using Bezier Cubic Splines

An Approximation of Bézier Curves by a Sequence of Circular Arcs

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