Fuzzy Interpolation Rational Bezier Curve

Wahab, Abd. Fatah; Zakaria, Rozaimi; Ali, Jamaludin Md

doi:10.1109/cgiv.2010.17

Cited by 17 publications

(9 citation statements)

References 14 publications

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“…Задачи аппроксимации и интерполяции данных стали появляться с развитием компьютерной техники, а также алгоритмических и математических методов. Известны работы с шестидесятых годов прошлого столетия [22], за последние десятилетия появилось много методов данного направления исследования [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15], но вопрос применимости методов при различном объеме и качестве исходных данных стоит и сейчас. В [16][17][18] представлены современные нелинейные методы фильтрации на основе PDE (Partial Differential Equations) и методы непрозрачного изображения, представлены основы теории интерполяции, приведена классификация методов, рассматриваются точные и приближенные, однопараметрические и многопараметрические методы.…”

Section: Introductionunclassified

Comparative Analysis of Missing Data Recovery Methods

Sorokin¹,

Dagaev²,

Borodyansky³

2020

IZVESTIYA SFedU. ENGINEERING SCIENCES

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Section: Introductionunclassified

Comparative Analysis of Missing Data Recovery Methods

Sorokin¹,

Dagaev²,

Borodyansky³

2020

IZVESTIYA SFedU. ENGINEERING SCIENCES

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“…The concept of a fuzzy tensor product Bézier surface was introduced in [1]. The construction of the fuzzy B-spline model, modeling of uncertain data based on B-spline model curve are discussed in [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Certain Algorithms for Modeling Uncertain Data Using Fuzzy Tensor Product Bézier Surfaces

Sarwar

Akram

2018

Mathematics

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Real data and measures are usually uncertain and cannot be satisfactorily described by accurate real numbers. The imprecision and vagueness should be modeled and represented in data using the concept of fuzzy numbers. Fuzzy splines are proposed as an integrated approach to uncertainty in mathematical interpolation models. In the context of surface modeling, fuzzy tensor product Bézier surfaces are suitable for representing and simplifying both crisp and imprecise surface data with fuzzy numbers. The framework of this research paper is concerned with various properties of fuzzy tensor product surface patches by means of fuzzy numbers including fuzzy parametric curves, affine invariance, fuzzy tangents, convex hull and fuzzy iso-parametric curves. The fuzzification and defuzzification processes are applied to obtain the crisp Beziér curves and surfaces from fuzzy data points. The degree elevation and de Casteljau's algorithms for fuzzy Bézier curves and fuzzy tensor product Bézier surfaces are studied in detail with numerical examples.

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“…Recently, geometric interpretations of data that uncertain truth were presented by Wahab and friends [4][5][6][7]. They studied geometric models of fuzzy and intuitionistic fuzzy data and gave fuzzy interpolation and Bézier curve modeling.…”

Section: Introductionmentioning

confidence: 99%