An Automatic Generation of G^1 Curve Fitting of Arabic Characters

Yahya, Fatimah; Ali, Jamaludin Md; Majid, Ahmad Abd.; Ibrahim, Arsmah

doi:10.1109/cgiv.2006.18

Cited by 14 publications

(2 citation statements)

References 12 publications

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“…They also showed the significance of monotone curvature in CAGD/CAM. In [39], Yahya et al, presented the automatic generation of Arabic characters and font designing by using G 1 continuity conditions. A Bézier curve with shape parameters was presented by Wang in [40].…”

Section: Introductionmentioning

confidence: 99%

Geometric Modeling of Novel Generalized Hybrid Trigonometric Bézier-Like Curve with Shape Parameters and Its Applications

et al. 2020

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The main objective of this paper is to construct the various shapes and font designing of curves and to describe the curvature by using parametric and geometric continuity constraints of generalized hybrid trigonometric Bézier (GHT-Bézier) curves. The GHT-Bernstein basis functions and Bézier curve with shape parameters are presented. The parametric and geometric continuity constraints for GHT-Bézier curves are constructed. The curvature continuity provides a guarantee of smoothness geometrically between curve segments. Furthermore, we present the curvature junction of complex figures and also compare it with the curvature of the classical Bézier curve and some other applications by using the proposed GHT-Bézier curves. This approach is one of the pivotal parts of construction, which is basically due to the existence of continuity conditions and different shape parameters that permit the curve to change easily and be more flexible without altering its control points. Therefore, by adjusting the values of shape parameters, the curve still preserve its characteristics and geometrical configuration. These modeling examples illustrate that our method can be easily performed, and it can also provide us an alternative strong strategy for the modeling of complex figures.

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Section: Introductionmentioning

confidence: 99%

Geometric Modeling of Novel Generalized Hybrid Trigonometric Bézier-Like Curve with Shape Parameters and Its Applications

et al. 2020

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“…PSO is used to find the best control point and weight, to enable us to generate the best fitted curve to the given data. To obtain the best solution, we use the sum squares error method proposed by Yahya et al (2006). We set number of iterations = 50, inertia 1.0 ω = and C 1 = C 2 = 2.0.…”

Section: (T 1) V (T) C (P (T) X (T)) C (G (T) X (T))mentioning

confidence: 99%

Curve Fitting Using Conic by Evolutionary Computing

R.¹

2012

Journal of Mathematics and Statistics

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Problem statement:A direct method, such as least squares technique is usually used to solve problems involving matching a curve or a surface to a set of data points. The solution obtained by this direct method is precise or very good in approximation, but computationally not very efficient. Thus, in this study, we propose an indirect approach using Particle Swarm Optimization (PSO) technique as an alternative. Approach: As a case study, we use conic curve which satisfy C 0 continuity to be fitted to a given set of data points. PSO, a soft computing method is employed to optimize the control points and weights which are then used in conic equations. Results: Best fitted conic curve that represents all the given data points is then obtained. Conclusion: We use an indirect technique of soft computing methods, i.e., PSO to fit a curve to a given data set. We believe that other types of soft computing based heuristic procedures may also be used to solve related problems or to find its effectiveness.

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