C-Bézier Curves and Surfaces

Zheng, Jian‐Guo

doi:10.1006/gmip.1999.0490

Cited by 55 publications

(23 citation statements)

References 5 publications

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“…C-Bezier curves and surfaces are also presented in ref. [4]. However, these bases do not interfere in the cases of high order.…”

Section: Introductionmentioning

confidence: 92%

ωB-splines

Fang¹,

Wang²

2008

Sci. China Ser. F-Inf. Sci.

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A new kind of spline with variable frequencies, called ω B-spline, is presented. It not only unifies B-splines, trigonometric and hyperbolic polynomial B-splines, but also produces more new types of splines. ω B -spline bases are defined in the space spanned by {cosω t, sinω t, 1, t, …, t n , …} with the sequence of frequencies ω, where n is an arbitrary nonnegative integer. ω B -splines persist all desirable properties of B-splines. Furthermore, they have some special properties advantageous for modeling free form curves and surfaces.ωB-splines, frequencies, B-splines, trigonometric polynomial B-splines, hyperbolic polynomial B-splines

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“…C-Bezier curves and surfaces are also presented in ref. [4]. However, these bases do not interfere in the cases of high order.…”

Section: Introductionmentioning

confidence: 92%

ωB-splines

Fang¹,

Wang²

2008

Sci. China Ser. F-Inf. Sci.

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“…(Francis, 1994); (Hearn and Baker, 1994); (Zhang, 1999); (Tony, 1988)) applied to generate the respective contour points of each object. For example, the shape descriptor for the miss america object displayed in Figure 1(a) is given in terms of significant points (denoted by ■) [25].…”

Section: Embedding Shape Informationmentioning

confidence: 99%

Detection and separation of generic‐shaped objects by fuzzy clustering

Ali

Karmakar

Dooley

2010

International Journal of Intelligent Computing and Cybernetics

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Received ( ) Revised ( ) Accepted ( ) ABSTRACT Purpose -Existing shape-based fuzzy clustering algorithms are all designed to explicitly segment regular geometricallyshaped objects in an image, with the consequence that this restricts their capability to separate arbitrarily-shaped objects. Design/Methodology/Approach -With the aim of separating arbitrary shaped objects in an image, this paper presents a new detection and separation of generic shaped objects (FKG) algorithm that analytically integrates arbitrary shape information into a fuzzy clustering framework, by introducing a shape constraint that preserves the original object shape during iterative scaling. Findings-Both qualitative and numerical empirical results analysis corroborate the improved object segmentation performance achieved by the FKG strategy upon different image types and disparately shaped objects. Originality/value-The proposed FKG algorithm can be highly used in the applications where object segmentation is necessary. Like this algorithm can be applied in MPEG-4 for real object segmentation that is already applied in synthetic object segmentation.

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“…In recent years, some other methods have been presented for representing curves and surfaces. Papers [1][2][3][4][5][6][7] presented successively C-curves, T-curves, TC-curves, andspline in trigonometric functions space. In order to improve the flexibility of product design, researchers give further consideration to introduce shape parameters.…”

Section: Introductionmentioning

confidence: 99%

Cubic B‐Spline Curves with Shape Parameter and Their Applications

Hou-jun

Xing

et al. 2017

Mathematical Problems in Engineering

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The present studies on the extension of B-spline mainly focus on Bezier methods and uniform B-spline and are confined to the adjustment role of shape parameters to curves. Researchers pay little attention to nonuniform B-spline. This paper discusses deeply the extension of the quasi-uniform B-spline curves. Firstly, by introducing shape parameters in the basis function, the spline curves are defined in matrix form. Secondly, the application of the shape parameter in shape design is analyzed deeply. With shape parameters, we get another means for adjusting the curves. Meanwhile, some examples are given. Thirdly, we discuss the smooth connection between adjacent B-spline segments in detail and present the adjusting methods. Without moving the control points position, through assigning appropriate value to the shape parameter, C 1 continuity of combined spline curves can be realized easily. Results show that the methods are simple and suitable for the engineering application.

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C-Bézier Curves and Surfaces

Cited by 55 publications

References 5 publications

ωB-splines

ωB-splines

Detection and separation of generic‐shaped objects by fuzzy clustering

Cubic B‐Spline Curves with Shape Parameter and Their Applications

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