Conversion Between Cubic Bezier Curves and Catmull–Rom Splines

Arasteh, Soroosh Tayebi; Kalisz, Adam

doi:10.1007/s42979-021-00770-x

Cited by 6 publications

(3 citation statements)

References 18 publications

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“…The curves are shown in Figure 13. 18,19 The analysis above underscores that the critical factor in selecting the appropriate Bezier curve is determining the number of control points for the curve. These control points encompass not only the pivotal points through which the curve passes but also the constraint points that govern the parameters.…”

Section: Improvement Methodsmentioning

confidence: 99%

Improvement design of blade profile on rotary wings of winder for synthetic filament: Analysis and experiment

Liu,

Li,

Wang

et al. 2024

Textile Research Journal

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The synthetic filament winder drives the filament through the traverse mechanism with rotary wings so that it can complete the transverse reciprocating motion when it is continuously wound and achieve the spiral distribution on the cylindrical package. When the existing traverse mechanism leads the filament, the filament is easy to oscillate and breaks away from the control of the rotary blade during the reversing process at both ends of the package, which directly affects its forming on the package. In this study, firstly, the filament leading process is analyzed from the filament leading principle of the traverse mechanism with rotary wings and the key points of the profile are identified. Secondly, we applied parameter constraints of key points and developed a blade profile that can not only meet the demand of filament reversing but also improve the above abnormal phenomena by curve-fitting, so that the blade can continuously and stably lead and control the filament during the reversing process. Finally, through the actual winding experiment, we contrasted the state of the filament leading process of the original blades with the improved blades, and verified the improvement effect. This study provides a design basis and optimization reference for realizing a smooth and stable relay between the filament and blades.

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Section: Improvement Methodsmentioning

confidence: 99%

Improvement design of blade profile on rotary wings of winder for synthetic filament: Analysis and experiment

Liu,

Li,

Wang

et al. 2024

Textile Research Journal

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“…Cubic Catmull-Rom spline is one of the common parametric curves defined by control points. Generally, the cubic Catmull-Rom spline is given by [2][3][4][5]…”

Section: Review Of the Cubic Catmull-rom Splinementioning

confidence: 99%

“…We cannot provide an exhaustive survey, but many of these methods can be referred to [1]. Among these methods, the cubic Catmull-Rom spline [2][3][4][5] is a well-known parametric interpolatory curve representation. But the shape of the cubic Catmull-Rom spline cannot be adjusted when the control points are fixed, which limits its applications to a certain extent.…”

Section: Introductionmentioning

confidence: 99%

The quartic Catmull–Rom spline with local adjustability and its shape optimization

Liu

2022

Adv Cont Discr Mod

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Parametric interpolatory curves play a vital part in geometric modeling. Cubic Catmull–Rom spline is a well-known tool for constructing parametric interpolatory curves, but it cannot be modified once its control points are fixed. We propose a novel quartic Catmull–Rom spline with free parameters to tackle this issue. The quartic Catmull–Rom spline owns shape adjustability based on inheriting the features of the cubic Catmull–Rom spline. Some modeling examples show that the shape of the quartic Catmull–Rom spline can realize both global adjustment and local adjustment by changing the free parameters. In addition, we give three schemes for optimizing the shape of the quartic Catmull–Rom spline, which can generate the spline with minimal internal energy, the shape-preserving spline, and the monotonicity-preserving spline. Numerical examples indicate that the proposed schemes are effective and the quartic Catmull–Rom spline is more practical than the cubic Catmull–Rom spline in data interpolation.

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