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Approximation curve for Example 4.

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Title: Approximation curve for Example 4.
Authors: Sana Zafar, Maria Hussain
Publication Year: 2025
Subject Terms: Biophysics, Biochemistry, Medicine, Cell Biology, Biological Sciences not elsewhere classified, Mathematical Sciences not elsewhere classified, Physical Sciences not elsewhere classified, unnecessary design features, different numerical examples, visually alluring curves, div >< p, remaining free parameters, free parameters ), fair curve designing, curvature variation energy, free parameters, stretch energy, fair curves, different choices, underlying curve, ball curve, two applications, proposed techniques, presented methods, optimization problems, objective functionals, introduced using, enough degrees, end points, control points
Description: Fair curves are visually alluring curves and are free of unnecessary design features. A new curve designing method is introduced using the tangential continuous rational cubic Said-Ball curve. Fair curves are achieved by controlling its length and variation in curvature. It has enough degrees of freedom (control points and free parameters). A family of curves can be obtained for different choices for the values of free parameters. The control points are fixed by employing the continuity conditions at the end points of the RCSBC. The optimal values of the remaining free parameters that are the weights of the underlying curve are obtained by constructing the optimization problems with stretch energy and curvature variation energy as the objective functionals. Different numerical examples are constructed to consolidate the effectiveness of the presented methods. Finally, two applications of the proposed techniques is also presented in the end.
Document Type: still image
Language: unknown
Relation: https://figshare.com/articles/figure/Approximation_curve_for_Example_4_/29494719
DOI: 10.1371/journal.pone.0324553.g004
Availability: https://doi.org/10.1371/journal.pone.0324553.g004
https://figshare.com/articles/figure/Approximation_curve_for_Example_4_/29494719
Rights: CC BY 4.0
Accession Number: edsbas.2A2F3ECC
Database: BASE
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– Name: Abstract
  Label: Description
  Group: Ab
  Data: Fair curves are visually alluring curves and are free of unnecessary design features. A new curve designing method is introduced using the tangential continuous rational cubic Said-Ball curve. Fair curves are achieved by controlling its length and variation in curvature. It has enough degrees of freedom (control points and free parameters). A family of curves can be obtained for different choices for the values of free parameters. The control points are fixed by employing the continuity conditions at the end points of the RCSBC. The optimal values of the remaining free parameters that are the weights of the underlying curve are obtained by constructing the optimization problems with stretch energy and curvature variation energy as the objective functionals. Different numerical examples are constructed to consolidate the effectiveness of the presented methods. Finally, two applications of the proposed techniques is also presented in the end.
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  Data: 10.1371/journal.pone.0324553.g004
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        Value: 10.1371/journal.pone.0324553.g004
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      – SubjectFull: Biophysics
        Type: general
      – SubjectFull: Biochemistry
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      – SubjectFull: Medicine
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      – SubjectFull: visually alluring curves
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      – TitleFull: Approximation curve for Example 4.
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