PUBLISHED PAPERS #05.09
| Volodymyr Zhydkov, Olha Khomiak. Coordinate Scaling for Making Naturally Parametrized Curve with Cubic Curvature |
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| Abstract. The research paper analyzes efficiency of coordinate scaling for inequality system in optimization problem of building plane naturally parametrized curve subject to certain geometric conditions, such as passing through specified points with given inclinations and curvature at them. The non-smooth optimization problem is presented in form of a system of four non-linear inequalities with four unknowns, describing building curve with cubic curvature distribution and its solution derived from Shor's r-algorithm. The results of conducted computational experiments revealed that for finding the problem solution with given accuracy, scaling coordinates reduces time required for finding solution. In conclusion, it is established that correct coordinate scaling plays essential role in computationally-efficient finding parameters for iterative modelling of aerodynamic and technical profiles' fragments. |
| Keywords: naturally parametrized curve, cubic curvature, non-smooth function, r-algorithm |
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| DOI: https://doi.org/10.30546/MaCoSEP2025.1473 |