Coordinate scaling for building naturally parametrized curve with cubic curvature
Keywords:
плоска крива, натуральна параметризація, кубічна кривина, негладка функція, r-алгоритмAbstract
The article explores topic of coordinate scaling for linear inequality system in problem of building flat naturally parametrized curve passing through 2 points with given inclinations and curvatures at them. The non-smooth optimization problem presented is equivalent to a system of four non-linear equations with four unknowns, which describes the problem of building curve with cubic curvature distribution and its solution method based on Shor’s r-algorithm modification. It is demonstrated, that for finding problem solution with given accuracy for less time it is really better to solve the problem with well scaled coordinates. Correct scaling plays essential role in choosing parameters for iterative modeling fragments of aerodynamic and technical profiles.
References
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