Визначення області розташування точки перегину при моделюванні обводу другого порядку гладкості

Abstract

UA: У роботі розглядається задача призначення положення точки перегину при моделюванні дискретно представленої кривої другого порядку гладкості. Положення особої точки та характеристик, що їй відповідають, визначаються всередині наперед визначених діапазонів, які враховують область можливого розв’язку задачі. EN:The problem of appointment of inflection points position at modelling of discretely represented curve (DRC) second-order of smoothness is considered in this article. The problem is solved taking into account provisions of the normals, tangents and curvature radiuses which are appointed at thе starting points of the curve. Position of the inflection point and the characteristics that correspond to it, are determined within the ranges which take into account the area of possible solutions of the problem. The following steps of appointment of the inflection point location are proposed in the work: definition of pre-regionof the inflection point location; clarification of the region with take into account the characteristics of curve, which appointed at the points that limit portion of DRC; appointment of position of the inflection point and the tangent which passes through it. Further, the problem is reduced to the formation of a convex and concave portions of KDP which are joined at the inflection point with the second order of smoothness. The results which are obtained in this work can be used for modelling of curves of the second order of smoothness with the regular change of curvature. The resulting curves canbe used as framework elements at modelling of surfaces, which interact with the medium (e.g., gas, liquid).