Разработана алгоритмизация и компьютерная программа моделирования прогноза растекания пятен любого происхождения на поверхности водной акватории.
Ключевые слова: кривые и поверхности, поликоординатные векторно-параметрические преобразования, весовые коэффициенты, гладкость преобразований.
Chorna L. Polycoordinate vectorial - parametrical curves and surfaces in geometric simulation analysis. – Manuscript.
The dissertation on reception of a scietific degree of Candidate of Technical Science on speciality 05.01.01 – “Applied geometry, engineering the graphics”. – The Kyiv National University of Building and Architecture. – Ukraine, Kyiv, 2006.
The thesis is dedicated to application of a method of polycoordinate vectorial parametrical conversions for simulation analysis of curves and surfaces. These methods are founded on polyfabric conversions, polycoordinate B-splines with involvement of polynomials in view of a special weighting coefficient. The coordinate reference lines and plant of probing are presented in a parametrical aspect. Probings properties of alternatives of optimization functionals are conducted in view of miscellaneous weighting coefficients. Their effect on reference dots of convertible plant is established experimentally. Is probed polycoordinate vectorial parametrical conversions of curves on a plane, parametrical cylindrical screw space curves, arbitrary parametrical space curves. The modes of shaping of a dimensioned frame of a kinematic surface, vectorial parametrical helicoid and arbitrary surface are designed, the applicable probings on their conversion are realized, in particular, at passage from the convex form in nonconvex and on the contrary.
The task of simulation analysis of curves and surfaces adequate control of their form is decided at the expense of polycoordinate vectorial parametrical conversions. The probings have shown, that the introducing of a special weighting coefficient on the basis of polycoordinate B - splines, and vectorial parametrical determination is expedient for simulation analysis both conversion of curves and surfaces, conversion are adequate and smooth, in particular, at passage from the convex form of plant in nonconvex and on the contrary. The proposed mode of simulation analysis of surfaces has the singularities at the expense of the introducing of two bases, one of which belongs - generatrix, second - directing.
In work the algorithms of simulation analysis of curves and surfaces are designed. Realization of algorithms realized by the language AutoLisp in a medium AutoCad.
The computer program of simulation analysis of the prognosis a spreading of spots of any derivation on a surface of aquatic harbour area is designed.
Keywords: curves and surfaces, polycoordinate vectorial parametrical conversions, weighting coefficients, smoothness of conversions.