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A brief history of parametric geometry creation in Russia and foreign countries is delivered. The term «parameter» is defined. Problems in geometric design solved by parametric geometry are: 1. Parametric area of geometric figures and their manifolds. 2. Parametric area of geometric conditions. 3. Study of geometric meaning of parameters. 4. Study of possibility of coexistence of geometric conditions. The article specifies a misconception about the parameterization of geometric conditions as referring exclusively to computer graphics. Geometric dependencies were in fact introduced into computer graphics from parametric geometry, it was parametric geometry that defined the number of parameters associated with a dependency. The parametric geometry method is based on parametric calculus. The main task is to research and determine the number of parameters of geometric shapes based on shape parameters, positions, and geometric conditions. The article shows that parametric geometry underlies the wireframe method of construction. Designing surfaces as a set of frames has certain advantages over other traditional mathematical methods, as in real production conditions the surface is made not as a continuous two-parameter set of points, but as a discrete family of lines, which is optionally smoothed. For example, the formation of the carriageway of the road, which is a general ruled surface, shows the use of parametric geometry in the construction of geometrical and mathematical models, without which it is impossible to visualize the road surface with a computer.
parametric geometry, enumerative geometry, parameter, geometrical parameters, parametric area of geometric shapes, enumerative method, analytic geometry.
Многие преподаватели начертательной геометрии, за редким исключением, плохо знают, что представляет собой параметрическая геометрия и для чего она нужна. Многие ошибочно считают параметраж, использующийся в компьютерной графике, совершенно отдельным элементом, независимым от параметрической геометрии и присущим исключительно компьютерной графике [29], что в корне неверно.
Попробуем популяризовать некоторые сведения, касающиеся параметрической геометрии, и донести до широких масс хотя бы небольшой их объем.
В 1839 г. Ю. Плюккер опубликовал работу [34]. С этого момента, как считается, было заложено начало развития параметрической геометрии. В этой работе речь идет о подсчете параметров алгебраических кривых и их уравнений.
Параметры – это некоторые независимые величины (числа), значения которых служат для различия элементов множеств между собой. В качестве параметров могут выступать коэффициенты уравнений, значения на числовой оси (осях координат), геометрические условия.
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