TO THE QUESTION OF MODELLING OF COMPARTMENTS OF TWO-DIMENSIONAL CONTOURS WITH IN ADVANCE SET CONTACT ORDER

The using of nonlinear transformations which is used for designing of surfaces gives the chance to receive surfaces in the form of a continuous frame of lines, to derive their equations, to vary them parameters, to predict properties, to operate a form of the modelled surface. Properties of the designed surfaces are defined by their continuous models – the univocities set on the plane of projections which properties, in turn, depend on characteristics of the original, mutual position in space and the used projection device. The revealed regularities connecting properties of compound models with properties and the mutual provision of their originals of the requirements imposed on projection devices allow to predict the mutual provision of two and more surfaces already at a stage of a task of their models. The purpose of the offered research described in article is studying of influence of mutual provision of two surfaces of the second order on interrelation of properties and characteristics of their continuous models, it becomes clear as the line of their crossing and contact is modelled on the drawing. Studying of this interrelation presents important to a component in problems of modeling of the two-dimensional contours satisfying to a number beforehand of the set conditions of position, metric and differential character. By means of stereographic projections of two projections which are crossed surfaces of the second order on the plane models of compound surfaces in the form of the central transformations with the general center are received. Creation of models of two surfaces at various versions of their mutual provision showed what lines of crossing is modelled by projections of lines, corresponding at the same time in two central transformations with the general center. At the same time the transformations, gain such properties as coincidence of some couples of basic lines, contact their invariant of curves, etc. The research of mutual provision of two these surfaces on features and characteristics of their models received according to the scheme of a method of two images is a necessary stage for development of algorithms of the solution of the return problem of modeling of surfaces. Materials of article are of practical value to the experts who are engaged in design of curvilinear shapes.

1. Ivanov G. S. Designing of technical surfaces. M.: Mechanical engineering ,1987.192р.

2. Ivanov G.S. Direct and return problems of modeling of surfaces//Applied geometry and engineering graphics. Kiev: Budivelnik, 1990. № 50. Pp.17-21

3. Kosyakova E.Y. Modeling of mutual provision of two квадрик on the two-picture drawing//Designing of surfaces and their technical applications (The thematic collection of scientific works of of Moscow Aviation Institute). 1992. Pp.17-21

4. Kosyakova E.Y. A research of influence of mutual provision of surfaces by sight their models in problems of designing of technical forms//Scientific works of Kuban State Technological University. 2017. №. 3. Pр. 51-56