Kokareva J. Analytic and computer aided modeling of surfaces of first order linear congruences

Object - the multi-parameter analysis model surfaces, oriented to computer visualization. Purpose - to working out on analytic apparatus of surfaces of first order linear congruences associated with the program of computer visualization and based on the program controlled surface forming applied to CAD/CAM problems. Research methods - analytical, computer graphic method. Theoretical and practical results - a general schema, mathematical model, algorithmic and software process managed forming linear surfaces obtained by singling out from first order linear congruences by embedding any curve that allows for a high level of automation of the program controlled surface forming. Novelty - the first time implemented in the analytical and programmatic view computer visualization of surfaces forming of linear surfaces that singled out from many of the seven types of first order linear congruences by embedding any curve; the first time parametric equations of elliptic, hyperbolic and parabolic elliptic congruences in parameters of elliptic, hyperbolic and parabolic rotation are obtained. The degree of implementation - the work was implemented at the establishment - DE "Donetsk PromstroyNIIproekt" (Ukraine), Donbas National Academy of Civil Engineering and Architecture (Ukraine). Scope of use - civil engineering, mechanical engineering.