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SOURCE:    Almanac of Modern Science and Education. Tambov: Gramota, 2016. № 10. P. 10-12.
SCIENTIFIC AREA:    Technical Sciences
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USE OF BIRATIONAL TRANSFORMATIONS WITH BEAMS OF SELF-CORRESPONDING CONICS IN GEOMETRIC MODELING OF CURVES AND SURFACES

Borovikov Ivan Fedorovich, Beskrovnyi Dmitrii Vyacheslavovich, Yakovuk Oleg Anatol'evich
Bauman Moscow State Technical University


Abstract. Geometric modeling of technical objects is advantageously carried out on the basis of birational transformations. As such transformations one can use nonlinear involutions with one-parameter sets (beams) of self-corresponding curves of the second order. The method considered in the article can be used in designing technical curves within a wide range of shapes and characteristics, in designing curves data bank and in surfaces simulation.
Key words and phrases: бирациональные преобразования, самосоответсвенные кривые, однопараметрическое множество кривых, фундаментальные точки, порядок преобразования, пучки окружностей, birational transformations, self-corresponding curves, one-parameter set of curves, fundamental points, transformation order, beams of circles
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References:
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