ONE-TO-ONE NONLINEAR TRANSFORMATION OF THE SPACE WITH IDENTITY PLANE

Autor: T V Starosolskaya, A. D. Malyi, T. V. Ulchenko, A. S. Shcherbak, Y U Y A Popudniak
Jazyk: angličtina
Rok vydání: 2016
Předmět:
Surface (mathematics)
space modelling
Computer science
Plane (geometry)
lcsh:TA1001-1280
020206 networking & telecommunications
02 engineering and technology
General Medicine
axiomatic design
graphic design
Algebra
non-linear surface
020303 mechanical engineering & transports
Transformation (function)
Analytic geometry
Transformation matrix
0203 mechanical engineering
Line (geometry)
0202 electrical engineering
electronic engineering
information engineering
Point (geometry)
МОДЕЛЮВАННЯ ПРОСТОРУ
КВАЗіЛіНіЙНі МОДЕЛі
ПЕРЕТВОРЕННЯ ПРОСТОРУ
НЕЛіНіЙНі ПОВЕРХНі
ГРАФіЧНА КОНСТРУКЦіЯ
АКСіОМАТИЧНА КОНСТРУКЦіЯ
SPACE MODELLING
QUASI-LINEAR MODEL
SPACE TRANSFORMATION
NON-LINEAR SURFACE
GRAPHIC DESIGN
AXIOMATIC DESIGN
МОДЕЛИРОВАНИЕ ПРОСТРАНСТВА
КВАЗИЛИНЕЙНЫЕ МОДЕЛИ
ПРЕОБРАЗОВАНИЕ ПРОСТРАНСТВА
НЕЛИНЕЙНЫЕ ПОВЕРХНОСТИ
ГРАФИЧЕСКАЯ КОНСТРУКЦИЯ
АКСИОМАТИЧЕСКАЯ КОНСТРУКЦИЯ
lcsh:Transportation engineering
space transformation
quasi-linear model
Transformation geometry
Zdroj: Nauka ta progres transportu, Vol 63, Iss 3, Pp 181-190 (2016)
ISSN: 2307-6666
2307-3489
Popis: Purpose.Study of geometric transformations. We will consider the so-called point transformations of space.Methodology.The most important are one-to-one transformations. They allow exploring and studying the properties of the transformed object using the properties of the original object (line, surface and figure) and the properties of the transformation. Cremona transformations occupy a special place in the set of one-to-one nonlinear transformations. Construction of one-parameter (stratifiable) transformations is carried out as one-parameter set of plane transformations, both linear and non-linear ones. The plane, in which the specific transformation is prescribed, moves in space by a certain law forming a one-parameter set of planes. The set of such plane transformations makes up the space transformation.Findings.The designed graphics algorithms and the established transformation equations allow building the visual images of transformed surfaces and conducting their research by analytical geometry methods.Originality.By completing elementary algebraic transformations of this equation, we obtain the cissoids equation. If the plane is continuously moved parallel to itself, it results in occurrence of surface, whose carcass will be the set of cissoids and the set of front-projecting lines.Practical value.The considered set of stratifiable algebraic transformations gives an effective means for exploring new curves and surfaces obtained by transforming the known algebraic lines and surfaces. These graphic algorithms allow graphically depicting the transformed lines and surfaces. The considered procedure of drawing up analytical formulas of specific transformations allows us to study the transformed surfaces and lines using the methods of analytic geometry. The above transformations can be of arbitrary high order, which is especially important during the design of complex technical surfaces such as aircraft components, parts of water and gas turbines, supports of the structures subject to strong flow of liquid, etc. Space modelling issues, including the building of graphic plane models of space, are relevant both in theoretical terms and in terms of application of the non-linear surfaces investigated on their basis for constructing the technical forms of parts and aggregates of construction machine movable elements, the middle surfaces of shells, the surfaces of turbulent blade, etc.
Databáze: OpenAIRE
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