THE RESEARCH OF CONIC SECTIONS IN AUTOCAD ENVIRONMENT
Proceedings: GRAPHICON'2019 PROCEEDINGS. VOLUME 1
Authors:
1.
DonNTU
Type:
Сonference article
Published:
20.11.2019
Subject area:
GRNTI 20.01 Общие вопросы информатики
GRNTI 50.07 Теоретические основы вычислительной техники
BBK 3297 Вычислительная техника
GRNTI 50.07 Теоретические основы вычислительной техники
BBK 3297 Вычислительная техника
Language:
Russian
Keywords:
computer graphics, solid modelling, cone section, canonical equation
Abstract (English):
The application of solid modelling tools is considered when creating three-dimensional models of a straight circular cone and when studying its sections in AutoCAD. The results are presented that AutoCAD allows obtaining for a section by planes almost parallel to one or two generators. The boundary values of the angles between the plane and the generators, which determine the presence or absence of parallelism, are found. Methods are proposed for obtaining the parameters of the canonical equations of curves representing conical sections for cases when the corresponding curve (hyperbola or parabola) is modelled in AutoCAD using splines. The application of the proposed methods in the educational process is described, which makes it possible to strengthen the relationship of what is stated in the study of sections of descriptive geometry of the material with the development of methods for generating three-dimensional models, solid-state modelling tools and analytical geometry.
The application of solid modelling tools is considered when creating three-dimensional models of a straight circular cone and when studying its sections in AutoCAD. The results are presented that AutoCAD allows obtaining for a section by planes almost parallel to one or two generators. The boundary values of the angles between the plane and the generators, which determine the presence or absence of parallelism, are found. Methods are proposed for obtaining the parameters of the canonical equations of curves representing conical sections for cases when the corresponding curve (hyperbola or parabola) is modelled in AutoCAD using splines. The application of the proposed methods in the educational process is described, which makes it possible to strengthen the relationship of what is stated in the study of sections of descriptive geometry of the material with the development of methods for generating three-dimensional models, solid-state modelling tools and analytical geometry.
Keywords:
computer graphics, solid modelling, cone section, canonical equation
computer graphics, solid modelling, cone section, canonical equation
1. Gordon V.O., Semencov-Ogievskiy M.A. Kurs nachertatel'noy geometrii. - M.: Nauka, 1973. - 366 s.
2. Efimov N.V. Kratkiy kurs analiticheskoy geometrii. - M.: Nauka, 1969. - 272 s.
3. Karabchevskiy V.V. Ispol'zovanie sredstv svyazi mezhdu dvumernymi i trehmernymi komp'yuternymi modelyami pri prepodavanii graficheskih disciplin // Materialy Vtoroy ukrainsko-rossiyskoy nauchnoprakticheskoy konferencii SPGM-07. Har'kov: HGUPT. - 2007. - S. 323-332.
