CONTROL OF ENERGY EFFICIENCY IN INDUSTRY AND HOUSING AND COMMUNAL SERVICES
Sign | Register
UDC 681.327.11
3d-model of quadric intersection with common focus points
A.L. Kheyfets, South Ural State University, Chelyabinsk, Russian Federation, heifets@yandex.ru
Abstract
The solution of the problem of quadric intersection combined with focus points or focus points of their sections is considered in the article. Ellipsoid, hyperboloid and paraboloid are quadrics formed by the rotation. All combinations of such quadrics are studied.It is shown that there is intersection by one or two conics. Peculiar features of spatial position of the quadric intersection lines are analyzed. It is shown that there are common periphery plane quadric such as elliptic cone or parabolic cylinder at adjustment of considered quadrics and necessary combination of parameters of a relative position. Moreover, common inner tangent sphere appears.The analysis is performed by 3d computer geometric simulation methods with Auto-CAD. The examples and algorithms for tangent quadric construction are given. The connection between the problem in question and well-known Monge theorem is studied.
Keywords
quadric, computer simulation, geometric simulation, descriptive geometry, G. Monge, 3d-technologies, AutoCAD
References
1. Monzh G. Nachertatel'naja geometrija [Descriptive geometry]. Izd-vo akademii nauk SSSR, 1947, 291 p.
2. Budarin O.S. Second order curves with a common focal point [K voprosu ob odnofokusnyh krivyh vtorogo porjadka]. Geometricheskie modeli i algoritmy: mezhvuzovskij sb. Trudov [Geometric models and algorithms: an inter-University collection of works]. L. LISI, 1988, pp. 106–115.
3. Kheyfets A.L., Loginovsky A.N. 3D-model of the intersection of Ellipsoids with a common focal point [3D-model' peresechenija sofokusnyh jellipsoidov]. Sovershenstvovanie podgotovki uchashhihsja i studentov v oblasti grafiki, konstruirovanija i standartizacii: Mezhvuzovskij nauchnometodicheskij sbornik. [Improving the training of pupils and students in the field of graphics, design and standardization: the interuniversity scientific-methodical collection]. Saratov, SGTU, 2012, pp. 20–26.
4. Chetveruhin N.F., Levickij V.S., Prjanishnikova Z.I. Nachertatel'naja geometrija [Descriptive geometry]. Moscow,Vysshaja shkola, 1963. 420 p.
5. Kheyfets A.L., Loginovsky A.N. 3D-models of ruled surfaces with three rectilinear quides [3D-modeli linejchatyh poverhnostej s tremja prjamoli-nejnymi napravljajushhimi]. Vestnik Juzhno-Ural'skogo gosudarstvennogo universiteta. Serija “Stroitel'stvo i arhitektura”[ Herald of the South-Ural state University. A series of “Construction and architecture”]. Cheljabinsk, SUSU, 2008, vol. 7. № 25(125), pp. 51–56.
6. Kheyfets A.L., Loginovsky А.N., Butorina I.V. 3D-modeling lines crossing surfaces [3D-modelirovanie linij peresechenija poverhnostej (AutoCAD)] Sovershenstvovanie podgotovki uchashhihsja i studentov v oblasti grafiki, konst-ruirovanija i standartizacii. Mezhvuzovskij nauchnometodicheskij sbornik. [Improving the training of pupils and students in the field of graphics, design and standardization: the interuniversity scientific-methodical collection]. Saratov, SGTU, 2004, pp. 127–133.
2. Budarin O.S. Second order curves with a common focal point [K voprosu ob odnofokusnyh krivyh vtorogo porjadka]. Geometricheskie modeli i algoritmy: mezhvuzovskij sb. Trudov [Geometric models and algorithms: an inter-University collection of works]. L. LISI, 1988, pp. 106–115.
3. Kheyfets A.L., Loginovsky A.N. 3D-model of the intersection of Ellipsoids with a common focal point [3D-model' peresechenija sofokusnyh jellipsoidov]. Sovershenstvovanie podgotovki uchashhihsja i studentov v oblasti grafiki, konstruirovanija i standartizacii: Mezhvuzovskij nauchnometodicheskij sbornik. [Improving the training of pupils and students in the field of graphics, design and standardization: the interuniversity scientific-methodical collection]. Saratov, SGTU, 2012, pp. 20–26.
4. Chetveruhin N.F., Levickij V.S., Prjanishnikova Z.I. Nachertatel'naja geometrija [Descriptive geometry]. Moscow,Vysshaja shkola, 1963. 420 p.
5. Kheyfets A.L., Loginovsky A.N. 3D-models of ruled surfaces with three rectilinear quides [3D-modeli linejchatyh poverhnostej s tremja prjamoli-nejnymi napravljajushhimi]. Vestnik Juzhno-Ural'skogo gosudarstvennogo universiteta. Serija “Stroitel'stvo i arhitektura”[ Herald of the South-Ural state University. A series of “Construction and architecture”]. Cheljabinsk, SUSU, 2008, vol. 7. № 25(125), pp. 51–56.
6. Kheyfets A.L., Loginovsky А.N., Butorina I.V. 3D-modeling lines crossing surfaces [3D-modelirovanie linij peresechenija poverhnostej (AutoCAD)] Sovershenstvovanie podgotovki uchashhihsja i studentov v oblasti grafiki, konst-ruirovanija i standartizacii. Mezhvuzovskij nauchnometodicheskij sbornik. [Improving the training of pupils and students in the field of graphics, design and standardization: the interuniversity scientific-methodical collection]. Saratov, SGTU, 2004, pp. 127–133.
Source
Bulletin of the South Ural State University. Ser. Computer Technologies, Automatic Control, Radio Electronics, 2013, vol. 13, no. 2, pp. 88-95. (in Russ.) (The main)