Defining the principal axes of the quadric cone - a general case with elliptic base section curve
Конференцијски прилог (Објављена верзија)
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This paper presents an constructive procedure of determining three mutually orthogonal principal axes (three planes of symmetry) of the quadric cone, the general case with elliptical base section curve.The constructive procedure is based on establishing correlative correspondence between the base curve plane (points and lines) and bundle of lines and planes at the vertex of the cone.At the base curve plane, two pairs of collocal, corelatively associated planes are set.
After overlapping two of them, the other two collocal planes become collinear. Three double points in two generally collinear planes are intersection points between three principal axes and base plain of the cone.
Кључне речи:
The general case of cone; / the main axes of cone / corellative transformation / polarity / auto polar tetrahedronИзвор:
Proceedings of the 2nd Int. Sci Conf. mpNGeometrija 2010, Belgrade, Serbia, 2010, 51-60Издавач:
- Faculty of Architecture, University of Belgrade
- Serbian Society for Geometry and Graphics
Колекције
Институција/група
GraFarTY - CONF AU - Čučaković, Aleksandar AU - Dimitrijević, Magdalena PY - 2010 UR - https://grafar.grf.bg.ac.rs/handle/123456789/3096 AB - This paper presents an constructive procedure of determining three mutually orthogonal principal axes (three planes of symmetry) of the quadric cone, the general case with elliptical base section curve.The constructive procedure is based on establishing correlative correspondence between the base curve plane (points and lines) and bundle of lines and planes at the vertex of the cone.At the base curve plane, two pairs of collocal, corelatively associated planes are set. After overlapping two of them, the other two collocal planes become collinear. Three double points in two generally collinear planes are intersection points between three principal axes and base plain of the cone. PB - Faculty of Architecture, University of Belgrade PB - Serbian Society for Geometry and Graphics C3 - Proceedings of the 2nd Int. Sci Conf. mpNGeometrija 2010, Belgrade, Serbia T1 - Defining the principal axes of the quadric cone - a general case with elliptic base section curve EP - 60 SP - 51 UR - https://hdl.handle.net/21.15107/rcub_grafar_3096 ER -
@conference{ author = "Čučaković, Aleksandar and Dimitrijević, Magdalena", year = "2010", abstract = "This paper presents an constructive procedure of determining three mutually orthogonal principal axes (three planes of symmetry) of the quadric cone, the general case with elliptical base section curve.The constructive procedure is based on establishing correlative correspondence between the base curve plane (points and lines) and bundle of lines and planes at the vertex of the cone.At the base curve plane, two pairs of collocal, corelatively associated planes are set. After overlapping two of them, the other two collocal planes become collinear. Three double points in two generally collinear planes are intersection points between three principal axes and base plain of the cone.", publisher = "Faculty of Architecture, University of Belgrade, Serbian Society for Geometry and Graphics", journal = "Proceedings of the 2nd Int. Sci Conf. mpNGeometrija 2010, Belgrade, Serbia", title = "Defining the principal axes of the quadric cone - a general case with elliptic base section curve", pages = "60-51", url = "https://hdl.handle.net/21.15107/rcub_grafar_3096" }
Čučaković, A.,& Dimitrijević, M.. (2010). Defining the principal axes of the quadric cone - a general case with elliptic base section curve. in Proceedings of the 2nd Int. Sci Conf. mpNGeometrija 2010, Belgrade, Serbia Faculty of Architecture, University of Belgrade., 51-60. https://hdl.handle.net/21.15107/rcub_grafar_3096
Čučaković A, Dimitrijević M. Defining the principal axes of the quadric cone - a general case with elliptic base section curve. in Proceedings of the 2nd Int. Sci Conf. mpNGeometrija 2010, Belgrade, Serbia. 2010;:51-60. https://hdl.handle.net/21.15107/rcub_grafar_3096 .
Čučaković, Aleksandar, Dimitrijević, Magdalena, "Defining the principal axes of the quadric cone - a general case with elliptic base section curve" in Proceedings of the 2nd Int. Sci Conf. mpNGeometrija 2010, Belgrade, Serbia (2010):51-60, https://hdl.handle.net/21.15107/rcub_grafar_3096 .