International Conference on Geometry and Graphics
ICGG 2018: ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics pp 2274–2281 Cite as
Geometric Analysis and Engineering Application of Conic Section
- Xu Yaqi 15 ,
- Zhang Chengfang 15 &
- Mi Xinwu 16
- Conference paper
- First Online: 07 July 2018
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1 Citations
Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 809))
When the plane truncates the right circular cone, a circle, an ellipse, a parabola, a hyperbolic curve, and a straight line are generated. In particular, when the angle between the truncated plane and the axis is larger than the top angle of the cone, the curve obtained by the truncated cone: circle and ellipse. This cutting method is an important way that it can make connection of pipe segments in the actual project. It is very important to analyze the laws of this cutting method. When making all the truncated planes pass through a specific point, the trajectory of these Elliptic short axis endpoints is on a parabola. In water Conservancy projects, it is often necessary to use a curved pipe to connect two pipes of different diameters. This curved pipe is a warp bend. The warp bending pipe, also known as the spherical shift surface, the horn surface, and the radial bending pipe, is an unexpandable surface. In water Conservancy projects, in the hydraulic transition section, which is rounded by Square, it is also constructed with circular curved surfaces.
- Ball shift surface
- Elliptic short axis endpoint
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Wuhan Huaxia University of Technology, Wuhan, 430070, Hubei, China
Xu Yaqi & Zhang Chengfang
Wuhan University, Wuhan, 430070, Hubei, China
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Correspondence to Zhang Chengfang .
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Department of Architecture and Urban Studies—DASTU, School of Architecture Urban Planning and Construction Engineering—AUIC, Politecnico di Milano, Milan, Italy
Luigi Cocchiarella
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Yaqi, X., Chengfang, Z., Xinwu, M. (2019). Geometric Analysis and Engineering Application of Conic Section. In: Cocchiarella, L. (eds) ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics. ICGG 2018. Advances in Intelligent Systems and Computing, vol 809. Springer, Cham. https://doi.org/10.1007/978-3-319-95588-9_219
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DOI : https://doi.org/10.1007/978-3-319-95588-9_219
Published : 07 July 2018
Publisher Name : Springer, Cham
Print ISBN : 978-3-319-95587-2
Online ISBN : 978-3-319-95588-9
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Abstract. When the plane truncates the right circular cone, a circle, an ellipse, a parabola, a hyperbolic curve, and a straight line are generated. In particular, when the angle between the truncated plane and the axis is larger than the top angle of the cone, the curve obtained by the truncated cone: circle and ellipse.