Geometric Analysis and Engineering Application of Conic Section

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.