Single-blade dual-surface in mathematical graphics

The curved surface generated when the hyperbolic curve rotates around its symmetric axis is a bilinear surface. In mathematics, Hyperbolic SurfaceIs a quadratic surface.
The single-leaf dual-surface can be expressed in the formula (x ^ 2)/(a ^ 2) + (y ^ 2)/(B ^ 2)-(Z ^ 2) /(C ^ 2) = 1

In reality, the structure of cooling towers in many power plants is in the shape of Single-blade dual-curved surfaces. Since a single-leaf dual-surface is a ruled surface, it can be built with a straight steel beam. In this way, the wind resistance will be reduced, and the knot can be maintained with the least amount of material.

Complete structure.

This article will show several algorithm and cut chart for generating single-leaf dual-surface. use the script code of the custom syntax to generate a mathematical image. for related software, see: Mathematical graphics visualization tool. This software is free and open-source. QQ chat group: 367752815

(1)

vertices = dimension1:72 dimension2:72u = from 0 to (2*PI) dimension1v = from (-4) to (4) dimension2x = cosh(v)*cos(u)z = cosh(v)*sin(u)y = sinh(v)

(2)

A single-leaf dual-surface is a straight line surface (ruled_surface. The single-leaf dual-Surface Obtained by rotating x = 1, y = T, Z = 2 t around the Z axis. The following is an example of generating a single-leaf dual-surface using a straight line:

vertices = dimension1:72 dimension2:72u = from 0 to (2*PI) dimension1v = from (-10) to (10) dimension2x = cos(u) - v*sin(u)z = sin(u) + v*cos(u)y = 2*v

(3) random single-blade dual-surfaces with elliptical openings

vertices = dimension1:72 dimension2:72u = from 0 to (2*PI) dimension1v = from (-5) to (5) dimension2a = rand2(1, 5)b = rand2(1, 5)c = rand2(1, 5)x = a*sqrt(1 + v*v)*cos(u)z = b*sqrt(1 + v*v)*sin(u)y = c*v

(4) random single-blade dual-curved surface with an elliptical opening.

vertices = D1:100 D2:100u = from 0 to (2*PI) D1v = from (-PI*0.45) to (PI*0.45) D2
a = rand2(1, 10)b = rand2(1, 10)c = rand2(1, 10)
x = a*sec(v)*sin(u)y = b*tan(v)z = c*sec(v)*cos(u)

(5) The upper part of a single-leaf dual-Surface

 

vertices = dimension1:72 dimension2:72u = from (PI*0.05) to (PI*0.499) dimension1v = from 0 to (2*PI) dimension2a = rand2(1, 5)b = rand2(1, 5)c = rand2(1, 5)x = a*cosh(u)*cos(v)z = b*cosh(u)*sin(v)y = c*sinh(u)

 

(6) lower half of a Single-leaf dual-Surface

 

vertices = dimension1:72 dimension2:72u = from (-PI*0.499) to (-PI*0.01) dimension1v = from 0 to (2*PI) dimension2a = rand2(1, 5)b = rand2(1, 5)c = rand2(1, 5)x = a*cosh(u)*cos(v)z = b*cosh(u)*sin(v)y = c*sinh(u)

 

(7) linear random Rotation Surface

vertices = 100u = from -10 to 10a = rand2(-5, 5)b = rand2(-5, 5)x = uy = (x + a) + bi = rand2(-2, 2)j = rand2(-2, 2)k = rand2(-2, 2)surface_slices = 72rotate = anchor[0, 0, 0], axis[i, j, k], angle[0, 2*PI]