Bilinear surface in mathematical graphics

The curved surface generated when the hyperbolic curve rotates around its symmetric axis is a dual-surface. The previous section describes the single-leaf dual-surface. This section continues with the dual-leaf dual-surface.

The mathematical formula of the double-leaf bilinear is as follows:

X * x/a/A + y * Y/B-z * z/C =-1

In mathematics,Hyperbolic SurfaceIs a quadratic surface. Using Cartesian coordinates, the dual surface can be expressed

( Single-leaf dual-Surface),

Or

( Dual-leaf dual-Surface).

IfRotate A Curved Surface.

This article will show several algorithms and cut diagrams for generating dual-blade dual-surfaces. 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)

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

(2)

vertices = D1:100 D2:100u = from 0 to (1*PI) D1v = from (0) to (2*PI) D2 gap[PI*0.5, PI*1.5]a = rand2(1, 10)b = rand2(1, 10)c = rand2(1, 10)x = a*tan(v)*sin(u)y = b*sec(v)z = c*tan(v)*cos(u)

(3)

I have previously written an article on the hyperbolic graph (1.10 ).

Rotate the hyperbolic curve for one week to generate a hyperbolic surface.

vertices = 360u = from -1 to 1 gap[0]x = uy = 1/xy = limit(y, -50, 50)surface_slices = 72rotate = anchor[0, 0, 0], axis[1, 1, 0], angle[0, 2*PI]

(4)

Hyperbolic surface (East-West opening)

vertices = 100t = from 0 to (2*PI) gap[PI*0.5, PI, PI*1.5]a = rand2(0.1, 10)b = rand2(0.1, 10)x = a*sec(t)y = b*tan(t)x = limit(x, -50, 50)y = limit(y, -50, 50)surface_slices = 72rotate = anchor[0, 0, 0], axis[1, 0, 0], angle[0, 2*PI]

Hyperbolic surface (North-South opening)

vertices = 100t = from 0 to (2*PI) gap[PI*0.5, PI, PI*1.5]a = rand2(0.1, 10)b = rand2(0.1, 10)x = a*tan(t)y = b*sec(t)x = limit(x, -50, 50)y = limit(y, -50, 50)surface_slices = 72rotate = anchor[0, 0, 0], axis[0, 1, 0], angle[0, 2*PI]