Ring of mathematical graphics

This section will show you how to generate a ring and various ring-related graphs, including cyclide surface, Horn torus, and tore de Klein.

For related software, see: Mathematical graphics visualization tool. Use script code with custom syntax to generate mathematical graphics.

I have previously written a C ++ program for generating a ring. The code is published on the Generation Algorithm of the ring graph.

 

(1) Ring

vertices = D1:72 D2:72u = from 0 to (2*PI) D1v = from 0 to (2*PI) D2r = 3*cos(u) + 7z = 3*sin(u)y = r*sin(v)x = r*cos(v)y = y + 5

(2) random radius Ring

Two methods are provided:

vertices = D1:72 D2:72u = from 0 to (2*PI) D1v = from 0 to (2*PI) D2a = 10.0b = rand2(0.5, a)x = (a + b*cos(v))*sin(u)y = b*sin(v)z = (a + b*cos(v))*cos(u)

#http://www.mathcurve.com/surfaces/tore/tore.shtmlvertices = D1:100 D2:100

u = from 0 to (PI*2) D1v = from 0 to (PI*2) D2
a = rand2(1, 10)b = rand2(1, 10)
x = (a + b*cos(v))*cos(u)z = (a + b*cos(v))*sin(u)y = b*sin(v)

(3) horn Torus

The radius of a small circle is equal to half of that of a large circle.

#http://mathworld.wolfram.com/HornTorus.htmlvertices = D1:100 D2:100u = from 0 to (PI*2) D1v = from 0 to (PI*2) D2x = (1 + cos(v))*cos(u)y = sin(v)z = (1 + cos(v))*sin(u)a = 10x = x*ay = y*az = z*a

(4) ring Bucket

vertices = D1:72 D2:72u = from 0 to (2*PI) D1v = from 0 to (2*PI) D2a = 10.0b = rand2(0.5, a)x = (a + b*cos(v))*sin(u)y = b*sin(v) + if(sin(v) > 0, 10, -10)z = (a + b*cos(v))*cos(u)

(5) Wheels

vertices = D1:72 D2:72u = from 0 to (2*PI) D1v = from 0 to (2*PI) D2a = 10.0b = rand2(0.5, a)x = (a + b*cos(v))*sin(u)y = b*sin(2*v)z = (a + b*cos(v))*cos(u)

(6) tore de Klein

#http://www.mathcurve.com/surfaces/klein/toredeklein.shtmlvertices = D1:100 D2:100u = from 0 to (PI*2) D1v = from 0 to (PI*2) D2a = rand2(1, 10)b = rand2(1, 10)k = rand_int2(1, 20)k = k / 2x = (a+b*cos(v))*cos(u)z = (a+b*cos(v))*sin(u)y = b*sin(v)*cos(k*u)

(7) twisted ring

#http://www.mathcurve.com/surfaces/tore/tore.shtmlvertices = D1:100 D2:100u = from 0 to (PI*2) D1v = from 0 to (PI*2) D2a = rand2(1, 10)b = rand2(0.5, a)t = sqrt(a*a - b*b)e = rand2(-2,2)x = t*sin(v)*cos(u) - e*(b + a*cos(v))*sin(u)z = t*sin(v)*sin(u) + e*(b + a*cos(v))*cos(u)y = b*sin(v)

(8) loop with multiple loops

vertices = D1:100 D2:100u = from 0 to (2*PI) D1v = from 0 to (2*PI) D2a = sin(u)b = cos(u)c = sin(v)d = cos(v)r = 3 + c + bo = 2 * vx = r*sin(o)y = a + 2*dz = r*cos(o)x = x*5y = y*5z = z*5

(9) Ring

vertices = D1:100 D2:100u = from 0 to (2*PI) D1v = from 0 to (2*PI) D2a = rand2(5, 10)c = rand2(1, a/2)b = sqrt(a*a - c*c)d = rand2(1, 10)w = a - c*cos(u)*cos(v)x = d*(c - a*cos(u)*cos(v)) + b*b*cos(u)y = b*sin(u)*(a - d*cos(v))z = b*sin(v)*(c*cos(u) - d)x = x/wy = y/wz = z/w