數學圖形之圓環

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(1)圓環

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

 

 

(2)隨機半徑的圓環

這裡提供了兩種寫法:

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

其特點是小圈半徑等於大圈的一半

#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)環桶

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)輪子

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)擰著的圓環

#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)多圈的環

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)偏圓環

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

 

(10)最後再補充下,圓環可以看做是一個圓圈繞一個軸旋轉產生的,所以可以有以下指令碼代碼

vertices = D1:100 D2:100u = from (0) to (2*PI) D1v = from 0 to (2*PI) D2r = 2m = rand2(r, r*10)n = r*cos(u) + my = r*sin(u)x = n*cos(v)z = n*sin(v)

 

 (11)補充一種環曲面:Bohemian

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