# 数学图形之圆环 – 叶飞影

(1)圆环

vertices = D1:72 D2:72
u = from 0 to (2*PI) D1
v = 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)随机半径的圆环

vertices = D1:72 D2:72

u = from 0 to (2*PI) D1
v
= from 0 to (2*PI) D2

a = 10.0
b
= 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.shtml
vertices = D1:100 D2:100

u
= from 0 to (PI*2) D1
v
= 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

#http://mathworld.wolfram.com/HornTorus.html

vertices
= D1:100 D2:100

u = from 0 to (PI*2) D1
v
= from 0 to (PI*2) D2

x = (1 + cos(v))*cos(u)
y
= sin(v)
z
= (1 + cos(v))*sin(u)

a = 10

x = x*a
y
= y*a
z
= z*a (4)环桶

vertices = D1:72 D2:72

u = from 0 to (2*PI) D1
v
= from 0 to (2*PI) D2

a = 10.0
b
= 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)轮子

vertices = D1:72 D2:72

u = from 0 to (2*PI) D1
v
= from 0 to (2*PI) D2

a = 10.0
b
= 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.shtml

vertices
= D1:100 D2:100
u
= from 0 to (PI*2) D1
v
= from 0 to (PI*2) D2

a = rand2(1, 10)
b
= rand2(1, 10)

k = rand_int2(1, 20)
k
= k / 2

x = (a+b*cos(v))*cos(u)
z
= (a+b*cos(v))*sin(u)
y
= b*sin(v)*cos(k*u) (7)拧着的圆环

#http://www.mathcurve.com/surfaces/tore/tore.shtml
vertices = D1:100 D2:100
u
= from 0 to (PI*2) D1
v
= from 0 to (PI*2) D2
a
= 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)多圈的环

vertices = D1:100 D2:100
u
= from 0 to (2*PI) D1
v
= from 0 to (2*PI) D2

a = sin(u)
b
= cos(u)

c = sin(v)
d
= cos(v)

r = 3 + c + b
o
= 2 * v

x = r*sin(o)
y
= a + 2*d
z
= r*cos(o)

x = x*5
y
= y*5
z
= z*5 (9)偏圆环

vertices = D1:100 D2:100
u
= from 0 to (2*PI) D1
v
= from 0 to (2*PI) D2

a = 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/w
y
= y/w
z
= z/w   