数学图形(2.16)三维螺线

    螺线,通俗来说就是绕圈圈的曲线.在前面我写过一些关于二维螺线的章节数学图形(1.12) 螺线,这一节中讲三维螺线.其实二维转三维只要再其添加一维数据即可.新一维数据的生成方式多种多样,可以让螺线帖在球面上,帖在圆锥面上,贴在柱面上,帖在抛物线曲面上.这样一来,三维螺线种类是二维螺线的N倍.这里,我只以阿基米德螺线为例,将其分别帖到球面,柱面,圆锥,抛物面上.

(1)球螺线

     前面的章节中我还写过一个数学图形(2.10)绕在球上的线圈,这就是球螺线

vertices = 3600

w = from 0 to 32

a = mod(w, 1) * 2 * PI

b = from 0 to PI

r = 10.0

x = r*sin(a)*sin(b)

y = r*cos(a)*sin(b)

z = r*cos(b)

(2)圆柱螺线

vertices = 32000

t = from 0 to (2*PI)

w = rand_int2(2, 32)

a = rand2(1, 10)

b = rand2(1, 10)

c = rand2(1, 10)

x = a*cos(w*t)

z = b*sin(w*t)

y = c*t

(3)圆锥螺线

vertices = 32000

t = from 0 to (2*PI)

w = rand_int2(2, 32)

a = rand2(1, 10)

b = rand2(1, 10)

c = rand2(1, 10)

x = a*t*cos(w*t)

z = b*t*sin(w*t)

y = c*t

(4)抛物螺线

vertices = 32000

t = from 0 to (2*PI)

w = rand_int2(2, 32)

a = rand2(1, 10)

b = rand2(1, 10)

c = rand2(1, 10)

x = a*t*cos(w*t)

z = b*t*sin(w*t)

y = c*t*t