前面发布了很多种二维的曲线图形,其实所有的二维图形再加一个维度值就可以变成三维图形.那么这一节的内容是将一个二维曲线帖到一个球面上,以生成三维曲线.

帖到球上的方式是以如下公式生成第三个维度的数值:

y = sqrt(a*a - x*x - z*z)

 

这里举个例子是之前发的一种二维曲线:

Cyclic-harmonic_sphere

vertices = 12000t = from 0 to (40*PI)a = 10e = 1n = rand2(0.1, 10);p = a*(1 + e*cos(n*t))x = p*cos(t)z = p*sin(t)r = array_max(p)y = sqrt(r*r - p*p)

folioide_sphere

#http://www.mathcurve.com/courbes2d/folioide/folioide.shtmlvertices = 12000t = from (-20*PI) to (20*PI)e = rand2(0.1, 10)a = 10 / ei = rand_int2(2, 10)j = rand_int2(1, 10)n = i/jp = a*(e*cos(n*t) + sign(t)*e*sqrt(1 - pow(cos(n*t), 2)))x = p*cos(t)z = p*sin(t)r = array_max(p)y = sqrt(r*r - x*x - z*z)

 

改变一下半径,可以生成一种草帽形的曲线

Cyclic-harmonic_hat

vertices = 12000t = from 0 to (40*PI)a = 10e = 1n = rand2(0.1, 10);p = a*(1 + e*cos(n*t))x = p*cos(t)z = p*sin(t)y = sqrt(a*a - x*x - z*z)

切图时,我给帽子设置的颜色不太好了,我直到切最后一个图时才意识到.