如何均匀地将球体表面上的点随机化？ [英] How to randomize points on a sphere surface evenly?

问题描述

这是我试过的：

  rx = rand（0.0f，PI * 2.0f）; 
 ry = rand（0.0f，PI）; 
 x = sin（ry）* sin（rx）* range; 
 y = sin（ry）* cos（rx）* range; 
 z = cos（ry）* range; 
  

其结果为：

img http://img716.imageshack.us/img716/3320/sphererandom.jpg

和：

  rx = rand（-1.0f，1.0 F）; 
 ry = rand（-1.0f，1.0f）; 
 rz = rand（-1.0f，1.0f）; 
 x = rx *范围; 
 y = ry *范围; 
 z = rz *范围; 
  

其结果为：

img2 http://img710.imageshack.us/img710/5152/squarerandom.jpg

（虽然没有制作一个球体，但是opengl并没有说明有什么区别。）

看，总是有一些角落，平均点数多。我怎样才能在一个球体上创建随机点，并将点均匀分布？

解决方案

你可以这样做

b
$ b

  z = rand（-1,1）
 rxy = sqrt（1-z * z）
 phi = rand 0，2 * PI）
x = rxy * cos（phi）
y = rxy * sin（phi）
  

这里rand（u，v）从interal [u，v]中抽取一个统一的随机数

Im trying to make stars on the sky, but the stars distribution isnt even.

This is what i tried:

rx = rand(0.0f, PI*2.0f);
ry = rand(0.0f, PI);
x = sin(ry)*sin(rx)*range;
y = sin(ry)*cos(rx)*range;
z = cos(ry)*range;

Which results to:

img http://img716.imageshack.us/img716/3320/sphererandom.jpg

And:

rx = rand(-1.0f, 1.0f);
ry = rand(-1.0f, 1.0f);
rz = rand(-1.0f, 1.0f);
x = rx*range;
y = ry*range;
z = rz*range;

Which results to:

img2 http://img710.imageshack.us/img710/5152/squarerandom.jpg

(doesnt make a sphere, but opengl will not tell a difference, though).

As you can see, there is always some "corner" where are more points in average. How can i create random points on a sphere where the points will be distributed evenly?

解决方案

you can do

z = rand(-1, 1)
rxy = sqrt(1 - z*z)
phi = rand(0, 2*PI)
x = rxy * cos(phi)
y = rxy * sin(phi)

Here rand(u,v) draws a uniform random from interal [u,v]

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