CDF FOR UNIFORM DISTRIBUTION FREE
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Vector x(nSample), y(nSample), z(nSample) įor(int i = 0 i &x, const vector&y, const vector&z)Ĭout << "Error opening file for output" << endl Int writeData(const vector&x, const vector&y, const vector&z) Revised codes are given in later section.
Let's distribute the points uniformly on the surface of a sphere. Now we can use these to generate $x$, $y$ and $z$.
If we solve for $\theta$ and $\phi$, we get the following inverse functions of the CDFs In other words, let $v = F(\phi)$ and $u = F(\theta)$ be independent uniform random To distribute points such that any small area on the sphere expected to contain same number of points, we choose two random variables $u,v$ which are uniform on the interval $$. The probability that a point lies in an infinitesimal cone is $$P(\Omega)d\Omega$$ As defined above, $\Omega$ is the solid angle.
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