My Webworkers do not seem to be calculating correctly

Question

I am writing a JavaScript application to generate random points on the surface of a sphere. I found this formula on Wolfram to get phi and theta (http://mathworld.wolfram.com/SpherePointPicking.html#eqn2). Phi is the one I am having issues with phi = cos^(-1)(2v-1) where v is a random variables of (0,1). The following is the JavaScript I wrote to calculate phi. However, when it executes it returns NaN very often. Can anyone tell me if I am misinterpreting the formula? The only thing I can think of is Math.random() generates (0,1] and the 0 can throw an error. But in running multiple tests, I don't think Math.random() is generating a 0 every time I execute the line.

var phi = Math.acos(2 * (Math.random()) * - 1);

Answer 1

It's because the arc cosine of a number greater than 1 (the Math.acos() function) returns NaN, and Math.random() * 2 sometimes returns numbers greater than 1.

How to fix?

I see the maths cos^(-1)(2v-1)

as something like

v = someValue;

Math.acos(2 * v) - 1;

To do this with you want, you probably want

phi = Math.acos(2 * Math.random() - 1);

as your Javascript code.

Conclusion:

To fix, all you need to do is replace

phi = Math.acos(2 * Math.random() * - 1);

with

phi = Math.acos(2 * Math.random() - 1);

(remove the * -1)

Answer 2

You have an extra multiplication.

var phi = Math.acos(2 * (Math.random()) * - 1);

should be

var phi = Math.acos(2 * Math.random() - 1);