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I am writing a Gaussian blur filter in graphics shader code. I want to make the blur parameterized by radius from the users perspective. The best method I can figure to do this is to pick a suitable stopping point for y, say .001, and solve for the variance to plug into the normal distribution function that will achieve that value of y.

Unfortunately I cannot for the life of me solve this equation for v...

$x = 10$ (blur radius)

$$.001 = \frac{1}{2 \pi v^2}e^{-\frac{x^2}{2v^2}}$$.

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    I have tried to convert to latex (which you can do by enclosing in `$` signs), so if things aren't what you expect, let me know.2010-09-04
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    It looks like there is a typo here. If this is supposed to be the probability density function for an isotropic binormal distribution in 2d and $x$ is the radial coordinate, then it needs to be multiplied by $x$. (This won't change the solution *methods* already proposed, but it affects the details.) A few Newton-Raphson iterations should suffice to find the solution quickly.2010-09-15

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