How to create a random vector offset by a certain angle

[marcosimonvfx]

Hi folks,

let's get the disclaimer out of the way first: This question is rather technical. I use "the problem" in a rendering circumstance and therefore I thought people here might have the answer - but it could also be used somewhere else. Here we go:

 

I'm trying - for my own learning - to build a raytracer in VOPs - it has been done before, but I want to build it from scratch to get the most out of it.

Currently I'm stuck on the "diffuse/blurry reflection" of a ray, or adding randomness to the direction of a vector.

Here I couldn't find a good manual on how to do it so I figured it might work with expressing the vector in radial coordinates and then adding a random offset to the angle (and converting it back for further use). Seems cumbersome but so far it was my only solution. Here's what I got:

Picture 1 shows the vector I'd like to randomly transform - let's say by about 10 degrees (+/-5 north-south, +/-5 east-west). Picture 2 shows the result. That's looking rather good. The problem comes when the initial direction of the vector is close to the up-vector (y-Axis in this case) - Picture 3. Picture 4 shows it from the top.

As I use the approach detailed on Scratchapixel (as far as I could follow), I first offset theta, the angle to the up vector and afterwards phi - the angle between x and z. The problem is that if the initial vector is very close to the up vector and the random offset for theta happens to be close to 0, the offset of phi afterwards just turns the vector around itself - not "down" towards the plane of the x/z axis.

Any help is much appreciated - not just on how to solve this, but also for a better approach on how to do this. Thanks a bunch!