If we consider generated points with a given Angle1, we notice that as the angle approaches 90 degrees (or we are getting closer to the poles on the Z-axis) the points sit on a circle of decreasing circumference so the points will end up closer together.

To resolve this, you could bias the generation of Angle1 so that it is more likely to be close to 0 which will counteract this property or if Unreal Engine can generate Gaussian or normally distributed random values you can generate 3d points which if they are not zero their distance to the centre of the sphere can be normalised so that they have the correct radius. Extending these to ellipsoids (what I assume you mean by 'warped' spheres) I am not so sure about.

Do you know what kind of bias for Angle1 I would need to make points evenly distributed? Otherwise, I think clamping doesn't sound so bad, when you put it like that... at least that's some maths I understand ^^

do {
  float x = FMath::SRand() * 2.f - 1.f;
  float y = FMath::SRand() * 2.f - 1.f;
  float z = FMath::SRand() * 2.f - 1.f;
} while (x * x + y * y + z * z < 1.f);
x *= ExtX;
y *= ExtY;
z *= ExtZ;

No trigonometry, no square roots, and you can tell it's correct just by looking at it. The only drawback is that the worst case performance is terrible, but it makes up for it by being that much faster in the average case.

I would go for "a light breeze"'s implementation for any practical application, but it's fun to think of alternatives.

Similarly for the case of the circle, pick a random radius as the cubic root of a random number picked from a uniform distribution between 0 and 1. Then pick a point uniformly on the sphere of that radius.

Picking a point uniformly on a sphere (of radius 1, say) can be done in several ways. My two favorite methods are:

1. Pick z uniformly between -1 and 1, then pick an angle at random to determine x and y. This really does work!!
2. Pick three numbers from a Gaussian distribution, then normalize the resulting vector.

true

alvaro said:

I would go for "a light breeze"'s implementation for any practical application, but it's fun to think of alternatives.

Similarly for the case of the circle, pick a random radius as the cubic root of a random number picked from a uniform distribution between 0 and 1. Then pick a point uniformly on the sphere of that radius.

Picking a point uniformly on a sphere (of radius 1, say) can be done in several ways. My two favorite methods are:

1. Pick z uniformly between -1 and 1, then pick an angle at random to determine x and y. This really does work!!
2. Pick three numbers from a Gaussian distribution, then normalize the resulting vector.

Either I am misunderstanding something or your method 1 would create a higher density of points around the poles (0, 0, -1) and (0, 0, 1). Could you explain in more detail?

The z coordinate of a uniformly distributed random point on a sphere is uniformly distributed. I know this fact is surprising, which is why I gave it a double exclamation mark.

3blue1brown has a video about the formula for the area of a sphere that centers around the same fact: https://youtu.be/GNcFjFmqEc8