Sample of a subset of a plane

Sample of a subset of a plane

I have the equation of a plane $ax+bx+cx+d$ and a point $(x_0, y_0, z_0)$
on that plane.
I defined the neighborhood of that point on that plane as the system
between the plane equation and the equation: $(x-x_0)^2 + (y-y_0)^2 +
(z-z_0)^2 \le \epsilon^2$
(I'm right?)
Now I need to sample that neighbor to get some points, how can I do it?
Thanks in advance.