Suppose that we have a surface f(x,y,z) = s just like the image below (found it randomly):
Given a line equation: $$p(k) = p_0+k \cdot r$$
I would like to know how many times does this line intersects with the surface above if the direction vector
parallel to the
x, y, or z axis.
Also, what if the direction vector
perpendicular to the
x, y, or z axis ?
This is how i think of it (out of intuition):
Perpendicular: to x or y then it intersects one time. if it is perpendicular to z, then intersects twice.
Parallel: to x one time, to y two times and finally parallel to z one time.
I am not sure even if this correct, but is there a formal way to say what is what here?