Let $f:A\in\mathbb R^2\rightarrow B\in\mathbb R^2$ and $(x_0,y_0)\in A$ be a point of discontinuity of $f$ s.t. $lim_{(x,y)\rightarrow(x_0,y_0)} f(x,y)$ doesn't exist uniquely. What is a real life example of such a situation? I thought that projecting an image of an object on the screen via projector is a good example of such a mapping but I wonder how to visualize the points of discontinuity (if any) in this example? May be, an image with a scratch/white spot/blur/distortion for $f(x_0,y_0)$?
If there exists a more suitable example for this, then please help me to visualize it.
Edit: My aim is to visualize a complex mapping and I know that one way is through the visualization of a mapping from $\mathbb R^2$ to itself, so if possible, can someone please give a possible way of visualization of a complex function?
Sweep a laser beam--left/right and up/down--across a complex three-dimensional scene, such as trees in a forest or furniture in a home. The location of the spot jumps discontinuously. Then image the three-dimensional scene with a camera off to the side, so that each point in the scene leads to a point on the two-dimensional sensor of the camera. Hence we have a discontinuous mapping from the $\mathbb R^2$ laser projection space to the $\mathbb R^2$ space on the camera sensor.