In this WebApp, you can visualize the effects of different mappings between the S plane and the Z plane.
You can place and move singularities in the S diagram (left) and see its mapping in the Z diagram (right). You can also place line segments corresponding the sets of singularities like a line with constant real part.
You can also play with a second order system (bellow) and see how the discretized system functions. Move the poles to change the system and compare the different methods of discretization.

Press OK to see the function of each element in the WebApp.