Map s-plane to z-plane

For a digital system of sampling time T, there is a certain area in the S-plane that meats the requirements of the designer. The function szmap plots this area in the S-plane and maps/plots it into Z-plane. This design area is the area bounded by the limits of relative stability parameters (i.e. damping ratio, damped natural frequency of complex poles and time constant of the pole).
The inputs to the functions are the bounds of the design area defines by subset of the following variables:
1. Limits of real part of desired poles (sigma).
2. Limits of damped natural frequency of complex poles (omega_d).
3. Limits of damping ratio of complex poles (zeta).
4. Sampling time of the digital system.