In polytopic model based controller synthesis, the vertices of the model determine the achievable performance. This paper demonstrates a complete and tractable design process exposing the polytopic qLPV model generation and a polytopeshaping technique through the example of the TORA (Translational Oscillator with a Rotational Actuator) system. The demonstrated apparatus allows for systematically improving the control performance through the manipulation of the polytopic structure based on the MVSA (Minimal Volume Simplex Analysis) algorithm. The proposed approach fits to the framework of TP Model Transformation.