The SFIM Group has been involved for ten years in the fabrication of active and adaptive optics, with such realizations as the 8.2 meter diameter primary active mirror of the Very Large Telescope built by its subsidiary REOSC. During its works in this field, the SFIM Group has developed original algorithms aimed at designing low-cost active deformable mirror with high performance. The purpose of optimization is to reduce the number of actuators used, which is the main driver of the mirror cost. This reduction is first achieved by minimizing high frequency defaults due to the pad located between each actuator and the mirror. Then, an optimization of the actuator location is performed, which allows minimizing defaults due to edge effects. This optimization is discussed in part II of this article. Pad optimization is performed by means of a simple model, based on a spectral analysis of the mirror deformation, which accurately coincides with finite element calculation. This work has led to the design of an optimized pad which allows a dramatic decrease of the sampling error, up to a factor of 5 for some deformations with a wide spectral bandwidth. This allowed designing a low cost active mirror proposed to the Commissariat à l' Énergie Atomique, in the scope of the French Laser MégaJoule program.