This paper presents the development of an active discretely deformable surface that makes use of mechanical interpolation in order to limit the number of required actuators. First, a planar interpolation mechanism is proposed and optimized in order to minimize the interpolation errors. Then a four-DOF spatial interpolation mechanism with the actuators in the corners is designed based on the planar mechanism. The kinematics of this mechanism are also derived. Finally, a prototype—built in order to illustrate the concept—is presented. The prototype consists of a small-scale dynamically reconfigurable stage for puppet theater performance, referred to as a Castelet. The prototype was used for the creation of two shows that clearly demonstrate the potential of the Castelet in theater performance as well as in other applications.