The programmable matter has paved the way for the emergence of new paradigms in the fields of computer science, design, Haptics, and material science. Several kinetic-based approaches have been developed to represent an object via surface deformation using a set of patterned actuators. Therefore, a loss of shape is noticed in the physical rendering as the actuation is applied in a single direction. This work considers a deformable interface having a chained architecture, in which smart materials such as shape memory alloy are used as a controllable hinge mechanism allowing to perform bidirectional self-folding capabilities. Such an interface can render 3D models through two main operations: NURBS slicing and segment fitting operations. More precisely, models are downscaled to match the configuration of the interface (chains × hinges per a chain), then angles are exported and replicated by the controllable shape memory effect of shape memory alloy using the Joule effect. Unlike the existing architectures, this approach affords to render a physical model with a low digital to physical conversion loss by means of its geometric complexity (e.g., cavities, lateral shape variation). The proposed approach has been modeled and validated through numerical simulation using COMSOL Multiphysics® software.