This paper proposes a novel tangible interface system to enhance the immersive experience in virtual reality environments. The proposed system allows representing physical properties of the tool, such as the deflection of the elastic rods, which users handle in a virtual and physical environment. This system is composed of two parts; one is an articulated interface to visually represent the physical behavior and the other is a computational algorithm that can compute a set of 6-DOF positions of the links. The proposed computational algorithm extends an active contour model, which is used primarily in computer vision and image processing, incorporating a spring and damping constraint energy functional. An elastic rod is modeled as a series of rigid line segments with a symmetric relationship between neighboring segments, and its shape is modeled to be influenced by energies that are induced by a user, and the external deformation of the spline. The symmetric and sparse properties of the proposed model enable an efficient energy minimization process, and the modification of a number of the line segments. Based on this configuration, we construct an energy generation method based on the positional displacement of the base element to generate the deflection behavior of the contour according to the user's motion in the space. Therefore, the physical device can simulate a variety of deformable objects by modulating energy parameters during the energy minimization process. Experimental results demonstrate the feasibility of emulating various behaviors of deformable splines, and applying to virtual reality system without interfering with the motion-to-photon latency. We also discuss the method's limitations and explore its potential.