In this paper, we propose a novel three-dimensional interaction system based on a shape-changeable mobile interface. We utilize multiple serially linked line segments to physically collocate virtual objects in real space. More specifically, the proposed system provides users with geometric information by physically enclosing the target virtual object with its outer shape. To this end, we further propose an algorithm that controls each joint of the system, such that the corresponding links are aligned with the virtual surface, based on an active-contour model. An experiment was conducted to verify the proposed interaction scheme, wherein geometric information was provided in the form of mechanical shape change of the interface. Our experimental results indicate that the proposed method is effective as a system for interacting with 3D virtual objects, provided that only a mobile interface is used.