In this paper, we present a robotic surface display that physically imitates the orientation of virtual 3D geometry touched through a 2D flat screen. The proposed approach renders the surface orientation of 3D geometry such that users can tactually obtain relative geometric information, which plays a significant role in the process of real-world haptic object perception. Taking advantage of the planar aspect of touch surfaces, the system constructs a rotation matrix to control the pose of a surface with minimal mechanical movements with given partial geometric information (i.e., normal vector at the point of touch). To evaluate the proposed rendering scheme, we conducted a geometric task (two alternative forced choices) with a set of hand-sized cylindrically curved geometries in which participants were asked to identify which of the two surfaces they perceived as being more curved. Curvatures with the same polarities (i.e., convex-convex and concave-concave) were employed in the study and psychometric curves estimated to obtain the threshold of the curvature difference and to validate the proposed rendering scheme. Possible applications of the proposed system and its limitations are also presented.