In this paper we discuss about the tactile information required for touchscreen interfaces, and propose a lateral-force-based 2.5-dimensional haptic display. The use of a lateral-force-based display enabled virtual bump sensations to be presented. Recently touchscreen interfaces have become popular worldwide. However, few touchscreens provide tactile feedback. Little hardware is commercialized for such kind of touchscreen. From our consideration, "press," "guide," and "sweep" movement are essential information for touchscreens. However, these devices have some operational disadvantages of these information. We intend to cope with these disadvantages by introducing the new idea of lateral-force-based display. We developed an experimental prototype of lateral-force-based display, investigated 2.5-dimensional sensations, realized a part of these essential information, and confirmed the requirement of displayed force control according to spatial wavelength. Furthermore we propose measuring method of spatial wavelengths employing multi-resolution analysis based on Haar wavelet transformation.