Motion parallax is important to recognize the depth of a 3D image. In recent years, many 3D display methods that enable parallax images to be seen with the naked eye have been developed. In addition, there has been an increase in research to design interfaces that enable humans to intuitively interact with and operate 3D objects using their hands. However, realizing 3D object interaction as if the user is actually touching the object in the real world is quite difficult. One of the reasons for this is that the screen shape in conventional methods is restricted to a flat panel. In addition, it is difficult to achieve a balance between displaying the 3D image and sensing the user input. Therefore, we propose a novel full-parallax 3D display system that is suitable for interactive 3D applications. We call this system RePro3D. Our approach is based on a retro-reflective projection technology [Inami et al. 2000]. A number of images from a projector array are projected onto the retro-reflective screen. When a user looks at the screen through a half mirror, he or she, without the use of glasses, can view a 3D image that has motion parallax. We can choose the screen shape depending on the application. Image correction according to the screen shape is not required. Consequently, we can design a touch-sensitive soft screen, a complexly curved screen, or a screen with an automatically moving surface. RePro3D has a sensor function to recognize the user input. Some interactive features, such as operation of 3D objects, can be achieved by using it.