We will report our recent developments in DFD (Depth-fused 3D) display and arc 3D display, both of which have smooth movement parallax. Firstly, fatigueless DFD display, composed of only two layered displays with a gap, has continuous perceived depth by changing luminance ratio between two images. Two new methods, called “Edge-based DFD display” and “Deep DFD display”, have been proposed in order to solve two severe problems of viewing angle and perceived depth limitations. Edge-based DFD display, layered by original 2D image and its edge part with a gap, can expand the DFD viewing angle limitation both in 2D and 3D perception. Deep DFD display can enlarge the DFD image depth by modulating spatial frequencies of front and rear images. Secondly, Arc 3D display can provide floating 3D images behind or in front of the display by illuminating many arc-shaped directional scattering sources, for example, arcshaped scratches on a flat board. Curved Arc 3D display, composed of many directional scattering sources on a curved surface, can provide a peculiar 3D image, for example, a floating image in the cylindrical bottle. The new active device has been proposed for switching arc 3D images by using the tips of dual-frequency liquid-crystal prisms as directional scattering sources. Directional scattering can be switched on/off by changing liquid-crystal refractive index, resulting in switching of arc 3D image.