To simulate the natural three-dimensional (3D) display, both binocular parallax and smooth motion parallax are required. Normally, it requires a huge amount of spatial information to increase the number of views and to provide smooth motion parallax for natural 3D display similar to real life. Holographic stereogram can be used to display a description of 3D discrete images or a set of 3D data points. Here, three methods are used to realize natural 3D displays with smooth motion parallax, which are functionally equivalent to the holographic stereogram. With digitally generated active partially pixelated masks in the liquid crystal panel combining with a precision lenticular lens array, the 3D display with 1200 views from a computer numerical model is demonstrated in 56° viewing angle. The displayed depth is more than 40 cm and the screen size is 50.7 cm×28.5 cm. With a holographic functional screen with a size of 1.3 m×1.8 m, a demonstrated system including optimally designed camera-projector arrays and a video server can display the fully continuous 3D scene with more than 1 m image depth. Based on the digitally generated tompographic images, a 3D display with smooth motion parallax is demonstrated in a 50 inch (1 inch=2.54 cm) LCD panel with the resolution of 3840 pixel×2160 pixel.