We have developed a novel automultiscopic display, CAGRA (Computer-Aided Graphical Real-world Avatar), which can provide full parallax both horizontally and vertically without imposing any other additional equipment such as goggles on users. CAGRA adopts two axes of rotation so that it can distribute reflected light all around. In our previous work, it was proved that the display can present a black and white image of a 3D object at 1 Hz with both horizontal and vertical parallax. Here, we discuss two important problems that remain unsolved in our previous work: optimal parameter setting and the rendering method. As for finding optimal parameters, the relationship among the rotation speed of two axes and the diffusion angle of the holographic diffuser is discussed. The rendering method was implemented so that accurate view is presented in spite of the unique mechanical structure of CAGRA. Furthermore, the synchronization mechanism between projection of images and rotation of the mirror, which was also a remaining problem, is also implemented. Findings obtained through solving these problems clarify the characteristics of this novel display system, CAGRA, and lead to its further development.