This paper presents a fast elemental image generation algorithm, called the Viewpoint Vector Rendering (VVR), for the computer-generated integral imaging system. VVR produces a set of elemental images in real-time by assembling the segmented area of the directional scenes taken from a range of viewpoints. This algorithm is less affected by system factors such as the number of elemental lens and the number of polygons. It also supports all display modes of the integral imaging system, real, virtual and focused mode. This paper first describes the characteristics of integral imaging system. It then discusses the design, implementation, and performance evaluation of the VVR algorithm, which can be easily adapted to render the integral images of complex 3D objects.