Because of its simplicity and intuitive approach, point-based rendering has been a very popular research area. Recent approaches have focused on hardware-accelerated techniques. By applying a deferred shading scheme, both high-quality images and high-performance rendering have been achieved. However, previous methods showed problems related to depth-based visibility computation. We propose an extended point-based rendering method using a visibility map. In our method we employ a distance-based visibility technique (replacing depth-based visibility), an averaged position map and an adaptive fragment processing scheme, resulting in more accurate and improved image quality, as well as improved rendering performance.