A hidden-surface algorithm with anti-aliasing

Abstract

In recent years we have gained understanding about aliasing in computer generated pictures and about methods for reducing the symptoms of aliasing. The chief symptoms are staircasing along edges and objects that pop on and off in time. The method for reducing these symptoms is to filter the image before sampling at the display resolution. One filter that is easy to understand and that works quite effectively is equivalent to integrating the visible intensities over the area that the pixel covers. There have been several implementations of this method - mostly unpublished - however most algorithms break down when the data for the pixel is complicated. Unfortunately, as the quality of displays and the complexity of pictures increase, the small errors that can occur in a single pixel become quite noticeable. A correct solution for this filter requires a hidden-surface algorithm at each pixel! If the data at the pixel is presented as a depth-ordered list of polygons then the average visible intensity can be found using a polygon clipper in a way similar to that employed by two known hidden-surface algorithms. All of the polygons in a pixel are clipped against some front unclipped edge into two lists of polygons. The algorithm is recursively entered with each new list and halts when the front polygon is clipped on all sides, thereby obscuring the polygons behind. The area weighted colors are then returned as the value to be added to the other pieces in the pixel.