All of the information necessary to perform the polygon set operations (union, intersection, and difference) and therefore polygon clipping can be generated by a single application of a process called polygon comparison. This process accepts two or more input polygons and generates one or more polygons as output. These output polygons contain unique homogenous areas, each falling within the domain of one or more input polygons. Each output polygon is classified by the list of input polygons in which its area may be found. The union contour of all input is also generated, completing all of the information necessary to perform the polygon set operations.

A general purpose method for generating shadows using a polygonal coordinate data base is presented. The method is based on an object space polygon clipping hidden surface removal algorithm. Output from the program is in the same three-dimensional polygon format as the input. Thus, a shadowed data environment may be easily created and viewed from any observer position with no additional depth sorting time required for the hidden surface removal process. Shadows can also be cast by more than one light source. Since the shadows are generated in object space, the results can be used for both visual display and numerical analysis.

A polygon hidden surface and hidden line removal algorithm is presented. The algorithm recursively subdivides the image into polygon shaped windows until the depth order within the window is found. Accuracy of the input data is preserved.The approach is based on a two-dimensional polygon clipper which is sufficiently general to clip a concave polygon with holes to the borders of a concave polygon with holes.A major advantage of the algorithm is that the polygon form of the output is the same as the polygon form of the input. This allows entering previously calculated images to the system for further processing. Shadow casting may then be performed by first producing a hidden surface removed view from the vantage point of the light source and then resubmitting these tagged polygons for hidden surface removal from the position of the observer. Planar surface detail also becomes easy to represent without increasing the complexity of the hidden surface problem. Translucency is also possible.Calculation times are primarily related to the visible complexity of the final image, but can range from a linear to an exponential relationship with the number of input polygons depending on the particular environment portrayed. To avoid excessive computation time, the implementation uses a screen area subdivision preprocessor to create several windows, each containing a specified number of polygons. The hidden surface algorithm is applied to each of these windows separately. This technique avoids the difficulties of subdividing by screen area down to the screen resolution level while maintaining the advantages of the polygon area sort method.