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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. COMPUTING REVIEWS CLASSIFICATION: 3.2, 4.9, 4.40, 4.41

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. COMPUTING REVIEWS CLASSIFICATION: 3.2, 4.9, 4.40, 4.41

A b s t r a c tAll 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. This paper introduces a polygon comparison algorithm which features reduced complexity due to its use of a graph data representation. The paper briefly introduces some of the possible approaches to the general problem of polygon comparison including the polygon set and clipping problems. The new algorithm is then introduced and explained in detail.The algorithm is sufficiently general to compare sets of concave polygons with holes. More than two polygons can be compared at one time; all information for future comparisons of subsets of the original input polygon sets is available from the results of the initial application of the process.The algorithm represents polygons using a graph of the boundaries of the polygons. These graphs are imbedded in a two dimensional geometric space.The use of the graph representation simplifies the comparison process considerably by eliminating many special cases from explicit consideration. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct co~ercial advantage, the ACM copyright notice and O]980 ACM 0-8979]-021-4/80/0700-0010 $00.75 10 Polygon operations like the ones described above are useful in a variety o! application areas, especially those which deal with problems involving two dimensional or projected two dimensional geometric areas. Examples include VLSI circuit design, cartographic and demographic applications, and polygon clipping for graphic applications such as viowporl clipping, hidden surface and line removal, detailing, and shadowing. I n t r o d u c t i o nPolygon comparison is the process where several input polygons are compared and output polygons are generated such that the area of each output polygon is unique (non-overlapping) and completely homogenous in terms of the number and identity of the input polygons which contain the output area (see figure 2-1). These results provide six common polygon manipulation operations including the polygon set operations: union, intersection, and difference (see figures 2-2a through 2-2d), and the polygon clipping operations (see figures 2-2e and 2-2f). Polygon clipping, as normally used in computer graphics, is a combination of the difference and intersection of the input polygons. This paper introduces a polygon comparison algorithm which represents an advance over its predece...

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