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There are several techniques for determining the relevancy and relative position of two polygons. Not all tests may be used with all hidden-surface algorithms, and some of the are not always conclusive. Sometimes we can use simple tests for many of the cases and resort to more costly tests only when all else fails.
One technique that is often useful is called the minimax test or boxing test. This test checks if two polygons overlap. The test provides a quick method to determine if two polygons do not overlap. It surrounds each polygon with a box by finding its extents (minimum and maximum x and y coordinates) and then checks for the intersection for any two boxes in both the X and Y directions. If two boxes do not intersect, their corresponding polygons do not overlap. In such a case, no further testing of the edges of the polygons is required.
If the minimax test fails (two boxes intersect), the two polygons may or may not overlap, as shown in Figure 3.10. Each edge of one polygon is compared against all the edges of the other polygon to detect intersections. The minimax test can be applied first to any two edges to speed up this process.
The minimax test can be applied in the Z direction to check if there is no overlap in this direction. In all tests, finding the extents themselves is the most critical part of the test. Typically, this can be achieved by iterating through the list of vertex coordinates of each polygon and recording the largest and the smallest values for each coordinate.
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