Minimax Tests for Typical Polygons and Edges:

The minimax test may be applied in the Z direction to check if there is no overlap in this direction. In all tests, determining the extents themselves is the most critical part of the test. Typically, this may be achieved by iterating through the list of vertex coordinates of each polygon and recording the largest and the smallest values for each coordinate.

  (a) Boxes Polygons Do Not Overlap                                    (b) Boxes Overlap and Polygons Do Not

           (c) Boxes and Polygons Overlap                            (d) Minimax Test of Individual Edges

Figure: Minimax Tests for Typical Polygons and Edges