Surrounding:

A polygon surrounds a viewport if it totally encloses or covers the viewport. This happens if none of its sides cuts any edge of the viewport. It is not enough if the x-y extent encloses the viewport, because even with the same extent, if the right edge of the viewport were to be shifted a little more to the right as illustrated dotted in Figure (a), the polygon's right edge would cut the top and right edges of the viewport. If the surrounding polygon is the closest to the viewer, the overall viewport is covered by the colour and other attributes of the polygon.

(a)                                         (b)                               (c)                          (d)

Figure: Subdivision Algorithm : (a) Surrounding; (b) Contained; (c) Disjoint; and (d) Overlapping or Intersecting