Overlapping or Intersecting:

A polygon overlaps or intersects the current background if any of its sides cuts the edges of the viewport as depicted at the top right corner of the viewport.

The extent of a polygon overlapping the viewport is just a necessary but not enough condition, because even if the extent overlaps, the polygon can be disjoint

It can be seen that only the surrounding and contained cases (a) and (b) can be decided on the basis of the simple rules of relationship among the x-y extents of the polygon and the viewport. All of other cases need further investigation, as:

We begin with the entire viewport, and examine all of the polygons for surrounding or containment. Whatever polygons may be classified as Case (a) or Case (b) may be stored or not based on whether they are visible or not.

For any remaining polygons, the viewport is divided into four quarters, and each quarter representing a viewport segment is evaluated against the polygon portions in that quarter for cases (a) and (b). The quarter or quarters in which such determination may not be made shall again be subdivided into four further quarters each, and each quarter (which can be termed a "viewport segment") examined for the similar kind of relationship decisions.

This process is applied with successive subdivisions yet all the polygons and sub-regions may be resolved as (a) or (b). Frequently, the procedure can have to be repeated until the last quartering decrease to a single pixel.

Due to the four branches formed with each quartering step, the method is also called the Quad tree method. At last, the method illustrates the difference among hidden-line and hidden-surface algorithms. In a specific viewport segment, it can happen that there are no edges at all, but two or more surfaces are surrounding the viewport segment. Here, hidden line has no relevance, but hidden surface has.