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Area Subdivision Method

Area subdivision method :

         It is an example of image space method.  The basic principle of this algorithm is to divide are of projection plane into smaller and smaller areas in such a way that each small area belongs to a single surface or no surface at all.

       Following are the possible relations of viewing area with surfaces of the scene :-

  1. Surrounding surface :-> This is the case when surface completely encloses the viewing area.
    Surrounding surface
  2. Overlapping surface :->  This is the case when overlapping surface is partly inside and partly outside.
    overlapping surface
  3. Inside surface :->  The surface is completely inside the area.
    Inside surface
  4. Outside surface :->  Surface is completely outside the area.
    Outside surface
Normally, we divide the viewing plane into four subareas whenever division of area is required as shown in figure.
Area subdivision

Subdivision of a specified area is not needed if any of following tests is true.
Test 1 :-> All surfaces are outside surface with respect to area.  This test can be done by checking the bounding rectangles of all surfaces against area boundaries.  This is shown below in figure.

Test 1

Test 2 :-> Only one inside, overlapping or surrounding surface is in the area.  This test can also be done by using bounding rectangles in xy plane to identify an inside surface these cases are shown in figure.
Test 2

          If a single inside, overlapping or surrounding surface has been identified, its pixel intensities are transferred to frame buffer.  If a single bounding rectangle intersects the area in some way, additional checks are used to determine.

Test 3 :->  A surrounding surface obscures all other surfaces within the area boundaries.  This test can be done by two ways :

  • Calculate the depth (Z-min, Z-max) for each surface.  If for any surface Z-max is greater than Z-min of all other surfaces, then this test is satisfied.
  • Find the minimum depth among all the surfaces using plane equations. Surface with minimum depth is the surface when obscures other surfaces.
     If neither above mentioned test is true, then we subdivide the area into four parts and perform the tests ( test 1 to test 3) again and so on.

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