AREA-SUBDIVISION METHOD

                                             This technique for hidden-surface removal is basically an image-space method, but object-space operations will be wont to accomplish depth ordering of surfaces. The area-subdivision method takes advantage of area coherence in a very scene by locating those view areas that represent a part of one surface. We apply this method by successively dividing the entire viewing area into smaller and smaller rectangles until each small area is that the projection of a part of n single visible surface or no surface in any respect. To implement this method, we'd like to ascertain tests that may quickly identify the realm as a part of one surface or tell us that the realm is just too complex to research easily. Starting with the entire view, we apply the tests to work out whether we should always subdivide the entire area into smaller rectangles.

If the tests indicate that the view is sufficiently complex, we subdivide it. Next, we apply the tests to every of the smaller areas, subdividing these if the tests indicate that visibility of one surface continues to be uncertain. We continue this process until the subdivisions are easily analyzed as belonging to one surface or until they're reduced to the scale of one pixel. a simple thanks to do that is to successively divide the realm into four equal parts at each step. This approach is analogous to it utilized in constructing a quad tree. A viewing area with a resolution of 1024 by 1024 may well be subdivided ten times during this way before a sub area is reduced to a pint.

Tests to work out the visibility of one surface within a specified area are made by comparing surfaces to the boundary of the realm. There are four possible relationships that a surface can have with a specified area boundary. we are able to describe these relative surface characteristics within the following way.

Surrounding surface - One that completely encloses the realm
Overlapping surface - One that's partly inside and partly outside the realm
Inside surface - One that's completely inside the realm
Outside surface - One that's completely outside the realm

The tests for determining surface visibility within a vicinity will be stated in terms of those four classifications. No further subdivisions of a specified area are needed if one in every of the subsequent conditions is true:

1. All surfaces are outside surfaces with relation to the realm.
2. only 1 inside, overlapping, or surrounding surface is within the area.
3. A surrounding surface obscures all other surfaces within the realm boundaries.

Test 1 will be meted out by checking the bounding rectangles of all surfaces against the realm boundaries. Test 2 also can use the bounding rectangles within the xy plane to spot an enclosed surface. For other styles of surfaces, the bounding rectangles will be used as an initial check. If one bounding rectangle intersects the realm in how, additional checks are wont to determine whether the surface is surrounding, overlapping, or outside. Once one inside, overlapping, or surrounding surface has been identified, its pixel intensities are transferred to the suitable area within the buffer store. One method for implementing test 3 is to order surfaces in line with their minimum depth from the view plane. for every surrounding surface, we then compute the most depth within the realm into consideration. If the maxi mum depth of 1 of those surrounding surfaces is closer to the view plane than the minimum depth of all other surfaces within the realm, test 3 is satisfied.

Another method for polishing off test 3 that doesn't require depth sorting is to use plane equations to calculate depth values at the four vertices of the realm for all surrounding, overlapping, and inside surfaces, If the calculated depths for one in every of the encircling surfaces is a smaller amount than the calculated depths for all other surfaces, test 3 is true. Then the realm will be stuffed with the intensity values of the encircling surface.

For some situations, both methods of implementing test 3 will fail to spot correctly a surrounding surface that obscures all the opposite surfaces. Further testing may well be meted out to spot the one surface that covers the realm, but it's faster to subdivide the realm than to continue with more complex testing. Once outside and surrounding surfaces are identified for a vicinity, they're going to remain outside and surrounding surfaces for all subdivisions of the realm. Furthermore, some inside and overlapping surfaces will be expected to be eliminated because the subdivision process continues, so the areas become easier to research. within the limiting case, when a subdivision the scale of a pixel is produced, we simply calculate the depth of every relevant surface at that time and transfer the intensity of the closest surface to the buffer store.

As a variation on the essential subdivision process, we could subdivide areas along surface boundaries rather than dividing them in half. If the surfaces are sorted in line with minimum depth, we are able to use the surface with the tiniest depth value to subdivide a given area. The projection of the boundary of surface S is employed to partition the initial area into the subdivisions A, and A2. Surface S is then a surrounding surface for A, and visibility tests 2 and three will be applied to work out whether further subdividing is critical. In general, fewer subdivisions are required using this approach, but more processing is required to subdivide areas and to research the relation of surfaces to the subdivision boundaries.