Q. Explain the concept of area subdivision method. Write the conditions, when no further subdivision is needed and how we can test these condition.

Ans. Area Subdivision This technique for hidden- surface removal is essentially an image- space method, but object- space operations can be used to accomplish depth ordering of surface. The area sub- division methods takes advantages of area coherence in a scene by locating those view areas that represented part of a single surface. We apply this method by successively dividing the total viewing area into smaller and smaller rectangles until each small area is the projection of a single visible surface at all. To implement this method, we need to establish tests that can quickly identify the area as part of a single surface or tell us that the area is too complex to analyze easily. Starting with the total view, we apply the tests to determine whether we should subdivide the total area into smaller rectangles. If the test indicates that the view is sufficiently complex, we subdivide it. Next, we apply the tests to each of the smaller areas, subdividing these if the tests indicated that visibility of a single surface is still uncertain. We continue this process until the subdivisions are easily analyzed as belonging to a single surface or until they are reduced to the size of single pixel. An easy way to do this is to successively divide the area into four equal parts at each step as shown in fig. 1. This approach is similar t that used in constructing a quad tree. A viewing area with a resolution of 1024 by 1024 could be subdivided ten times in this way before a sub area is reduced to point. Tests to determine the visibility of a single surface within a specified area are made by comparing surfaces to the boundary of the area. There are four possible relationships that a surface can have with a specified area boundary. We can describe these relative surface characteristics in the following way (fig.2): Surrounding surface - One that completely encloses the area. Overlapping surface - One that is partly inside and partly outside the area. Inside surface - One that is completely inside the area. Outside-One that is completely outside the area. The tests for determining surface visibility within an area can be stated in terms of these four classifications. No further subdivisions of a specified area are needed if one of the following conditions is true: 1. All surfaces are outside surfaces with respect to the area.  2. Only one inside, overlapping or surrounding surface is the area.  3. A surrounding surface obscures all other surface within the area boundaries. Test 1 can be carried out by checking the bounding rectangles of all surfaces against the area boundaries. Test 2 can also use the bounding rectangles in the x y plane to identify an inside surface. For other types of surfaces the bounding rectangles can be used as an initial check. If a single bounding rectangle intersects the area in some way additional checks are used to determine whether the surface is surrounding overlapping of outside. Once a single overlapping of surrounding surface has been identified its pixel intensities are transferred to the appropriate area within the appropriate area within the frame buffer. One method for implementing test 3 is to order surface according to their minimum depth from the view plane. For each surrounding surface we then compute the maximum depth within the area under consideration. If the maximum depth of one of these surrounding surface within the area test 3 is satisfied. Another method for carrying out test 3 that does not require depth sorting is to use plane equations to calculate depth values at the four vertices of area for all surrounding overlapping and inside surface. If the calculated depths for one of the surrounding surfaces is less than the calculated depths for all other surface test 3 is true. Then the area can be filled with the intensity values of the surrounding surface. For some situations both methods of implementing test 3 will fail t identifies correctly a surrounding surface that obscures all the other surfaces. Further testing could be carried out to identify the single surface that covers the area but is factor to subdivide the area than to continue with more complex testing. Once outside and surrounding surfaces have been identified for an area they will remain outside and surrounding surfaces for all subdivisions of the area. Furthermore some inside and overlapping surface can be expected to be eliminated as the subdivision process continues so that the area becomes easier to analyze. In the limiting case when a subdivision for the size of a pixel is produced we simply calculate the depth of each relevant surface at that point and transfer the intensity of the nearest surface to the frame buffer. As a variation on the basic on the basic subdivision process we could subdivide areas along surface boundaries instead of dividing them in half. If the surfaces have been sorted according to minimum depth we can use the surface with the smallest depth value to subdivide a given area.