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Assumptions for Area Subdivision Method
a) ¾ Plane of projection is z=0 plane
b) ¾ Orthographic parallel projections
c) ¾ Direction of projection as d= (0,0,-1)
d) ¾ suppose here, the viewing (screen) area is a square
e) ¾ Objects are made up of polygon faces.
To apply the area-subdivision method, we should identify whether the area is part of a single surface or a complex surface by means of visibility tests. If the tests specify that the view is sufficiently complicated, we subdivide it. Furthermore, we apply the tests to each of the smaller regions and then subdivide additionally, whether the tests specify that, the visibility of a particular surface is still not certain. We continue this process till the subdivisions are simply analyzed as belonging to a particular surface or till they are decreased to the size of a single pixel. Beginning with the full screen as the initial area, the algorithm divides an area at all stages in four smaller area, as demonstrated in figure 8 that is similar to quad-tree approach.
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To prove: P (u = 0) = p0 Solution : = p 0 B n,0 (u) + p 1 B n, 1 (u) +...... + p n B n, n (u)...............(1) B n,i (u) = n c i u i (1 - u) n-i B n,0
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