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Example of Area Subdivision Method
The procedure will be explained with respect to an illustrative problem, with the image consisting of five objects, namely a triangle (T), quadrilateral (Q), square (S), horizontal rectangle (H), and vertical rectangle (V). The viewport PQRS is 16 pixels by 16 pixels, containing only part of the image. The square is behind the quadrilateral and the triangle and the two rectangles are in front of the quadrilateral.
For ease of understanding, all five polygons are assumed to be parallel to the x-y plane, not intersecting one another. The same procedures can, however, be applied to handle the intersection of two polygons. Figure 3.14(a) shows the problem as presented; (b) is the pixel-wise representation of the polygon edges; (c) shows the external (disjoint) part of the quadrilateral clipped away.
What is complexity of an algorithm? What is the basic relation between the time and space complexities of an algorithm? Justify your answer by giving an example.
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