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2D Line Segment Generation
A digitally plotted line is basically an approximation of infinite number of points on an abstract line segment by only a finite number of points on a computer display. This is needed because the display devices can only plot a finite number of points, however large the resolution of the device may be. So, the key concept of any line drawing algorithm is to provide an efficient way of mapping a continuous abstract line into a discrete plane of computer display.
This process is called rasterization or scan conversion. These algorithms basically approximate a real valued line by calculating pixel coordinates to provide an illusion of line segment. Since the pixels are sufficiently small, the approximation gives a good illusion of a continuous line segment to the human eyes. To understand what is meant by rasterization, we plot a line segment on a pixel grid as shown in Fig (a). The segment points are scan converted and approximated by a single shaded pixel as shown in Fig (b). Here we have shown a pixel by a square, but you know that a pixel actually has a disc shape with the boundary marked as the visible portion of the dot formed by the striking electron gun. The pixel shown here is the bounding rectangle of that dot.
xy-Shear about the Origin - 2-d and 3-d transformations Suppose an object point P(x,y) be moved to P'(x',y') as a outcome of shear transformation in both x- and y-directions a
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