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Shri P. M. Agrawal

Shri V. J. Patel

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A world-coordinate area selected for display is calleda window.

An area on display device to which a window ismapped is called a viewport. The window defines what is to be viewed; the

viewport defines where it is to be displayed. -

device coordinates is referred to as a viewingtransformation.

Sometimes the 2D viewing transformation is simplyreferred to as the window-to-viewport

transformation or the windowing transformation. But, in general, viewing involves more than just the

transformation from the window to the viewport.

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Fig 5.1 illustrates the window-to-viewport

mapping. A point at position (xw, yw) in thewindow is mapped into position (xv, yv) in theassociated viewport.

viewport as in the window we require that

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Solving these equations for the viewportpostion (xv, yv), we have

xv = xvmin + (xw xwmin)sx

yv = yvmin + (yw ywmin)sy 5.1

Where the scalin factors are

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Equation 5.1 can also be derived with a set oftransformations that converts the window area in to

the viewport area. This conversion is performed withthe following sequence of transformations:1. Perform a scaling transformation using fir-point position

of (xwmin, ywmin) that scales the window are to the size ofe v ewpor .

2. Translate the scaled window area to the position of theviewport.

Relative proportions of objects are maintained if thescaling factors are the same (sx = sy). Otherwise,

world objects will be stretched or contracted inwither the x or y direction when displayed on theoutput device.

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Generally, any procedure that identifies thoseportions of a picture that are either inside oroutside of a specified region of space isreferred to as clipping algorithm or simply

.

is to clipped is called a clip window. Point clipping

Line clipping

Area clipping (polygon) Curve clipping

Text clipping

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Assuming that the clip window is a rectangle instandard position, we save a point P = (x, y) for

display if the following inequalities are satisfied:xwmin x xwmaxywmin y ywmax

,

xwmax, ywmin, ywmax) can either the world-coordinate window boundaries or viewportboundaries.

If any one of these four inequalities is notsatisfied, the point is clipped (not saved fordisplay).

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