MACHINE DRAWING & COMPUTER GRAPHICS
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First, the normalized view volume provides a standard shape for representing any sized view volume. The unit cube then can be mapped to a workstation considerations of any size clipping procedures are simplified and standardized with unit clipping planes or the viewport planes, and additional clipping planes can be specified within the normalized space before transforming to device coordinates. Depth cueing and visible- surface determination are simplified, since the z axis always points toward the viewer. The following figure shows the expanded transformation pipeline.
Figure 28: Expanded Transformation Pipeline
Mapping positions within a rectangular view volume to a three – dimension rectangular viewport is accomplished with a combination of scaling and translation, similar to the operations needed for a twodimensional window – to –viewport mapping. We can express the three- dimensional transformation matrix for these operations in the form Dx
0
0
Kx
0
Dy
0
Ky
0
0
Dz
Kz
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