[Angel p150-151, p160-166; Foley p201]
Introduction to Geometric Transformations
Translation, rotation, scaling, and shearing are all examples of geometric
transformations. Multiple copies of an object can be created by drawing
the same object using a series of different transformation matrices.
(image courtesy of Robert Lansdale)
The Graphics Pipeline
Most rendering algorithms can be separated into two or more distinct stages.
The graphics pipeline is a useful abstraction of the rendering process
as well as a block diagram for dedicated graphics hardware.
Definitions Related to Geometric Transformations
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affine transformation
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A transformation which preserves the parallelism of lines, but not necessarily
angles or lengths.
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homogeneous coordinates
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In homogeneous coordinates, each cartesian point (x,y,z) is represented
in a redundant manner by 4 coordinates, (h*x,h*y,h*z,h). Setting h=0 can be
thought of as a point at infinity or, more simply, a direction.
The homogeneous coordinate is also sometimes denoted as 'w', as in
the figure below.
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right-handed and left-handed coordinate systems
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