Linear yet Non-Linear?
What does it mean for the projection mapping to preserve planes and lines,
yet, have a non-linear mapping of z values. How can this be?
Consider these examples:
As the parameter t is varied from 0 to 1, what geometric object is described?
Linearity of the space is preserved, but linearity of the parameterization is not.
So, suppose we have function of that maps one of these forms to one of the others.
Allow this function to even change the actual values of
x0, y0, dx, and dy,
as long as this linear combination form is preserved.
Does this mapping preserve lines?
What is the advantage of doing this?
Why do we care?
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