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- Define Point Subtraction:
- Q-P means such
that for .
- Define Point Blending:
- we may write
- The following ratio holds for
- If Q breaks the line segment into the
- Legal vector combinations:
Vectors can be formed into any combinations
(a ``linear combination'').
- Legal point combinations:
Points can be formed into combinations iff
The coefficients sum to 1:
The result is a point (an ``affine combination'').
The coefficients sum to 0: The result is a vector
(a ``vector combination'').
- Parametric Line Equation
has geometric meaning (in an affine sense):
The weights t and (1-t) create an affine combination.
The result is a point (on the line).
Readings: White book, Appendix A
CS488/688: Introduction to Interactive Computer Graphics
University of Waterloo
Computer Graphics Lab