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Affine Combinations

Define Point Subtraction:
Q-P means such that for .

By Extension:

Define Point Blending:
means with
we may write where .

By Extension:


Legal vector combinations:

Vectors can be formed into any combinations (a ``linear combination'').
Legal point combinations:

Points can be formed into combinations iff

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