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# Affine Combinations

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

By Extension: Define Point Blending: means with Alternatively:
we may write where .

By Extension: Geometrically:

• The following ratio holds for   \

• If Q breaks the line segment into the ratio then 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

cs488@cgl.uwaterloo.ca