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 Define Point Subtraction:


 QP 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 (1t) 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