next up previous
Next: Affine Transformations Up: Affine Geometry and Previous: Linear Combinations

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:

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

cs488@cgl.uwaterloo.ca