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Next: 3D Transformations Up: Affine Geometry and Previous: Compositions of Transformations


3 Types of Transformations:
  1. (between two spaces)
  2. (``warp'' an object within its own space)
  3. T: change of coordinates

Changes of Coordinates:
What is the length of ?
Its length is       , regardless of its frame of representation.

we have and

Do we care?

the meaning of |P'-P|
  1. |P'-P|=0
  2. |P'-P| has no meaning

We need
  1. A matrix
  2. A domain space
  3. A range space
  4. A coordinate frame in each space
to fully specify a transformation.

Most of the time not all will be specified!

...So be careful out there.

CS488/688: Introduction to Interactive Computer Graphics
University of Waterloo
Computer Graphics Lab