Compositions of Transformations

Suppose

we want to rotate around an arbitrary point .

• Could derive a more general transformation matrix ...
• Alternative idea: Compose simple transformations
  1. Translate P to origin
  2. Rotate around origin
  3. Translate origin back to P
• Suppose
• The the desired transformation is

  

• Note where P maps: to P.
• Won't compute these matrices analytically;
  Just use the basic transformations,
  and run the matrix multiply numerically.

Order is important!

Readings: Hearn and Baker, Section 5-3; Red book, 5.4; White book, 5.3