The document discusses 2D geometric transformations including translation, rotation, scaling, and matrix representations. It explains that transformations can be combined through matrix multiplication and represented by 3x3 matrices in homogeneous coordinates. Common transformations like translation, rotation, scaling and reflections are demonstrated.

1. 2D Geometric Transformations Taher S. Vijay Computer Academy August 2011

4. Example: 2D Geometric Transformation Taher S. - VCA- 2011 Modeling Coordinates World Coordinates

5. Example: 2D Scaling Taher S. - VCA- 2011 Modeling Coordinates World Coordinates Scale(0.3, 0.3)

6. Example: 2D Rotation Taher S. - VCA- 2011 Modeling Coordinates Scale(0.3, 0.3) Rotate(-90) World Coordinates

7. Example: 2D Translation Taher S. - VCA- 2011 Modeling Coordinates Scale(0.3, 0.3) Rotate(-90) Translate(5, 3) World Coordinates

8. Example: 2D Geometric Transformation Taher S. - VCA- 2011 Modeling Coordinates World Coordinates Again?

9. Example: 2D Geometric Transformation Taher S. - VCA- 2011 Modeling Coordinates World Coordinates Scale Translate Scale Rotate Translate

30. Pivot-Point Rotation Taher S. - VCA- 2011 Translate Rotate Translate (x r ,y r ) (x r ,y r ) (x r ,y r ) (x r ,y r )

31. General Fixed-Point Scaling Taher S. - VCA- 2011 Translate Scale Translate (x f ,y f ) (x f ,y f ) (x f ,y f ) (x f ,y f )