The document discusses 2D geometric transformations including translation, rotation, scaling, and their matrix representations. It explains that transformations can be combined through matrix multiplication and represented as sequences of transformations applied to modeling coordinates to obtain world coordinates. Basic transformations include translation, scaling, rotation, and shearing, which can be expressed as 3x3 matrices using homogeneous coordinates.

1. 2D Geometric Transformations 고려대학교 컴퓨터 그래픽스 연구실

4. Example: 2D Geometric Transformation Modeling Coordinates World Coordinates

5. Example: 2D Scaling Modeling Coordinates World Coordinates Scale(0.3, 0.3)

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

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

8. Example: 2D Geometric Transformation Modeling Coordinates World Coordinates Again?

9. Example: 2D Geometric Transformation Modeling Coordinates World Coordinates Scale Translate Scale Rotate Translate

30. Pivot-Point Rotation Translate Rotate Translate (x r ,y r ) (x r ,y r ) (x r ,y r ) (x r ,y r )

31. General Fixed-Point Scaling Translate Scale Translate (x f ,y f ) (x f ,y f ) (x f ,y f ) (x f ,y f )