transform
- Modeling
- View transformation (Viewing)
The 2 d transformation
The zoom
Reflection (symmetry)
shear
The y-coordinate stays the same, the level changes
rotating
By default, it rotates around (0, 0), counterclockwise
Linear transformation
Homogeneous coordinates
Why do we need homogeneous coordinates?
Translational transform
Translation cannot be expressed in matrix form
Translation is not a linear transformation
Add a dimension
Translation matrix representation
Affine Transformations
Affine map = linear map + translation
Use homogeneous coordinates
Inverse transformation
Combination of transformation
A complex transformation can consist of multiple simple transformations, the order of which is crucial (matrices do not satisfy commutative laws).
Transform decomposition
3 d transform
Homogeneous coordinates
- 3D point =
- 3D vector =
Matrix representation
Yan Lingqi < introduction to Modern Computer Graphics >>