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content/notes/03-2d-transforms.md
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@ -35,8 +35,24 @@ transformations
- rotation from U towards V, not anti/clockwise - rotation from U towards V, not anti/clockwise
- $[u',v'] = [cos(0) - sin(0), sin(0) cos(0)][u,v]$ - $[u',v'] = [cos(0) - sin(0), sin(0) cos(0)][u,v]$
- inverse - inverse
- combinations - inverse of translate is translating by negative
- inverse of scaling by $s$ is scaling by $\frac{1}{s}$
- inverse of rotating by $\theta$ is rotating by $-\theta$
- inverse of rotation matrix is its transpose
- ![](https://i.imgur.com/HSiqyQb.png)
- combinations
- e.g., rotate 45 about (2,1)
- shift by (-2,-1)
- rotate by 45
- shift by (2,1)
- ![](https://i.imgur.com/NI6luaG.png)
homogenous coordinates homogenous coordinates
- represent 2D points as 3 points
- all linear transformations become 3x3 matrices
- ![](https://i.imgur.com/aksrjQw.png)
>[!DIFFICULT]
homogenous transforms homogenous transforms