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content/notes/03-2d-transforms.md
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look into how colours work together look into how colours work together
Points lines Points lines
- point is 2d location $ - point is 2d location $(u,v)$
- two points define a link - two points define a line
- a polyline with k segments is a sequence of k+1 points - a polyline with k segments is a sequence of k+1 points
- a polygon is a polyline where the beginning and ened are the same, we often omit the duplicate point - a polygon is a polyline where the beginning and ened are the same, we often omit the duplicate point
- points are vectors - points are vectors
> [!INFO] > [!INFO] polygon and polylines will be specifies in the code
> [!INFO] $[u v]^T$ high T indicates vector
coordingate systems coordingate systems
- mathematical - mathematical
- image based - image based
- matrix based - matrix based
- ![|300](https://i.imgur.com/m6OAA5T.png)
> [!INFO] make sure to check you are using the right coordinate system
transformations transformations
- translation - translation
> [!INFO] value of change (delta) for each coordinate. for a shape, apply the transformation to each point
- scaling - scaling
- rotation - rotation
- rotate by an abgle about the origin
- rotation from U towards V, not anti/clockwise
- $[u',v'] = [cos(0) - sin(0), sin(0) cos(0)][u,v]$
- inverse - inverse
- combinations - combinations
homogenous coordinates homogenous coordinates
homogenous transforms homogenous transforms