vault backup: 2023-03-13 15:25:41

content/notes/03-2d-transforms.md

@@ -35,8 +35,24 @@ transformations
 	- rotation from U towards V, not anti/clockwise
 	- $[u',v'] = [cos(0) - sin(0), sin(0) cos(0)][u,v]$
 - 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
+- represent 2D points as 3 points
+- all linear transformations become 3x3 matrices
+- ![](https://i.imgur.com/aksrjQw.png)
+
+>[!DIFFICULT] 
+
 homogenous transforms