>[!tip] Best modeled using [[../Math/Homogeneous Coordinates|Homogeneous Coordinates]]. In graphics, typically only 3 transformations are used, [[../Math/Resize Transformation|Resize Transformation]], [[../Math/Affine Rotation|Rotation]], and [[../Math/Affine Transformations|Translations]]. All other transformations are simply [[../Math/Composition|Compositions]] of these 3 (see [[../Math/Matrix Product|Matrix Product]]). ### Scaling $\huge \begin{align} \text{Uniform} \rightarrow H_{\alpha} &= \mat{ \alpha & 0 & 0 \\ 0 & \alpha & 0\\0&0&1}\\ \text{NonUniform} \rightarrow H_{\alpha, \beta} &= \mat{ \alpha & 0 & 0 \\ 0 & \beta & 0\\0&0&1} \end{align}$ > The reason for the greek is [[../Math/Homothety|Homothety]]. ### Translation $\huge T_{\vec v} = \mat{ 1 & 0 & v_{x} \\ 0 & 1 & v_{y} \\ 0 & 0 & 1} $ ### Rotation $\huge R_{\theta} = \mat{ \cos \theta & -\sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \\ } $ > *Where $\theta$ represents the [[Counter-Clockwise]] rotation.*