Zandbakje:
M t r a n s f o r m e d = [ x y 1 ] ⋅ [ a b c d e f g h j ] = [ x ⋅ a + y ⋅ d + 1 ⋅ g x ⋅ b + y ⋅ e + 1 ⋅ h x ⋅ c + y ⋅ f + 1 ⋅ j ] {\displaystyle M_{transformed}={\begin{bmatrix}x&y&1\end{bmatrix}}\cdot {\begin{bmatrix}\color {Blue}a&\color {Red}b&\color {OliveGreen}c\\\color {Blue}d&\color {Red}e&\color {OliveGreen}f\\\color {Blue}g&\color {Red}h&\color {OliveGreen}j\end{bmatrix}}={\begin{bmatrix}\color {Blue}{x\cdot a+y\cdot d+1\cdot g}&\color {Red}{x\cdot b+y\cdot e+1\cdot h}&\color {OliveGreen}{x\cdot c+y\cdot f+1\cdot j}\end{bmatrix}}} M t r a n s l a t e d = [ x y 1 ] ⋅ [ 1 0 0 0 1 0 t x t y 1 ] = [ x ⋅ 1 + y ⋅ 0 + 1 ⋅ t x x ⋅ 0 + y ⋅ 1 + 1 ⋅ t y x ⋅ 0 + y ⋅ 0 + 1 ⋅ 1 ] = [ x + t x y + t y 1 ] {\displaystyle M_{translated}={\begin{bmatrix}x&y&1\end{bmatrix}}\cdot {\begin{bmatrix}\color {Blue}1&\color {Red}0&\color {OliveGreen}0\\\color {Blue}0&\color {Red}1&\color {OliveGreen}0\\\color {Blue}t_{x}&\color {Red}t_{y}&\color {OliveGreen}1\end{bmatrix}}={\begin{bmatrix}\color {Blue}{x\cdot 1+y\cdot 0+1\cdot t_{x}}&\color {Red}{x\cdot 0+y\cdot 1+1\cdot t_{y}}&\color {OliveGreen}{x\cdot 0+y\cdot 0+1\cdot 1}\end{bmatrix}}={\begin{bmatrix}\color {Blue}{x+t_{x}}&\color {Red}{y+t_{y}}&\color {OliveGreen}{1}\end{bmatrix}}} M s c a l e d = [ x y 1 ] ⋅ [ s x 0 0 0 s y 0 0 0 1 ] = [ x ⋅ s x + y ⋅ 0 + 1 ⋅ 0 x ⋅ 0 + y ⋅ s y + 1 ⋅ 0 x ⋅ 0 + y ⋅ 0 + 1 ⋅ 1 ] = [ x ⋅ s x y ⋅ s y 1 ] {\displaystyle M_{scaled}={\begin{bmatrix}x&y&1\end{bmatrix}}\cdot {\begin{bmatrix}\color {Blue}s_{x}&\color {Red}0&\color {OliveGreen}0\\\color {Blue}0&\color {Red}s_{y}&\color {OliveGreen}0\\\color {Blue}0&\color {Red}0&\color {OliveGreen}1\end{bmatrix}}={\begin{bmatrix}\color {Blue}{x\cdot s_{x}+y\cdot 0+1\cdot 0}&\color {Red}{x\cdot 0+y\cdot s_{y}+1\cdot 0}&\color {OliveGreen}{x\cdot 0+y\cdot 0+1\cdot 1}\end{bmatrix}}={\begin{bmatrix}\color {Blue}{x\cdot s_{x}}&\color {Red}{y\cdot s_{y}}&\color {OliveGreen}{1}\end{bmatrix}}}
