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Unformatted text preview: resenta:on •  Transforma:ons combined by mul:plica:on ! x ' $ ! a b $! e # &=# &# y ' % " c d %# g # & " " f $! i &# h &" k %# j $! x $ &# & &# l %" y & % Matrices are a convenient and efficient way to represent a sequence of transformations! 21 2x2 Matrices •  What types of transforma:ons can be represented with a 2x2 matrix? 2D Scale around (0,0)? x ' = sxx y ' = syy ! & x ' ) & sx 0 )& x ) # +=( + +( " ⇔( # ( y ' + ( 0 sy +( y + *' *' * $' 22 2x2 Matrices •  What types of transforma:ons can be represented with a 2x2 matrix? 2D Rotate around (0,0)? $ x ' = x cosθ − y sin θ " ' x ' * ' cosθ ,=) # ⇔) y ' = x sin θ + y cosθ % ) y ' , ( sin θ $( + − sin θ cosθ *' x * , ,) +) y , ( + 23 2x2 Matrices •  What types of transforma:ons can be represented with a 2x2 matrix? 2D Mirror about Y axis? x ' = −x y' = y " ' x ' * ' −1 0 *' x * $ ,=) , # ⇔) ,) $ ) y ' , ( 0 1 +) y , + ( + %( 24 2x2 Matrices •  What types of transforma:o...
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