22_2DGraphicsIntro.3up

# x 1 0 tx x x tx y

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Unformatted text preview: resenta:on •  Transforma:ons combined by mul:plica:on ! x ' \$ ! a b \$! e # &amp;=# &amp;# y ' % &quot; c d %# g # &amp; &quot; &quot; f \$! i &amp;# h &amp;&quot; k %# j \$! x \$ &amp;# &amp; &amp;# l %&quot; y &amp; % 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 ! &amp; x ' ) &amp; sx 0 )&amp; x ) # +=( + +( &quot; ⇔( # ( 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 &quot; ' 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 &quot; ' x ' * ' −1 0 *' x * \$ ,=) , # ⇔) ,) \$ ) y ' , ( 0 1 +) y , + ( + %( 24 2x2 Matrices •  What types of transforma:o...
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