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22_2DGraphicsIntro.3up

2d mirror about y axis x x y y x 1 0

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Unformatted text preview: - y*sinΘ –  y’ = x*sinΘ + y*cosΘ X1 = (0.25*x)cos(90) – (0.25y)sin(90) Y1 = (0.25*x)sin(90) + (0.25*y)cos(90) 18 Basic 2D Transforma:ons •  Transla:on: –  x’ = x + tx –  y’ = y + ty •  Scale: –  x’ = x * sx –  y’ = y * sy •  Rota:on: –  x’ = x*cosΘ - y*sinΘ –  y’ = x*sinΘ + y*cosΘ X1 = (0.25*x)cos(90) – (0.25y)sin(90)+5 Y1 = (0.25*x)sin(90) + (0.25*y)cos(90)+3 Note: Order of opera-ons is important. What if you translate ﬁrst? 19 Matrix Representa:on •  Represent 2D transforma:on by a matrix !a b\$ # & "c d% •  Mul:ply matrix by column vector ⇔ apply transforma:on to point # x ' = ax + by ! & x ' ) & a b )& x ) +=( + " ⇔( +( y ' = cx + dy # ( y ' + ' c d *( y + * ' * \$' 20 Matrix Rep...
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