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22_2DGraphicsIntro.3up

# P v x x p v py v y 10 p

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Unformatted text preview: ns can be represented with a 2x2 matrix? 2D Translation? x ' = x + tx y ' = y + ty ! & x ' ) & a b )& x ) # +=( + " ⇔( +( # ( y ' + ' c d *( y + * ' * \$' NO! Only linear 2D transformations can be represented with a 2x2 matrix 25 Homogeneous Coordinates •  Q: Can we represent transla:on as a 3x3 matrix? 26 Homogeneous Coordinates •  Homogeneous coordinates –  represent coordinates in 2 dimensions with a 3- vector ! \$ !x\$ #x& # &⇒# y & # & "y% #1& " % •  Homogeneous coordinates simplify 2D transforma:ons 27 Homogeneous Coordinates •  Q: How can we represent transla:on as a 3x3 matrix? ! A B C \$! x \$ ! x + tx \$ Ax + By + C = x + tx # #D E #G H " &# &# F &# y & = # y + ty I &# 1 & # 1 %" %" & & ⇔ Dx + Ey + F = y + ty & Gx + Hy + I = 1 % 28 Homogeneous Coordinates •  Q: How can we represent t...
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