{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

P v x x p v py v y 10 p

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online