Lecture 1 - Projections and Transformations (slides)

they have a 4th ordinate allowing us to use the last

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Unformatted text preview: atrix? I.e. But how can we do this with a matrix? I.e. 1 0 10 1 0 ! x x 0 10 1 0 + 2 1 x +A @ ? A @y A = @ x y 2 ! @ ? A @y A = @ y A z z ! z z … c be be . . . can’tan’tdonedone ! . .!. can’t be done Graphics Lecture 1: Slide 37! 30 / 47 Homogenous Coordinates Homogenous Coordinates Homogenous Coordinates ! •  answer to is 4D homogenous coordinates TheThe answer useto use 4D homogenous coordinates.! The answer isisto use 4D homogenous coordinates. . •  They have a 4th ordinate allowing us to use the last Theyhave a a th translation ! have 4th ordinate allowing us to use the last column for Theycolumn4for ordinate allowing us to use the last column for translation translation 0 01 0 0 01 0 xx 11 B0 C B By y 0 C B 00 BC=B C=B B 0A @ @ @ z 0zA @ 00 11 00 00 11 00 00 00 00 11 00 10 1 10 1 22 xx C BC 0 0C By y C CB C CB C A @A 0 0A @ z z A 11 11 which, whenmultiplied out, gives: •  which, multiplied out, gives: which, when when multiplied out, gives: ! 0 00= y0 = = xx= xx + 2 y 0 = y y z 0z = z z +2 Gr...
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