Unformatted text preview: an apply a general translation by (tx, ty, tz ) to the points of a
scene by using the following matrix multiplication
0
10 1 0
1
1 0 0 tx
px
px + tx
B 0 1 0 t y C B p y C B py + t y C
B
CB C = B
C
@ 0 0 1 t z A @ p z A @ pz + t z A
0001
1
1 Graphics Lecture 1: Slide 41! Inverting a translation Inverting a translation !
Since we know what a translation matrix physically does, we can
â€¢â€¯ Since its know what a translation matrix physically does,
write down we inversion directly
we can
For example: write down its inversion directly, e.g.! ! Translation matrix
Translation matrix
0
1
1 0 0 tx
B0 1 0 t y C
B
C
@0 0 1 t z A
0001 inverse !
inverse
0 1
B0
B
@0
0 0
1
0
0 0
0
1
0 1 tx
ty C
C
tz A
1 â€¢â€¯ Can show that that the product of these matrices is the
Can you you show the product of these matrices is the identity?
identity? ! Graphics Lecture 1: Slide 42!
35 / 47 Scaling a matrix
Scaling withwith a matrix !
â€¢â€¯ Scaling simply multiplies each ordinate by a scaling
factor. !
Scaling simply multiplies each ordinate by a scaling factor. It can
â€¢â€...
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 Spring '14
 Cartesian Coordinate System, Computer Graphics, Orthographic Projection

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