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Unit 9: Translation

control unit also contains three translation buffers, in which are stored the most recently accessed Notes
virtual addresses, which, in many situations, enables the virtual translation/FIFO control unit
to translate the virtual address using less memory accesses.

9.5 The Inverse of a Translation

To undo a translation by t x , t y , t z apply the matrix

È 1 0 0 0˘
Í ˙
T = Í 0 1 0 0 ˙
–1
Í 0 0 1 0˙
Í ˙
Î Í -t x -t y -t z 1 ˚ ˙
We can now complete scaling about an arbitrary fixed point and rotation about an arbitrary
turn. To scale about F= [x f y f z f ] use the composition of matrices
È 1 0 0 0˘ Ès x 0 0 0˘ È 1 0 0 ˘ 0
Í 0 1 0 0 ˙ Í 0 s 0 0 ˙ Í 0 1 0 0 ˙
˙ Í
˙ Í
Í Í 0 0 1 0˙ Í Í 0 0 y s 0˙ Í 0 0 1 ˙ ˙ 0
Í ˙ Í z ˙ Í ˙
Î Í -x f -y f -z f 1 ˚ ˙ Î 0 0 0 1 Í x f y f z f 1 ˚ ˙
˚ Î
when multiplied out yields?

È s 0 0 0˘
Í x ˙
Í 0 s y 0 0 ˙
Í x 1 - s ) y 1 - s ) z 1 - s ) 1 ˙
(
(
(
Î f x f y f z ˚
So a scaled point [X Y Z 1] becomes,
È s x 0 0 0˘
Í 0 s 0 0 ˙
[x y z 1] = [x y z 1] Í y ˙
Í 0 0 s 0˙
Í z ˙
Î Í x 1 ( - s ) y 1 ( - s ) z 1( - s ) 1 ˚ ˙
x
f
f
z
f
y
In a similar manner you can determine that rotation about a pivot R = [Xr Y r ] results in
x = x r + (x – y r ) cos θ – (y – y r ) sin θ
y = y r + (x – y r ) cos θ – (x – x r ) sin θ
Self Assessment Questions
6. Translation is one of the ……………………. a translation moves all points of an object.
7. Simple straight line is movement of the …………….. in x and y direction.
8. This function takes as parameters a reference to ………………… that holds the current
state of the transformation and the X and Y translation values.
9. ..…............. capable of reading from, and writing to virtual memory.

10. We can develop the matrix involved in a straight forward manner by considering the
translation of a ………………...

11. CPU translated address is known as …………………
( a) virtual address. (b) physical address.
( c) bus address. (d) None of these.

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