Hardware Reference
In-Depth Information
Fig. 5.3
(
a
) An example of
the digital object
corresponding to the heater;
(
b
) the isothetic convex
envelope (
ICE
) that tightly
encloses the forbidden region
of R
2
; optimal placement of a
reservoir R
2
in the presence
of a reservoir R
1
,aDED
1
,
and a heater H
a
heater
L
RH
Forbidden region of
the reservior with
respect to the heater
reservoir
Digital object corresponding to
the heater
b
The union of
digital objects
L
RR
L
RH
≥
L
RH
H
(center
of the
layout)
R
1
≥
L
RD
≥
L
DH
The best
position for
R
2
D
1
L
RD
generated. In our iterative method, first we choose the first device in Q
dev
(which is
written as d
p
1
) and place it at the origin .0; 0/ of the layout grid. Then, the second
device in Q
dev
(which is written as d
p
2
) is chosen for placement.
We draw a circle of radius
.d
p
1
;d
p
2
/ with its center at d
p
1
. While placing d
p
2
,
we flag all the grid points that lie inside the circle as being in the “forbidden” region
for d
p
2
. The digital object for d
p
1
, O
.d
p
1
;d
p
2
/
, can also be derived.
Thus d
p
2
may be placed on any electrode that is not an element in O
.d
p
1
;d
p
2
/
to
satisfy the separation constraint. At any instant of time, let us assume that the devices
d
p
1
;d
p
2
;:::;d
p
k
have already been placed. When considering the placement of
the device d
p
k
C
1
, we proceed as follows: for each device d
p
i
already placed, we
draw a forbidden circle centering at d
p
i
with radius
C
.d
p
i
;d
p
k
C
1
/, and derive the
corresponding digital object O
.d
p
i
;d
p
k
C
1
/
. The union of all these digital objects,
which is written as O
.d
p
1:::k
;d
p
k
C
1
/
,isdefinedasfollows:
C
O
.d
p
1:::k
;d
p
k
C
1
/
D
O
.d
p
1
;d
p
k
C
1
/
[
O
.d
p
2
;d
p
k
C
1
/
:::
[
O
.d
p
k
;d
p
k
C
1
/
:
