
9.6. A FRAMEWORK FOR USER-GROUPED CIRCULAR DRAWING 305
Figure 9.23 Circ ul ar- tr ack force-directed technique. Figure taken from [ST03b].
Remember t hat Hooke’s Law [HR88] gives us the following equation for the potential
energy V in a spring system:
V =
X
ij
k
ij
[(x
i
− x
j
)
2
+ (y
i
− y
j
)
2
] (9.3)
where k
ij
is the spring constant for the spring between nodes i and j. Equation (12.3) can
be rewritten using (12.1) and (12.2):
V =
P
(i,j)∈E
k
ij
[((x
α
+ r
α
∗ cos(θ
i
)) − (x
β
+ r
β
∗ cos(θ
j
)))
2
+
((y
α
+ r
α
∗ sin(θ
i
)) − (y
β
+ r
β
∗ sin(θ
j
)))
2
] (9.4)
where node j belongs to grou p β, (x
β
, y
β
) is the center and r
β
is the radius of the embedding
circle on which β appears. Thus, we have: ...