This energy conveys two constraints related to :
- the distance between the nodes,
- the angle formed by three successive nodes.
xi : node in the network (random variable),
xic: associated node on the map.
: the angle formed by three consecutive nodes
xi,xj and xk.
: the angle formed by the same nodes in the map.
With :
U1c (xi,xj) = fi,j(dist(xi,xj))
-
,
convex function defined on
,
taking its minimum value at the point
-
takes its minimum value for
, and increases with the difference between
and
.
These energy terms :
- are invariant through a global translation or rotation of the network x,
- are based on the hypothesis of reliability of the relative position
of the nodes on the map.
- Potential U1c : the road given
by the map is in dashed line, so the road 1 has a potential
U1c inferior to the one of road 2.
- Potential U2c : the potential
associated to the series of three nodes in position related to road 1
is lower to the one associated to road 2.
Guillaume Rellier
1999-11-10