LABELING STREETS
IN INTERACTIVE MAPS
USING EMBEDDED LABELS
frame ft
screen space
at time t
sj
bj
segment
bk
`
bk +1
`0
P
C (bi ) = e ce (bi )
with cost ce (bi ) caused by
C (`) =
criterion e
Angle Criterion a
bi
Pk
i =j
Crossing Criterion x
bi
` → `0 ⇒ C (`) ≤ C (`0 )
⇒ eval starts at bends only
C (bi )
View Criterion v
bj
`
`0
C (`) ← C (`) + constv
C (`0 ) ← C (`0 ) + 0
cx (bi ) = constx
}
Simplification Criterion s
bk
bj
≥
T
<T
≥T
cs (bj , . . . , bkP
)=
k
ws · ( i =j +1 αi )2
}
α
ca (bi ) = wa · α2
weight factor wa
in each frame. . .
GPS
monitor
Example: GPS
etc.
el
CA
La
b
B Street
. . . and correct label orientations
l
Frame Rate [FPS]
A Street
La
C Ave
B Street
Label
A Street
. . . try to label each unlabeled street
/
e
Lab
Algorithm
La
bj −1
ce (bj ) = 0
Results
Label
Discretization
Evaluating a label position `
}
Evaluations
University of Osnabrück, Germany
? embeds labels into streets,
? while avoiding intersections and strong bends,
? computes overlap-free labelings,
? and reacts to user interactions in real time.
The corresponding optimization problem (labelnumber maximization) is NP-hard even for one frame.
Evaluating a bend bi
bi
Jan-Henrik Haunert
2
We present the first algorithm that
screen space
at time t + 1
frame ft +1
si
2
University of Würzburg, Germany
world map
Contrib.
1
Alexander Wolff
1
b el
Nadine Schwartges
1
Example: Monitor
150
100
50
fluid
0
all
lamut.informatik.uni-wuerzburg.de/dynalinelab.html