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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
the. disadvantage of labeling a reduced number of objects
compared to paper maps.
For simplification, labeling algorithms like the proposed
approach uses a rectangular approximation of the label.
It is obvious that the label size depends on the scale of the map.
The size of the label is not growing or shrinking in proportion to
the map scale, which causes the relabeling after each zooming —
change of scale. The label size (/abSize) could be approximated
by an exponential function for a target scale (scale) in
dependence on a reference size (re/LabSize) and reference scale
(refScale) as follows:
scale \ with v € [0..0.15] the growing and
=
shrinking can be adjusted. More details can be found in
previous papers (Petzold, 2003; Petzold et. al. 1999).
labSize = sl
In contrast to other approaches we are using the concept of
sliding labels or more precise labeling spaces. These labeling
spaces represents the convex hull of all possible label positions
and are simple computable geometric shapes like rectangular
boxes for point objects.
boundingBox, / boundingBox,
legend:
e position of the object
8
= |
3 Y i ; ;
a. ou object symbol (symSize,, )
3 dSymLab ij E symSize, © obj y! y! idttheignt
D AN © distance between symbol and
£2 gl [ PE ? label (dSymLab)
9. rad 1
€ 2 | | symSize,,, — label box to be placed
gu + me = L— (labSize, tem e
ë Ee
= | labSize it + {{CO labeling space (bounding box)
1
I -
boundingBox, din
Figure l. The labeling space of a point object
As shown in Figure 1 for point objects, the label positions are
not restricted to a certain number, but the label can freely move
or more precisely slide along the inside border of the labeling
space. The overlapping with the symbol is not allowed.
legend:
302,0° . n ;
P en ^ t label center point
$$ object to be labeled e cent
distance between e center label
= symbol and label box
| ] labeling space (bounding box) A 244.
"4 24.4
e =
scoring(302.0°) = 0.5 [J label box to be placed
Figure 2. The continuous scoring of label positions in a
labeling space — an example for a label position or
rather angle and its scoring.
According to cartographic rules, some positions are in favor of
others. This is covered by adapting the scoring of label positions
as proposed in (Imhof, 1962).
For labeling point objects, a continuous scoring function using
the angle between the horizontal line passing through the center
of the point object and the center of the label position can be
used (Figure 2).
The label of a line object wriggles along its symbol (Figure 3
a)). Due to the constant distance between the symbol of the
object and the label, the concept of a buffer can be used to
define the labeling space, as shown in Figure 3. This slight to
huge buffer, especially at the end of the lines where a label will
never be placed, will be taken into account for faster
computation and easier handling. For scoring label positions,
the distances of the label between start and end point of the line
object, the twist of the line beneath or above the label will be
used (Christensen; 1995; Edmondson, 1996; Petzold et. al.,
1997).
c)
jen
1-distanceSymboiLabel
7-3-symbolHeight
Figure 3. Labeling space of a line object is shown in a). It is
derived by the buffer of the line object b) and c).
The labeling of area objects is reduced to the labeling of line
objects. Otherwise the labeling space of an area object would
correspond to its area and would increase the number of
(potential) conflicts with other labels dramatically.
3. MODELING OF CONFLICTS
The modeling process is divided into two parts: First, the
recognition of conflicts with accompanying algorithms, and
second, the representation of them with accompanying data-
structures. It is obvious that only this information is gathered
which can be represented in the data-structure.
At first sight it seems paradox to model conflicts if the objective
is to avoid conflicts, like the title of this paper pretends.
However, it is less difficult to determine conflicts, to represent
them in a data-structure, and finally to exploit this knowledge to
obtain a conflict free labeling than the other way round as we
will see in the following.
3.1 Characteristic of conflicts
This subsection deals with labeling conflicts and pictorially
describes how they “emerge”, “disappear” and which
characteristics have conflicts in common.
In the following example, the focus is on two objects to be
labeled and we will start the description in a huge scale where
no labeling conflicts exist (Figure 4). If the scale gets smaller —
zooming out — the objects move closer to each other, but the
label size almost remains constant. The label shrinks much
slower than the other map objects, as mentioned in the
cartographic background section. At first the labels might move
away from each other to avoid conflicts if there is enough space
and the cartographic rules allow this.
deselection..
ON “‘eutting scale
small ofSiegburg. -. Ring large
pe river “| ~
»:
a scale
no conflict ETT TTA no conflict
Figure 4. Life cycle of a conflict: 1) Before a conflict — large
scale; 2) conflicts starts — cutting scale; 3) conflict
ends / removal of one label — deselection scale.
Finally, this leads to a touch and later to an overlap between the
labels of both objects. The scale of the first "touch" is called
cutting scale. If we zoom out further, the overlapping area
grows. This results in a very small scale where each label will
overlap each other. It is obvious that it is not possible to label
all objects. So we need a deselection criterion that decides
below which scale an object will not be labeled any further. As
we will see later this deselection scale belongs to the object and
is “passed” to the conflict.
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