The starting point for height data integration at least for a
2.5D approach is the geometric-topological data structure
for vectorial data that combines nodes, edges, and areas.
Using the entity-relationship (ER) model the following 2D
data structure is given
— a wr = -
Point Class Line Class Area >
^e kong to "et Belong to gn
i
us
E Belong to
c int wre) (ton Feature Area =>
presented ry Part of Mc pe Part of eei Part of
/
een 3 (ne Line em i 2S € A ee)
is-a a J} Part of is-a s Part of is-a w Part of
Begin /^ AR
A Edge kg
er Points m ge, ^y
li Buildin
End uA ne um sins)
TUTTA
Compe)
Figure 1: 2D geometric-topological data structure of GIS
The extension of this data structure was first proposed by
D. Fritsch (1991) and M. Molenaar (1992). In the mean-
time, some proposals are made taking into account a real
integration of topographic geometry and topology with the
counterparts of planimetry (M. Pilouk/O. Kufoniyi, 1994,
P. van Osterom et al., 1994, D. Fritsch/D. Schmidt, 1994).
2 DTM INTEGRATION
The integration of digital terrain models in GIS is an-
nounced by some vendors of GIS products. But a closer
look indicates that the D'T'M is not at all linked with the x, y
geometry and therefore represented only as an additional
isolated data layer z — z(z,y). In this case, a weak 2.5D
description is reached that might be adequate for medium
scale applications but not for large scale mapping.
In country-wide applications a DTM is often modelled by
a grid of fixed raster cells or variable raster cells (e.g.
quadtree structure). As mentioned before the underlying
data structure is differentiated in its topological elements
and geomorphological features (see fig. 2)
If there is no link between the two structures (fig 1) and
(fig. 2) then undesired results appear, particularly because
of superimposed graphical output, for instance, contour
lines are derived within the planimetric ring polygon of a
building, and are on top of street surfaces etc.
216
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
N
X
(ront ca) Cie Class >
(mac >
A: Bong to ^i Belong to
e
c > (ne re) < roe)
grep vor Part of pores “0 Part of Bd Part of
ES s
Point Entity Line imeem GN Area Entity
TA. Belong to
is-a E of is-a m of is-a Ye Part of
Begin quite
9 break OE grid cells, ^v
Nodes, Points i dure it dead areas
SE d Structure lines Lans À
SEEN
Na Xyz
Figure 2: Geometric-topological data structure for a DTM
of fixed raster cells
A useful topological data structure for the presentation
of irregular distributed points on the Earth' surface is
performed by triangulation algorithms. Very often, a
Delaunay triangulation is carried out that can be derived
from the Voronoi diagram (see fig. 3). For the points
pi V1 <1 <n, the Voronoi diagram consists of n regions
V (i) with the characteristics that if (x,y) € V (i) then pi
is the nearest neighbour of (x,y). If H(pi,p;) is the half-
plane with the set of points closer to p; than to p;, then
V(1) = 1; H(pi,p;)
with d(v,pi) < d(v,p;)Vv € H(pi,p;)
The Voronoi diagram delivers one method to derive the tri-
angulation after Delaunay. The straight lines dual to this
diagram form the edges of the triangles. A defining prop-
erty of the Delaunay triangulation is that the circumcircle
of each triangle does not include any other point in its in-
terior. Fig. 4 demonstrates the dual-graph property of the
Voronoi diagram and the Delaunay triangulation.
Figure 3: Voronoi diagram
A corresponding geometric-topological data structure of a
triangulation in comparison with a gridded DTM delivers
a similar |
ular trian
DTM is t
resent vel
simply fr«
cretizes th
in which ;
Repr
Figure 4
Fig. 4 is
structure.
organizat
ively, are
2.1 1:
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The link
ized by t
identical :
superimp
no real ir
Contrary
is no dou
vector ar
and aspe
equate de
ition of a
the sense
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manner.
2.2 I
The inte;
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et al. (1€
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