;ringulation leads
I'T). This is one
] solid modelling,
ata are captured.
ome proposals to
1994). The DTT
it is quite similar
)
P
Lo
yr
m (a) and the
pyright / Courtesy:
s the straight-line
is constructed by
J. Voroni influence
je Delaunay tetra-
ur adjacent points
ertex, which is the
ie Delaunay tetra-
jedral tessellation
roposed in a fur-
al. (1994). It 1s
ons but also voxel
ic-topological data
)JUERY
E
extends the query
New spatial op-
; structured query
tabases, has to be
sses of queries can
untain), also called
e Boolean (e.g. is point B visible from point A?), also
called spatial predicates or boolean operators
e Operators to create new spatial objects, also called
object-generating functions
These three groups of spatial operators will be examined
in more detail. It is interesting to see that already the
2.5D approach delivers an considerable improvement of the
query space.
1. Measurement functions (for vectorial data)
HEIGHT interpolates within the GRID, TIN or
HYBRID DTM for the height of an arbitrary po-
sition (z, y).
SLOPE derives and interpolates the maximum slope
(gradient) for an arbitrary position (z, y).
EXPOSITION derives and interpolates the direc-
tion of the gradient for an arbitrary point (z, y).
DISTANCEs; computes the Euclidean distance
on top of the DTM. (The equivalent for 2D is
DISTANCE).
PERIMETER; computes the length of a spatial
polygon positioned with coordinates (5,9, 7). The
distance function is a sub-function of PERIMETER.
(There is also an equivalent for 2D).
AREA, 5 computes the area of a polygon defined
by (z,y,z) coordinates. (The equivalent for 2D is
AREA.)
VOLUME computes the volume of two different
D'TMs.
2. Spatial predicates (ordered for points, lines and
faces)
e point/point
POINT.EQUALS: point is identical with
another point
DISJOINT: point is separated from another
one
VISIBLE: points are mutually visible
e point/line
INSIDE/CONTAINS: point is located on
an edge, arc, spline etc., an edge (arc, spline)
contains a point
BORDERED.BY/BORDERS: point bor-
ders an edge, point is start (end) node of an
edge
e point/face
INSIDE/CONTAINS: point is located in-
side a face (area), area contains point
BORDERED.BY/BORDERS: point bor-
ders is located onto the bordering polygon of
the face
DISJOINT: point is not located within a
closed polygon representing the face
e line/line
TANGENT.TO: the line is a tangent to a
polygon (polyline)
CROSS: the line crosses another line (poly-
gon) /
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
LINE_EQUALS: the line coincides with an-
other line (polyline)
DISJOINT: the line is not crossing and bor-
dering another line (polyline)
e line/face and face/face: equivalent predicates
as cited before can be defined (D. Fritsch/D.
Schmidt, 1994)
3. Object-generating functions
INTERSECTION computes new areas (faces)
by the intersection of DTM faces with planimetric
areas.
FLOW MODELLING computes for instance the
water flow in terrain
SQL3 is the new draft proposal presented by ISO/ANSI.
It adresses new features for object-orientation like encap-
sulation, subtypes, inheritance and polymorphism. It is
planned to integrate also the spatial queries that are given
before.
5 PROBLEMS AND PROSPECTS
5.1 Open system architectures
Most recently, the problem: of data integration is a matter
of great interest not only in the field of GIS. The uniform
database scheme for one (logical) central database is no
longer an absolute necessity. Also the idea, that all data
that are needed for an application, should be stored in
one database system, is no more obligatory. Very radical
and open system solutions are under discussion that allow
various modelling concepts and also data levels. These dis-
cussions will also have some impact onto 2.5D and 3D GIS
and associated products.
In this vision it is generally open, onto which platforms
the spatial datasets are stored. A planimetric geometric-
topological dataset can be stored on a server on location A,
and the topographic dataset on a server or client located
in B. The main point is here the link of the two datasets
that virtually defines one closed database. This idea of de-
central data distribution is researched in computer science
since the 1980s under the headline of distributed databases.
5.2 Object oriented modelling techniques
Since the 1960s a new technique of software coding is under
development that has led to paradigm of object-oriented
programming. An important advantage of object-oriented
software development is the better correspondence between
objects of the real world and objects defined in software de-
velopment. Every physical object can be transformed to
an object in the programming language.
Object-oriented analysis methods provide a tool for design-
ing object-oriented systems. There is a general use of ob-
jects from analysis through design to implementation. The
object-oriented paradigm provides several advantages, as
cited in the following: the reuse of software and design,
increased quality of software, easier maintenance, and the
most adaptive interface for human cognition.
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