Handbook of Research on Geoinformatics - Hassan A. Karimi Part 3 pps

68
Map Overlay Problem
lie strictly either on the left or right side
of the line are stored in the corresponding
subtree. The segments that intersect the line
are stored in both. The process continues
until there are only a few segments of one
color, and the brute force algorithm can be
run for them.
• R-tree allows
( ) ( )( )
knkn +∗+Ο log
run-
ning time and
( )
kn +Ο
space in the worst
case (van Oosterom, 1994). It is based on
the spatial data structure R-Tree (Guttman,
1984). It could also be used to deal with
distributed data in a non-uniform way. The
insertion algorithm creates more nodes in
the areas with a larger number of line seg-
ments. Thus, it will automatically adapt to
the distribution of the data. The R-Tree has
been designed to work efciently with large
amounts of data that do not t in primary
memory. Therefore, it can handle the expen-
sive operations of swapping memory pages
between primary and secondary memory.
Spatial Ordering Algorithms: Because al-

gorithms based on plane partitions divide the
space without considering the topology of the
input, they run in quadratic time. However, we
can consider spatial ordering algorithms that use
an aboveness ordering to reduce the number of
comparisons between segments. A segment A
is above B if some vertical line intersects A at a
greater y-coordinate than B. Some examples are
(Andrews et al. 1994):
• Bentley-Ottman sweep has a running
time in the worst and average case of
( )
nknn loglog ∗+∗Ο
, and a
( )
nΟ
size
space (Bentley & Ottman, 1979). This
algorithm is based on the plane sweep tech-
nique. A vertical line is moved across the
plane, stopping at each node (event) of the
subdivisions. It uses two data structures: a
priority queue for storing the nodes of both
subdivisions, ordered by the x-coordinate,
in aboveness order; and a binary search
tree for the segments that intersect the line
at the events if corresponding. The initial
subdivisions are stored in a Doubly-Con-
nected Edge List (DCEL) (frequently used
for representing planar subdivisions of the

space, keeping a record for each node, edge
and face. It also considers the topological
relationships among elements, which allow
operations such as traversing the edges along
a face boundary, reporting the incident edges
of a node, or determining which edges are
shared by two faces.
• Trapezoid Sweep provides
( )
knn +∗Ο log

average and worst case running time, and
( )
nΟ
space (Chan, 1994). This algorithm is
an extension of a classical algorithm based
on plane-sweep (Bentley-Ottman sweep),
which also works with other types of curves.
In the algorithm by Bentley and Ottman the
intersections are sorted according to the X
coordinate. Then, each intersection takes
logarithmic time, which leads to
nk log*

complexity. On the other hand, the Trap-
ezoid Sweep avoids the logarithmic factor
by computing the segment intersections in
a way that does not require sorting.
Blue trapezoidation is dened as the decompo-
sition of the plane into closed trapezoids formed

by the blue segments and some vertical segments
which are vertical extensions of the endpoints of
the segments spanning from the next blue seg-
ment above the point to the next blue segment
below it (Figure 1). The algorithm is based on a
sweep from left to right stepping through each
blue trapezoid. Once the whole plane is swept,
all intersections are reported.
• Hereditary Segment Tree allows
( )
nn log∗Ο

running time in the average and worst cases.
It also takes
( )
nΟ
size space (Chazelle et
al. 1990; Palazzy & Snoeyink, 1994). The
Hereditary Segment Tree is the basic data
69
Map Overlay Problem
structure for computing the red-blue inter-
sections. Firstly, all the segments and end-
points are sorted using a horizontal sweep.
The result is a sweep tree which as traversed
in-order and returns the sorted list of points
and segments. As input the algorithm takes
two lists of segments and points in topologi-
cal order. Then, it assigns each segment and
point to its respective slab and computes the

number of intersections per slab.
r aster Algorithms
Overlay algorithms for raster maps are much
simpler than vector ones. The former make use
of map algebra, which is the application of
boolean operators (AND, OR, NOT and XOR)
to the corresponding layers (Chang, 2006). To
apply these operators, both layers must have the
same level of resolution, otherwise the layer with
the coarsest resolution is converted into the nest
resolution. It is also necessary that both layers
cover the same geographic area; otherwise the
operation is performed only on the intersecting
area. Other problems could be introduced by
a wrong orientation of the pixels. In this case,
rotations or resampling can be applied in order
to adjust the layers.
T
he m
ost widely used data structures to
represent raster maps in GIS are as follows:
• Qua
dtree is one of the best known data
structures for representing raster maps. The
initial map must be a power of two sizes.
The map is recursively divided along the
axes coordinates into four quadrants of
equal size, which are labeled as NW, NE,
SW, and SE. The division stops when the
whole quadrant is in a homogeneous region

and therefore the value of the region is stored
in it. The data structure is represented as a
tree with the root as the whole map. Every
time a quadrant is divided, the four children
that represent the new smaller quadrants are
inserted to the corresponding node into the
tree.
•
Run
-length codes stores each row’s rst and
last columns as the index of the region along
with its thematic value.
• Block codes uses the same idea as run-length,
and is extended into two dimensions using
square blocks to ll in the map regions. The
data structure consists of the origin (center
or bottom left corner) and the size of each
square.
•
Cha
in codes encodes the contour of a region
by means of an origin dened by the user
and a clockwise sequence of vectors in the
direction of the cardinal points: (east=0,
north=1, west=2, south=3). The length of a
vector indicates the number of pixels. For
example: 010, 37, 23, 13, 25, 33,
24, 17 (Figure 5), starting from the
pixel on row 4 and column 6, where the rst
number of each pair represents the direction

and the second number (after the symbol )
represents the length of the vector.
conc Lus Ion
One of the principal applications of GIS is to
analyze geographic data. In order to implement
complex operations that involve more than one
layer it is necessary to overlay several maps or
Figure 1. A blue trapezoidation
70
Map Overlay Problem


Figure 2. QuadTree
Figure 3. Run Length codes
Figure 4. Block codes
Figure 5. Chain codes
partitions so that a single map that relates all the
inputs is obtained. In this article we have covered
the principal techniques and algorithms for the
Map Overlay Problem, which is one of the widely
used spatial analysis operations in GIS. There are
several problems that can be solved through map
overlay: ranging from complex queries involv-
ing more than one layer, and Boolean operations
between polygons, to windowing and combined
buffering.
71
Map Overlay Problem
references
Andrews, D. S., Snoeyink, J., Boritz, J., Chan,

T., Denham, G., Harrinson, J., & Zhu, C. Fur-
ther Comparison of Algorithms for Geometric
Intersection Problems. In Proceeding of the
10
th
International Symposium of Spatial Data
Handling.
Balaban, I. J. (1995). An optimal algorithm for
nding segment intersections, In Proceeding of
the 11
th
Annual ACM Symposium of Computational
Geometry, 211-219.
Bentley, J. L. & Ottmann, T. A. (1979). Algorithms
for reporting and counting geometric intersec-
tions, IEEE, Transactions on Computers, 28(9),
643-647.
Chan, T. M. (1994). A simple trapezoid sweep
algorithm for reporting red/blue segment intersec-
tions, Proceeding of the 6
th
Canadian Conference
of Computational Geometry.
Chang, Kang-tsung. (2006). Introduction to
Geographic Information Systems. Third Edition.
McGraw-Hill. New York, NY.
Chazelle, B., & Edelsbrunner, H. (1992). An
Optimal Algorithm for Intersecting Line Seg-
ments in the Plane. Journal of the Association
for Computing Machinery, 39(1), 1-54.

Chazelle, B., Edelsbrunner, H., Guibas, L. &
Shair, M. (1990). Algorithms for bichromatic
line segment problems and polyhedral terrains.
Technical Report UIUC DCS-R-90-1578, Dept.
Comp. Sci., Univ. Ill. Urbana.
de Berg, M., van Kreveld, M., Overmars, M. &
Schwarzkopf, O. (2000). “Computational Geom-
etry: Algorithms and Applications”, Springer, 2,
19-42.
de Hoop, S., van Oosterom, P., & Molenaar, M.
(1993). Topological Querying of Multiple Map
Layers. In COSIT’93, Springer-Verlag, 139-157.
Finke, U. & Hinrichs, K. (1995). “Overlaying sim-
ply connected planar subdivision in linear time”,
In Proceeding of the 11
th
Annual ACM Symposium
of Computational Geometry, 119-126.
Franklin, W. R. (1989). Efcient intersection
calculations in large databases. In International
Cartographic Association 14
th
World Conference,
Budapest, A62-A63.
Franklin, W. R., Kankanhalli, M. & Naraya-
naswami, C. (1989). Geometric computing and
uniform grid data technique. Comput. Aided
Design, 410-420.
Franklin, W. R., Kankanhalli, M., Narayanas-
wami, C., Sun, D., Zhou, C. & Wu, P. Y. F. (1989).

Uniform grids: A technique for intersection
detection on serial and parallel machines. In
Proceedings of Auto Carto 9: Ninth International
Symposium on Computer-Assisted Cartography,
Baltimore, Maryland, 100-109.
Guttman, A. (1984). R-Trees: A Dynamic Index
Structure for Spatial Searching. ACM SIGMOD,
13, 47-57.
Kriegel, Hans-Peter, Brinkhoff, Thomas & Sch-
neider, Ralf. (1992). An Efcient Map Overlay
Algorithm Based on Spatial Access Methods
and Computational Geometry, Springer-Verlag,
194-211.
Mairson, H. G. & Stol, J. (1988). Reporting and
counting intersections between two sets of line
segments. Theoretical Foundations of Computer
Graphics and CAD, NATO ASI Series F, Volume
40, Springer-Verlag, 307-325.
Palazzy, L. & Snoeyink, J. (1994). Counting and
reporting red/blue segment intersections. CVGIP:
Graph. Mod. Image Proc.
Preparata, F. P., & Shamos, M. I. (1985). Compu-
tational Geometry, Springer-Verlag, New York.
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Map Overlay Problem
Shaffer, C. A., Samet, H. & Nelson, R. C. (1990).
QUILT: A Geographic Information System based
on Quadtrees. In J. GIS, 103-131.
van Oosterom, Peter. (1994). An R-tree based
Map-Overlay Algorithm. EGIS/MARI´94, 1-10.

Van Oosterom, Peter. (1990). A modied Binary
Space Partition for Geographic Information Sys-
tems. Int. J. GIS, 133-140.
Wu, Peter Y. (2005). The Notion of Vicinity: in
Space, Time, and WorkFlow Automation. URISA
Journal.
key ter Ms
Combined Buffer: Buffers are generated
around points or lines. To obtain the combined
buffer of two or more points and/or lines, the
unions of the generated buffers for each one is
computed.
Line Segments Intersection: Consists in
computing the intersections between two sets of
line segments. It is also known as the red-blue line
segments intersection when one set contains red
segments and the other contains blue segments.
In this case, intersections between red and blue
segments are reported.
Map Overlay: Overlay two or more thematic
maps obtaining a single output map.
Plane Sweep: A computational geometry
technique, mostly used in nding intersections
between lines. It consists of moving a line across
a plane while stopping at certain events stored in
a priority queue. The events are then taken ac-
cording to their priorities. A binary search tree is
also used to represent the state of the line at each
moment. The problem is partially solved for all
the area that has already been swept by the line

at each event. It is completely solved when the
line nishes with the last event.
Subdivision Overlay: It is the process of gen-
erating an output plane subdivision from overlay-
ing two or more input plane subdivisions. A plane
subdivision is a set of points, lines, and the regions
determined by such points and lines. The output
subdivision must contain all the points from the
input maps plus the points of intersection between
the input subdivision segments. The lines in the
output subdivisions will be those made up by the
input lines divided at the intersection points and
the input lines that do not intersect. The output
regions will be the union and intersection of all
the input regions.
Windowing: Overlaying a rectangular win-
dow to a map and discarding everything that it
is not inside of the window.
73
Chapter X
Dealing with 3D Surface
Models:
Raster and TIN
Mahbubur R. Meenar
Temple University, USA
John A. Sorrentino
Temple University, USA
Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.
Abstr Act
Three-dimensional surface modeling has become an important element in the processing and visualiza-

tion of geographic information. Models are created from a nite sample of data points over the relevant
area. The techniques used for these activities can be broadly divided into raster-based interpolation
methods and vector-based triangulation methods. This chapter contains a discussion of the benets
and costs of each set of methods. The functions available using 3D surface models include elevation,
queries, contours, slope and aspect, hillshade, and viewshed. Applications include modeling elevation,
pollution concentration and run-off and erosion potential. The chapter ends with a brief discussion of
future trends, and concludes that the choice among the methods depends on the nature of the input data
and the goals of the analyst.
Introduct Ion
A surface can be dened as a continuously vari-
able and measurable eld that contains an innite
number of points. It typically embodies a great
deal of information, and may vary in elevation or
proximity to a feature (Bratt, 2004, O’Sullivan et
al., 2003). The points that create a 3D topographic
surface store elevation or z-values on the z-axis
in a three-dimensional x, y, z coordinate system.
Other examples of using continuous 3D surfaces
are climate, meteorology, pollution, land cover,
74
Dealing with 3D Surface Models
and natural resources (McCloy, 2006, Lo et al.,
2002, Schneider, 2001).
In a Geographic Information Systems (GIS)
environment, a surface cannot measure or record
the z-values of all of the innite points stored
inside it. A surface model, commonly known as
a Digital Terrain Model (DTM), or more gener-
ally, a Digital Elevation Model (DEM), is used to
create 3D surfaces in various areas of science and

technology. The surface model primarily follows
a two step process in recording and storing data:
sampling and interpolation (O’Sullivan et al.,
2003, Heywood et al., 2002). The model selects
sample observation points, either systematically
or adaptively; takes values of this nite number
of points; interpolates the values between these
points; and nally stores the output information
(McCloy, 2006; Bratt, 2004, Heywood et al.,
2002).
There are six alternative ways, as shown in
Figure 1, to express the continuous variation of
a surface in digital representation: (1) regularly
spaced sample points (e.g., a 10 meter spacing
DEM); (2) irregularly spaced sample points
(e.g., temperature recorded at different weather
stations); (3) rectangular cells (e.g., values of re-
ected radiation in a remotely sensed scene); (4)
irregularly shaped polygons (e.g., vegetation cover
class of different parcels); (5) irregular network of
triangles (e.g., elevation in a Triangulated Irregular
Network or TIN); and (6) polylines representing
contours (e.g., elevation in contour lines) (Longley
et al., 2005b).
Among all these surfaces, numbers 1 and 3
are rasters and the remaining four are vectors,
which use points (number 2), lines (number 6), or
polygons (numbers 4 and 5). The DEMs or DTMs
may be derived from a number of data sources,
including contour and spot height information,

Figure 1. Six alternative digital surface representations (Adapted from Longley et al., 2005b)




( 1) (2) (3)







(4)


( 5)

(6)

75
Dealing with 3D Surface Models
stereoscopic aerial photography or photogramme-
try, satellite images, cartography (existing maps),
and ground surveys (Heywood et al., 2002, Lo et
al., 2002, Cohen-Or et al., 1995). Table 1 gives
an idea about different surface data collection
methods and the techniques they use.
In a raster, a DTM is structured as a regular
grid consisting of a rectangular array of uni-

formly-spaced equally-sized cells with sampled
or interpolated z-values. In vector GIS, a more
advanced, more complex, and more common form
of DTM is the TIN, which is constructed as a set
of irregularly located nodes with z-values, con-
nected by edges to form a network of contiguous,
non-overlapping triangular facets (Bratt, 2004,
Longley et al., 2005b, Heywood et al., 2002,
Lo et al., 2002). Figure 2 displays examples of
raster and TIN surfaces. Both surfaces can be
created using two main methods: interpolation
and triangulation.
bAckground
creating and Interpolating a
Raster Surface
Spatial interpolation is the prediction of exact
values of attributes at unsampled locations – a
process of intelligent guesswork which is invoked
without the user’s direct involvement (Longley
et al., 2005b, O’Sullivan et al., 2003, Siska et
al., 2001, Schneider, 2001, McLean et al., 2000).
An interpolation method assumes that spatially-
distributed objects are spatially correlated. Using
this method, cell values are predicted in a raster
from a limited number of sample geographic point
data, such as elevation, rainfall, or temperature.
Such points can be either randomly, strategically,
or regularly-spaced features.
The several interpolation methods used to cre-
ate raster surfaces are Inverse Distance Weighted

(IDW), Kriging, Spline, Natural Neighbors, and
Trend. The IDW is the simplest and most com-
monly used method that weights the points closer
to the processing cell more heavily than those
located further away. Such weights are dened
following the inverse square of distances: w
i
=
1/d
i
2
. This method is useful when a variable being
mapped decreases in inuence with distance from
the sampled location (Kennedy, 2006, Bratt, 2004,
Longley et al., 2005b, Clarke et al., 2002).
Kriging, a popular geo-statistical method,
assumes that the distance or direction between
sample points reects a spatial correlation that can
be used to explain variation in the surface. In this
method, values between points are interpolated
by considering the nearest eight points covaried
Table 1. DTM data collection methods
• Ground Survey
° Suitable for large-scale surface modeling for engineering projects
° Data can be acquired using GPS or Electronic Tacheometer
• Photogrammetry
° Suitable for smaller-scale surface covering larger geographic areas
° Data can be acquired using Analog Stereoplotter, Analytical Plotter,
and Digital Photogrammetry
• Cartography

° Suitable for digitizing maps of smaller-scale areas having regional or na-
tional coverage
° Data can be prepared by digitizing or scanning
Source: Lo et. al, 2002
76
Dealing with 3D Surface Models
within a circular kernel (Hupy et al., 2005). Krig-
ing is mostly used in geology or soil science where
the data might have spatially-correlated distance
or directional bias (McCloy, 2006, Kennedy,
2006, Bratt, 2004, Longley et al., 2005b, Clarke
et al., 2002). Studies have shown that the Kriging
method provides reasonable results in regions
with sufciently dense observations (Hoerka
et al., 2002).
The Spline method may be thought of as the
mathematical equivalent of tting a thin sheet
of rubber to a series of data points (Clarke et
al., 2002). It is the best method for gradually-
varying surfaces such as elevations or pollution
concentrations, but not appropriate for surfaces
with signicant changes within short horizontal
distance or regions where there are no nearby
control points (Kennedy, 2006, Bratt, 2004,
O’Sullivan et al., 2003).
The Trend method uses a least-squares re-
gression t. In the Natural Neighbors method,
the raster surface is interpolated using the input
points that are natural neighbors of a cell. It cre-
ates a Delaunay Triangulation of the input points,

which is part of the TIN creation process and is
discussed in the following section (McCloy, 2006,
Kennedy, 2006, Bratt, 2004).
creating a TIN Surface
The TIN surfaces are usually created from a
combination of point (mass point), line (breakline),
and polygon data, at least some of which should
have z-values. The vertices of the TIN triangles
represent peaks, pits, depressions, and passes; the
edges represent ridges, river channels, and valleys;
and the surfaces of each triangle provide area,
slope (gradient), and aspect (orientation) (Ken-
nedy, 2006, Heywood et al., 2002, Lo et al., 2002,
O’Sullivan et al., 2003). In vector GIS, TINs are
stored as polygons, each with three sides.
Mass points are the primary input features
for creating a TIN, as they determine the overall
shape of a surface. These mass points with their z-
values become nodes in the triangulated network.
Breaklines and polygons can provide more control
over the shape of the TIN surface. Breaklines may
or may not have height measurements, and they
represent natural or built features such as a stream
or a road. Two types of breaklines are available,
hard and soft. Hard breaklines are used to show
the abrupt changes in a surface, whereas the soft
breaklines do not indicate any change in slope, but
may display a study area boundary. Polygons are
separately-interpolated areas, and they represent
surface features that have areas, such as lakes or

ponds (Bratt, 2004).
According to Heywood et al. (2002), there are
two methods available to achieve the linking of
TIN vertices. In the distance-ordering method, the
distance between all pairs of points is calculated,
and then sorted, and nally the closest points are
connected. This method can produce, however,
too many short triangles.
In the Delaunay Triangulation method, a
convex hull is created for a dataset. Then non-
overlapping straight lines are drawn from interior
points to points on the boundary of the convex
hull and to each other. Thus the hull is divided
into a set of polygons and then divided again
into triangles by drawing more lines between the
vertices of the polygons (McCloy, 2006, Longley
et al., 2005b, Clarke et al., 2002, Okabe et al.,
1992). This method is better than the other one
for the following reasons: (1) the triangles are as
equi-angular as possible, which reduces potential
numerical precision problems created by long, thin
triangles; (2) the triangles ensure that any point on
the surface is as close as possible to a node; and
(3) the triangulation is independent of the order
in which the points are processed (Geocities web
site, 2006). Delaunay Triangulation breaks down
when (a) the observation points get further apart
than the feature(s) being mapped; (b) the surface
becomes more anisotropic; and (c) the data do
not match the shape of the features in the surface

(McCloy, 2006).
77
Dealing with 3D Surface Models
Another type of irregular network, known as
Tetrahedral Irregular Network and not often used,
creates a volumetric representation of a 3D set
of points by using tetrahedron cells to ll the 3D
convex hull of the data (Clarke et al., 2002).
r Aster And t In: pros And
cons
Some advantages of raster surfaces are as follows:
(1) they give a uniform density of point data that
is easy to process; (2) they do not need to store
spatial coordinates explicitly for every control
point; (3) each z-value’s position can be easily
found (because of the GRID structure), as well
as its spatial relationship to all the other points;
and (4) they can be processed using array data
structures available in most computer program-
ming languages (O’Sullivan et al., 2003).
Since an interpolation method relies heavily
on the spatial correlation of points, the accuracy
of the raster DTM depends on the complexity of
its surface and the grid spacing (McCloy, 2006,
Kennedy, 2006, Heywood et al., 2002, Siska et
al., 2001). Any feature that is more precise than
the size of the grid cell cannot be located in a
raster. Whether an input point falls on the center
or other part of a cell, there is no guarantee that
the whole cell will have the same value as that

input point (Bratt, 2004). For this reason, the more
input points in a raster surface and the more even
their distribution, the more reliable or accurate
will be the results (Bratt, 2004, Lo et al., 2002,
Siska et al., 2001).
On the other hand, because of the irregular
shapes of the triangles the TIN DTM can have
higher resolution in areas where the surface is
more complex (such as mountainous areas) by
including more mass points, and have lower
resolution in areas that are relatively at (Longley
et al., 2005b, Bratt, 2004, Heywood et al., 2002).
Thus TIN surfaces can produce more accurate
results in spatial analysis, even if they are built
with a signicantly smaller number of sample
points compared to raster surfaces (Lo et al.,
2002, Siska et al., 2001).
The other advantage of a TIN model is the
efciency of data storage (Heywood et al., 2002,
Lo et al., 2002). In addition to nodes and edges,
other features such as roads and streams can be
used as input features in the TIN creation process
which makes it more precise than a raster GRID
(Bratt, 2004).
However, because of the complex data
structure, TIN surface models are considered
more expensive and time consuming, and thus
not as widely used as raster surfaces. TINs are
used mostly in smaller areas, for more detailed,
large-scale applications; raster surfaces are used

in more regional, small-scale applications (Bratt,
2004). Some other limitations of TINs are their
inability to deal with discontinuity of slope across
triangle boundaries, the difculty of calculating
optimum routes, and the need to ensure that peaks,
ridges, and channels are recorded (Longley et
al., 2005b).
Raster and TIN surfaces are interchangeable.
A TIN can be created from a raster to simplify
the surface model for visualization; a raster can


Figure 2. Raster and TIN surfaces of the same
area
78
Dealing with 3D Surface Models
be created from a TIN to extract slope or aspect
information (Bratt, 2004).
AnALyZIng 3d surf Ace s
Viewing a surface feature in a 3D perspective
along with symbols helps understand the nature
of the terrain of a certain area. Visualization,
which is an integral component of DTM, serves
two primary purposes: to communicate geo-
graphic information and to provide a means for
data exploration (Lo et al., 2002). A 3D surface,
which is one of the most exciting developments
in GIS technology, uses many (x,y,z) data points
to form a solid structure that may be visualized
in perspective view using sophisticated computer-

graphics techniques (Lo et al., 2002).
However, a surface feature, whether raster
or TIN, is not always considered as a true 3D
structure. The latter should contain multiple z-
values at the same (x,y) location, and thus is able
to model overhangs and tunnels, and support
accurate volumetric calculations (Longley et al.,
2005b). As surface structures have dimensional
properties between 2D and 3D with no underly-
ing or overlying information, they are sometimes
described as 2.5D data (Longley et al., 2005b,
Heywood et al., 2002).
In order to retrieve specic information or
answer specic queries from the surfaces, the
data needs to be analyzed. Analyzing raster or
TIN surfaces helps answer questions such as the
following: What is the elevation value of a loca-
tion? What is the temperature or concentration of
a pollutant at a certain location? How steep would
be a proposed trail from location A to location B?
What will be the run-off direction? Some com-
mon applications of Raster and TIN surfaces are
described in the following paragraphs and some
examples of different application elds are listed
in Table 2.
Query: Querying raster data gives elevation
information at a certain point. Querying TIN data
also gives information of slope and aspect, the
two ways of quantifying the shape of a surface
at a particular location (Bratt, 2004).

Contour: Contour lines connect all adjacent
points that have the same value, such as height,
pollution, or precipitation. Contour maps are very
useful to visually display any steep-slope area
that has such lines within very close proximity.
In a raster, the contour lines are interpolated
between the cell centers without following the
cell boundaries. In a TIN, the contour lines are
interpolated across each triangle that spans the
contour value (Bratt, 2004).
Slope and Aspect: Slope, also known as gradi-
ent, is the maximum rate of change of elevation
at a point measured as an angle in degrees or as a
percentage (Heywood et al., 2002, O’Sullivan et
al., 2003). It is usually used to nd a suitable loca-
tion for new construction or vulnerable location
for erosion or landslides (Bratt, 2004). Aspect is
the direction a slope faces, expressed in degrees
from north, and is usually used to determine how
much sun a slope might receive in order to model
the vegetative growth pattern, the snow melting
pattern, or the solar heating pattern of buildings
(Bratt, 2004, Heywood et al., 2002).
In a raster, slope and aspect are calculated
for each cell of the surface by tting a plane
to the z-values of each cell and its surrounding
eight neighbors. In a TIN surface, each triangle
face denes a plane with a slope and an aspect
(Bratt, 2004).
Hillshade: The Hillshade function is used

to add depth to a surface for 3D visualization.
Hillshade analyzes the pattern, intensity, and
duration of light and shadow that a surface shows
when illuminated from a particular angle (Bratt,
2004). It is calculated by evaluating the relation-
ship between the position of the light source and
the direction and steepness of the terrain (Bratt,
2004).
Viewshed: The Viewshed function determines
visibility on a surface from one point to another
along a line of sight or across the entire surface
79
Dealing with 3D Surface Models
by assigning code 1 for areas which are in view
and code 0 for areas which are not (Bratt, 2004,
Longley et al., 2005a, O’Sullivan et al., 2003).
Here the value of each cell indicates how many
observer points (containing points and nodes or
vertices of lines) can see that location. Some GIS
packages offer sophisticated visibility analyses
which allow the user to specify the height of the
viewing position or to incorporate barrier features
(such as buildings and trees) for more realistic
visualization, or even to ‘walk’ or ‘y’ through
a terrain model (Heywood et al., 2002).
future trends And
conc Lus Ion
Raster and TIN surfaces are not mutually ex-
clusive; they are rather used to complement one
another in practice (Lo et al., 2002). Whether a

raster or a TIN, the surface is only as good as
the quality, standard, and resolution of its input
data. The quality of any surface model can be
affected by the sparse and inadequate pattern of
control points. It is always difcult and expensive
to represent the extreme high and low values of a
surface. As a result, surfaces with high relief or
with poorly distributed sample points may have
more discrepancies or lower accuracies.
The choice of the interpolation method to
reconstruct a complete surface from sampled
data is also extremely critical. The parameters of
each method can be modied to create a raster
that suits the user’s needs. Although the research
into model-based interpolation continues, there
is no available automated methodology that can
select the best method and optimize its parameters
for any given datasets and applications (Longley
et al., 2005a).
Creating an interpolated surface has become
very easy in a GIS environment; however, the user
should be careful about choosing an appropriate
data-collection method. For example, among
different methods mentioned in Table 1, ground
survey produces the highest quality data, followed
by photogrammetry and cartography (Lo et al.,
2002). Besides understanding the interpolation
methods, the user also needs to be comfortable
with the data creation, acquisition, and quality-
control techniques. The quality of the sample

point set can affect the choice of interpolation
method as well.
Although at the early stages 3D surfaces were
used mostly for visualization purposes, their appli-
cations have become a common practice in various
surface-based geographic investigations – from
military applications to pollutant concentration
analysis. With the rapid technological advance-
ment of GIS software (for data processing) and
GPS or digital photogrammetry (for data creation),
it can be easily predicted that the use of 3D surfaces
will become more common and creative in many
more disciplines in the near future.
Table 2. Areas of applications of 3D surface models
• Surveying and Mapping
• Hydrological Modeling
• Geo-morphology and Geo-science
• Civil and Other Engineering
• Natural Resources Management Planning
• Landscape Planning
• Military Planning
• Cartography – production of contour, hillshade, slope, and aspect
80
Dealing with 3D Surface Models
references
Bratt, S., & Booth, B. (2004). Using ArcGIS 3D
Analyst. Redlands, California: ESRI.
Clarke, K., Parks, B., % Crane, M. (eds.) (2002).
Geographic Information Systems and Environ-
mental Modeling, New Jersey: Prentice-Hall, Inc.,

(pp. 252-285).
Cohen-Or, D., & Shaked, A. (1995). Visibility and
Dead-Zones in Digital Terrain Maps. Eurograph-
ics, 14(3), p. C-171-180.
Geocities web site. />pdoydee/GIS06.html, accessed on January 20,
2006.
Heywood, I., Cornelius, S., & Carver, S. (2002). An
Introduction to Geographic Information Systems.
Essex, England: Prentice-Hall, Inc. Imprint of
Pearson Education, (pp. 59-63, 128-130).
Hoerka, J., Mitasova, H., Parajka, J., & Mitas, L.
(2002). Multivariate Interpolation of Precipitation
Using Regularized Spline with Tension. Transac-
tions in GIS, 6(2), 135-150.
Hupy, J., Aldrich, S., Schaetzl, R., Varnakovida, P.,
Arima, E., Bookout, J., Wiangwang, N., Campos,
A., & McKnight, K. (2005). Mapping Soils, Veg-
etation, and Landforms: An Integrative Physical
Geography Field Experience. The Professional
Geographer, 57(3), 438–451.
Kennedy, M. (2006). Introducing Geographic
Information Systems with ArcGIS. Hoboken, New
Jersey: John Wiley & Sons Ltd. (pp. 449-514).
Lo, C. P., & Yeung, A. (2002). Concepts and
Techniques of Geographic Information Systems.
New Jersey: Prentice-Hall, Inc. (pp. 305-348).
Longley, P., Goodchild, M., Maguire, D., & Rhind,
D. (2005a). Geographic Information Systems and
Science. West Sussex, England: John Wiley &
Sons Ltd, (p. xix, 78).

Longley, P., Goodchild, M., Maguire, D., &
Rhind, D. (2005b). Geographic Information
Systems and Science – Principles, Techniques,
Management, and Applications. Hoboken, New
Jersey: John Wiley & Sons Ltd, (pp. 76-77, 189-
190, 333-337).
McCloy, K. (2006). Resource Management In-
formation Systems: Remote Sensing, GIS and
Modeling, Boca Raton, Florida: Taylor & Francis
Group. (pp. 414-426).
McLean, C., & Evans, I. (2000). Apparent Frac-
tal Dimensions from Continental Scale Digital
Elevation Models Using Variogram Methods.
Transactions in GIS, 4(4), 361-378.
Okabe, A., Boots, B., & Sugihara, K. (1992). Spa-
tial Tessellations: Concepts and Applications of
Voronoi Diagrams. New York: Wiley, (pp. 94).
O’Sullivan, D., & Unwin, D. (2003). Geographic
Information Analysis. Hoboken, New Jersey: John
Wiley & Sons Ltd. (pp. 209-243).
Schneider, B. (2001). Phenomenon-based Speci-
cation of the Digital Representation of Terrain
Surfaces, Transactions in GIS, 5(1), 39-52.
Siska, P., & Hung, I. (2001). Assessment of Kriging
Accuracy in the GIS Environment. Proceedings
at the ESRI International User Conference. San
Diego, California.
key t er Ms
Control Point: The points that provide known
values in the surface creation process. Such points

can be chosen randomly, located at important
places, such as peaks or pits, or located as GRID
samples.
Digital Photogrammetry: The technology of
acquiring topographic data from ortho-photos.
81
Dealing with 3D Surface Models
Delaunay Triangulation: The triangulation
which is equivalent to the nerve of the cells in a
Voronoi diagram, i.e., that triangulation of the
convex hull of the points in the diagram in which
every circumcircle of a triangle is an empty circle
(Okabe et al. 1992, p. 94).
GRID: A geographic data model representing
information as an array of equally sized square
cells arranged in rows and columns and referenced
by their geographic (x,y) locations.
Raster Surface: An evenly spaced grid con-
taining a value in each cell.
Spatial Interpolation: The prediction of exact
values of attributes at unsampled locations using
data from sampled locations.
TIN Surface: A surface upon which the ver-
tices of triangles form irregularly spaced nodes
which allows dense information in complex
areas.
Vector Surface: The surface data that is com-
prised of points, lines, and polygons.
82
Chapter XI

Web Map Servers Data Formats
Yurai Núñez-Rodríguez
Queen’s University, Canada
Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.
Abstr Act
Web map services, such as Google Maps and MapQuest, are among the most popular sites on the Internet.
One can easily access these services through a Web browser on a personal computer or mobile device.
The high accessibility and efciency offered by these sites is possible, in part, by the use of standard
image formats. The present review is a description of the most common image formats available from
web map servers nowadays, as well as other formats with great possibilities for the future. We describe
raster and vector formats and highlight advantages and disadvantages in each case. We also refer to
protocols and image formats supported by the Open Geospatial Consortium (OGC) standards.
Introduct Ion
Web map servers are currently very popular on
the Internet. By serving data through the standard
HTTP/HTTPS protocols many clients have access
to map information. Some examples of public
Web map servers are Google Maps and MapQuest
which provide map images that can be seen on a
regular Web browser. Web map servers may return
data in different formats in response to a query.
The most typical types of data provided by such
servers are map images, although some feature
descriptions and other properties are served as
well. Map image formats can be divided into
83
Web Map Servers Data Formats
two main classes: raster and vector maps. Several
formats from each class will be presented below
with a comparative analysis of them. For each

class, a table that outlines the comparison among
the formats is included. The author also refer to
some of the standards developed by the Open
Geospatial Consortium (OGC) and the image
data formats supported thereby.
rA ster for MAts
A raster or pictorial image consists of a 2-dimen-
sional array of pixels. An uncompressed raster
image is typically referred to as a bitmap. The
most commonly used raster formats on the Web
are GIF (W3C, 1990), JPEG (W3C, 2003a), and
PNG (W3C, 2006). These formats can be visual-
ized in every Web browser without the need of
any additional plug-in or component. Another
raster format that has been largely used in GIS
desktop applications is TIFF. A TIFF image can
contain tags with additional information such
as the georeferencing information of GeoTIFF.
It can also contain multiple layers in a single
image or different types of compression. These,
among other features, make TIFF a very exible
but complicated format. Therefore, common Web
browsers do not support TIFF and its use on the
Internet is very restricted.
JPEG shows its advantages over the rest of the
Web suitable raster formats by the compression
ratio that can be achieved. It is the best choice for
aerial photographs and satellite images. However,
GIF and PNG are better for compression of images
with evenly colored areas; their compression is

loss-less as opposed to JPEG. Some examples of
images that can be compressed as GIF or PNG
are those generated out of geometric elements
such as topography or road maps, also those with
homogeneous areas such as bathymetry images.
Furthermore, GIF and PNG support transparency
which is very useful when the elements in the
image do not cover the whole space so several
images can be superimposed on top of each other.
This is often the case when the elements included
in the maps are points and polylines. Even though
it is possible to superimpose images, it causes
problems of its own. The overlapping needs to
be implemented on the client side application,
which usually runs on a Web browser. Because
of differences in the way Web browsers layout
the page contents, and other incompatibilities,
the solution may be somewhat tricky.
Although GIF and PNG are very similar, some
differences can be pointed out. PNG is more re-
cent than GIF; it was created to fulll the patent
related problems with the algorithm used in the
compression of a GIF image. In addition, GIF is
limited to a maximum of 256 colors. Although
Feature \ Format JPEG GIF PNG TIFF
Transparency No Yes Yes Yes
Supported by Web
browsers
Yes Yes Yes With the use of plug-ins
Number of colors Over 16 million 256 Over 16 million Over 16 million

Compression Lossy, better for
photographs
Loss-less, better for
images with uniformly
colored areas. Formerly
patented
Loss-less, better for
images with uniformly
colored areas
Different methods
Georeferenced No No No Yes, with special tags
for it
Table 1. Comparison of raster formats supported by WMS
84
Web Map Servers Data Formats
the patent for the compression of the GIF format
has already expired, PNG still seems to be the
preferred format on Web map servers. See Table
1 for an outlined comparison among the raster
formats.
vect or for MAts
Vector images basically consist of geometric ele-
ments. One advantage of vector images over raster
images is that geometric elements are scalable so
they can easily adjust to any size without quality
loss, whereas raster map images appear differ-
ently depending on the screen resolution. The
ease of rescaling vector images allows operations
on the client side such as zoom-in and zoom-out
up to certain scaling factors, without the need of

performing new requests to the server. In vector
maps le sizes are usually smaller than the ras-
ter equivalents (Duce, 2002) (this difference is
accentuated on large images). Moreover, vector
images can be composed of several layers that
can be handled independently. The vector formats
that we consider here are actually hybrid formats
in the sense that they allow raster elements and
geometric elements together. Thus, all the ele-
ments needed for the map image can be included
in a single le or HTTP data stream, which makes
vector maps more powerful than purely raster im-
ages. Another important feature only available to
scalable formats is the possibility of performing
textual search inside their contents. This allows
Internet search engines to index precomputed
versions of vector maps. However, in spite of
all the advantages of vector maps, plug-ins or
other additional components are needed on Web
browsers for their visualization. This makes raster
formats the most popular at the moment.
Two standard vector-based formats are Scal-
able Vector Graphics (SVG) (W3C, 2003b) and
Web Computer Graphics Metale (WebCGM)
(W3C, 2001). Both formats follow the W3C re-
quirements for scalable graphics. WebCGM was
rst presented as a standard by W3C in 1999. It
has evolved from the ISO standard CGM, cre-
ated in 1997 for vector graphics. A new version
(2.0) of the WebCGM specication is available

(OASIS, 2005); although the last standard ver-
sion recommended by W3C is version 1.0 (W3C,
2001). SVG, rst released in 2001 and currently
in its version 1.1 (W3C, 2003), has had a greater
impact for the developers of Web browsers. SVG
was created to fulll the need of a graphic inter-
face for the Web services. For this reason, it is
based on XML and is more integrated to other
standards on the Web platform. At the moment
there are Web browser plug-ins available for both
formats. However, the most common plug-ins are
for SVG. SVG also offers a more sophisticated way
of interacting with the image through events and
actions whereas WebCGM only allows interaction
through hyperlinks. Furthermore, SVG includes
animations.
Macromedia Flash Format (SWF) (Adobe,
2005), on the other hand, is not an open stan-
dard. It is a vector-based format that has been
considered a de-facto standard. Its extensive use
on Web sites ensures that most of the Internet
browsers already have an installed plug-in to
visualize this type of content. However, recent
trends include direct support for the SVG format
in the Internet browsers. Signicant works have
been done towards supporting SVG in Mozilla-
based products (Birtles, 2005; Mozilla, 2006).
This could eventually start inclining the balance
towards the side of vector images.
Although SVG and SWF have many similari-

ties, main differences can be pointed out. SVG
includes elements that may be suitable for maps
not available in SWF. For example, texts that can
be rendered along a path, and curves such as arcs
and cubic splines. Arcs and elliptical curves can
be generated in SWF as quadratic splines, which
are acceptable approximations to cubic splines.
As mentioned above for SVG, SWF also includes
animations, events and actions. A slight but no-
table difference is that SVG offers an easy way to
85
Web Map Servers Data Formats
handle some events of interest for map services
such as zoom-in and zoom-out events. In terms
of coordinate systems and units, SVG allows a
higher level of precision and a wider variety of
measurement units, while SWF only support two
types of measurement units: one for length and one
for radial measurements. Compressed SVG les
can have similar sizes than SWF les; however,
SWF is an implicitly streamable format that lets
the viewers display the information as it arrives
to the client, while the rest of the content is still
being downloaded. This is very convenient when
dealing with large les.
Some other differences between SVG and
SWF come from the set of tools associated with
them. For example SVG les, written in XML,
allow access to the explicit textual features of
the image. However, the set of tools available for

SWF include text search and as it turns out, pres-
ently, most search engines use the tools provided
for SWF or their own mechanisms for indexing
Flash les. This is expected to be also applied to
SVG les in the future. The underlying language
for SVG (XML) makes the generation of maps by
scripts or programs a relatively easy task. Besides,
by transforming previously generated XML les,
using style sheets and XSTL transformations, one
can easily obtain different versions of a map. This
strategy of transformation has been used by Peng
et al. (Peng, 2004). Another advantage of SVG
is that it is an open standard which accepts the
contribution from the community of users and
developers. Nevertheless, the specication for
SWF and a set of tools to create the SWF les
is available for free under the agreements of the
corresponding Adobe (current software vendor for
the Flash products) license (Adobe, 2005). Despite
the differences between these two formats, they
are similar enough to attempt a conversion from
one to another; such are the efforts of Probets
et al. who have built tools to realize the conver-
sion from SWF to SVG (Probets, 2001). Table 2
summarizes the elements of comparison among
the presented vector-based formats. For more
elements of comparison, including a larger set
of common features, refer to Held et al. (Held,
2004).
Feature \ Format WebCGM SVG SWF

In WMS specication Yes Yes No
Animation No, although possible with the
new specication
Yes Yes
Event handling No Yes Yes
Hyperlinks can be included Yes Yes Yes
Support of geometric elements All, except text rendered on
path
All commonly used in GIS solutions All, except cubic spline
and text rendered on path
Streamable If implemented in the viewer,
as it complies to W3C Scalable
Graphics
If implemented in the viewer, as
the last version complies to W3C
Scalable Graphics on this point
Yes
Text search Yes Yes Yes
Styled No Yes No
Compression As JPEG, restricted to some
elements
Yes Yes
In Web browsers As plug-ins As plug-ins and also implemented
partially in some Web browsers
As plug-ins
Table 2. Comparison of the vector-based formats
86
Web Map Servers Data Formats
web MAp ser vIce
Web map servers have blossomed with the

emerging Web services technology on the Inter-
net. Web services, which also make use of the
HTTP/HTTPS protocols, use XML (W3C, 2004)
as their communication and description language.
Different GIS product builders have adopted
their own Web service interfaces according to
their needs. The rst standard for the interface
of spatial Web services came along in 2000,
developed by the Open Geospatial Consortium
(OGC) which had already been working in Web
mapping standardization since 1997. This effort
has led to the interoperability of several geospa-
tial products from different vendors across many
different platforms.
Among the specications developed by OGC
are Web Map Service (WMS) (OGC, 2006c), Web
Feature Service (WFS) (OGC, 2006b), and Web
Coverage Service (WCS) (OGC, 2003). This set
of standards covers most of the functionality
commonly offered by geospatial Web services.
WFS and WCS servers use only XML for their
communication. However, WFS uses a specic
subset of XML (GML) (OGC, 2006a) to encode
geographic information. WMS, in addition, uses
some of the map formats previously mentioned
combined with XML. There are already a large
number of GIS software vendors that have built
products compliant to OGC specications (OGC,
2006d; Skylab, 2006). Some experiments to test
the efciency of WMS’s have been carried out

with successful results (Bernard, 2002; Sayar,
2005). Unfortunately, some of the largest map-
ping services like the examples mentioned above
(Google Maps and MapQuest) do not comply with
the OGC standards, although some wrappers have
been built to make them available through the
standards. One example is the CubeWerx con-
nector for the OGC standards and Google Maps
(CubeWerx, 2005).
WMS supports the raster data formats previ-
ously presented: GIF, PNG, JPEG, and TIFF.
For vector maps only SVG and WebCGM are
supported. SWF is not included because it is not
an open standard.
conc Lus Ion
Web map servers support different types of data
formats. The map image formats are divided into
two main classes: raster, and vector maps. At the
moment, raster types of images are more widely
supported as they are implemented in all brows-
ers. Among the raster formats PNG seems to be
the best candidate except for photographic map
layers where JPEG reaches the best compression
ratios. Vector-based images allow smaller le
sizes, better image quality and more dynamic
maps. However, vector maps need plug-ins for
their visualization on Web browsers. The most
widely used plug-ins for vector-based images
are those for SWF. Unfortunately, SWF is not an
open standard and is not included in the current

WMS specication of the OGC. Good news in
favor of the vector-based images is that some Web
browsers are already including direct support
for SVG. SVG seems to be the format of future
Web map services, together with PNG and JPEG
raster formats.
r eferences
Adobe (2005). Macromedia Flash (SWF) and
Flash Video (FLV) File Format Specication
Version 8. />ing/developer/
Bernard, L. (2002). Experiences from an imple-
mentation Testbed to set up a national SDI.
Proceedings of the 5
th
AGILE Conference on
Geographic Information Science. Palma (Balearic
Islands, Spain).
Birtles, B. (2005). Implementing Scalable Vector
Graphics in Mozilla. University of Technology,
Sydney.
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Web Map Servers Data Formats
CubeWerx (2005). CubeWerx releases an OGC
Connector for Google Maps. ew-
erx.com/main/about_us/news/Google.html
Duce, D., Herman, I., & Hopgood, B. (2002). Web
2D Graphics File Formats. Computer Graphics
Forum, 21(1), 43. DOI:10.1111/1467-8659.00565.
Held, G., Ullrich, T., Neumann, A., & Winter, A.
M. (2004). Comparing SWF (ShockWave Flash)

and SVG (Scalable Vector Graphics) le format
specications. />comparison_ash_svg/
Mozilla (2006). Mozilla SVG Project. http://www.
mozilla.org/projects/svg/
OASIS (2005). WebCGM 2.0 OASIS Committee
Specication. Document Identier: WebCGM-
v2.0.
OGC (2003). OGC Web Coverage Service, Ver-
sion 1.0. Reference Number: OGC 03-065r6.
/>OGC (2006). OGC Geography Markup Language
(GML) simple features prole, Version 1.0. GML
3.1.1, Reference Number: OGC 04-049. http://
www.opengeospatial.org/
OGC (2006). OGC Web Feature Service Imple-
mentation Specication, Version 1.0. Reference
Number: OGC 04-094. ngeospa-
tial.org/
OGC (2006). OGC Web Map Service Implemen-
tation Specication, Version 1.3.0. Reference
Number: OGC 06-042. ngeo-
spatial.org/
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ucts. />Peng, Z. R., & Zhang C. (2004). The roles of ge-
ography markup language (GML), scalable vector
graphics (SVG), and Web feature service (WFS)
specications in the development of Internet
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of Geographical Systems, 6(2), 95 – 116. Springer
Berlin / Heidelberg. ISSN: 1435-5930.
Probets, S., Mong, J., Evans, D., & Brailsford,

D. (2001). Vector Graphics: From PostScript and
Flash to SVG. Proceedings of the ACM Symposium
on Document Engineering (DocEng’01) Atlanta,
Georgia. (pp. 135–143. 9–11).
Sayar, A., Pierce, M., & Fox, G. C. (2005). De-
veloping GIS Visualization Web Services for
Geophysical Applications. ISPRS International
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Turkey.
Skylab Mobilesystems Ltd. (2006). OGC WMS
Server List. lab-mobilesystems.
com/en/wms_serverlist.html
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Consortium. />xml-20040204
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/>88
Web Map Servers Data Formats
key t er Ms
GIF: Graphics Interchange Format. Image
format stored as a compressed rectangular array

of pixels. The pixel colors are limited to a maxi-
mum of 256. This format can contain transparent
areas.
JPEG: Joint Photograph Group. Standard
image format created to store photograph as a
compressed rectangular array of pixels. The com-
pressed images usually have lower quality com-
pared to the originals but, for some compression
ratios this is not noticeable by a human eye.
OGC: Open Geospatial Consortium Inc.,
founded in 1994, after the OpenGIS Project, is
an organization that involves entities from the
government, academics and private sector whose
mission is to develop standards for geospatial
products.
PNG: Portable Network Graphics. Image
format similar to GIF except that it has been
developed more recently and is able to store one
of over 16 million of colors per pixel.
SVG: Scalable Vector Graphics. Vector-based
open standard format developed by the W3C
Consortium.
SWF: Macromedia Flash format. Vector-based
format developed by Macromedia. A SWF le can
contain videos and animations including audio.
TIFF: Tagged Image File Format. Image
format designed to store high resolution images.
Its contents may or may not be compressed. It
can contain additional information in the form
of tags.

W3C: World Wide Web Consortium. Or-
ganization that denes the standards for the
Internet.
WMS: Web Map Service. The latest available
version of the WMS specication is 1.3.0 and it is
also available as ISO 19128 since 2005.
WebCGM: Web Computer Graphics Meta-
le. Internet version of the Computer Graphics
Metale created in 1987 as a standard format for
the interchange of graphic information.
XML: Extensible Markup Language. Denes
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89
Chapter XII
Overview, Classication and
Selection of Map Projections
for Geospatial Applications
Eric Delmelle
University of North Carolina at Charlotte, USA
Raymond Dezzani
University of Idaho, USA
Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.
Abstr Act
There has been a dramatic increase in the handling of geospatial information, and also in the produc-
tion of maps. However, because the Earth is three-dimensional, geo-referenced data must be projected
on a two-dimensional surface. Depending on the area being mapped, the projection process generates a
varying amount of distortion, especially for continental and world maps. Geospatial users have a wide
variety of projections too choose from; it is therefore important to understand distortion characteristics
for each of them. This chapter reviews foundations of map projection, such as map projection families,

distortion characteristics (areal, angular, shape and distance), geometric features and special properties.
The chapter ends by a discussion on projection selection and current research trends."
Int r oduc t Ion
Recent automation and increasing user-friendliness
of geospatial systems (such as Geographical Infor-
mation Systems -GIS) has made the production
of maps easier, faster and more accurate. Cartog-
raphers have at present an impressive number of
projections, but often lack a suitable classication
and selection scheme for them, which signicantly
slow down the mapping process. Map projections
generate distortion from the original shape of the
Earth. They distort angles between locations on
Earth, continental areas and distances between
points. Distortion, although less apparent on a
larger-scale map (because it covers a smaller area
and the curvature of the Earth is less pronounced),
misleads people in the way they visualize, cognize
or locate large geographic features (Snyder, 1993).
Map projections have been devised to answer
some of the distortion issues, preserving selected
geometric properties (e.g., conformality, equiva-
lence, and equidistance) and special properties.
Ignoring these distortion characteristics may lead
to an unconsidered choice of projection framework,
90
Overview, Classication and Selection of Map Projections for Geospatial Applications
resulting in a disastrous map, thereby devaluating
the message the map attempts to communicate.
It is urgent for users of geospatial technologies to

acquire a map projection expertise before interact-
ing with any cartographic software.
t he MAp pr oJect Ion pr oc ess
The Earth is essentially spherical, but is approxi-
mated by a mathematical gure –a datum surface.
For the purpose of world maps, a sphere with radius
R
E
= 6371km is a satisfying approximation. For
large-scale maps however (i.e., at the continental
and country scale), the non-spherical shape of the
Earth is represented by an ellipsoid with major
axis a and minor axis b. The values of a and b
vary with the location of the area to be mapped and
are calculated in such a way that the ellipsoid ts
the geoid almost perfectly. The full sized sphere
is greatly reduced to an exact model called the
generating globe (see Figure 1). Nevertheless,
globes have many practical drawbacks: they are
difcult to reproduce, cumbersome for measuring
distances, and less than the globe is visible at once.
Those disadvantages are eliminated during the map
projection process, by converting the longitude
and latitude angles (λ,φ) to Cartesian coordinates
(Canters and Decleir, 1989):
, )x f (j l
,

,y g( )j l
(1)

cLAssIf IcAt Ion of MAp
pr oJect Ions by f AMILIes
Three major projections classes are named after
the developable surface onto which most of the
map projections are at least partially geometrically
projected. All three have either a linear or punctual
contact with the sphere: they are the cylindrical,
conical and azimuthal. The advantage of these
shapes is that, because their curvature is in one
dimension only, they can be attened to a plane
without any further distortion (Iliffe, 2000). The
pseudocylindrical, pseudoconic, pseudoazimuthal
and pseudoconical projections are based on the
three aforementioned families (Snyder, 1987; Lee,
1944).
conical projection
When a cone wrapped around the globe is cut along
a meridian, a conical projection results. The cone
has its peak -also called apex- above one of the
two Earth’s poles and touches the sphere along one
parallel of latitude (Figure 2a). When unwrapped,
meridians become straight lines converging to the
apex, and parallels are represented by arcs of circle.
The pole is either represented as a point or as a line.
When the cone is secant to the globe, it bisects the
surface at two lines of latitude (Figure 2b).
Cylindrical Projection
A cylinder is wrapped around the generating globe,
so that its surface touches the Equator throughout
its circumference. The meridians of longitude are

of equal length and perpendicular to the Equator.
The parallels of latitude are marked off as lines
Figure 1. The map projection process: the sphere,
approximated by a mathematical gure is reduced
to a generating globe that is projected on a at
surface. (after Canters and Decleir 1989)
91
Overview, Classication and Selection of Map Projections for Geospatial Applications
parallel to the Equator, and spaced in such a way
to preserve specic properties, described further.
The nal process consists of cutting the cylinder
along a specic meridian yielding a cylindrical map
(Figure 2c). An example of a tangent projection
is the Plate Carrée projection with transformation
formulas x = R(l – l
0
) and y = Rφ, where λ
0
is the
longitude of the prime meridian. A secant cylindri-
cal projection is obtained when the cylinder bisects
the globe at two parallels (Figure 2d). The Behrman
projection is a secant projection characterized by
standard parallels at ±30º with transformation
formulas x = R(l – l
0
)cosφ
0
,
y Rj

, where φ
0

denotes the standard latitude.

Azimuthal Projection
An azimuthal projection results from the projec-
tion of meridians and parallels at a point on a plane
tangent on one of the Earth’s poles. The meridians
become straight lines diverging from the center
of the projection. The parallels are portrayed as
concentric circles, centered on the chosen pole.
Azimuthal projections are widely used to portray
the polar areas (Figure 3). Three different kinds
of azimuthal projection are possible:
Figure 2. Illustration of the tangent conical projection in (a) and a secant projection in (b). Illustration of the
tangent cylindrical projection in (c) and its secant counterpart in (d). Distortion is minimum on the contact
lines and increases away from those parallels of latitude.
Figure 3. Illustration of the azimuthal projection and the three resulting cases
92
Overview, Classication and Selection of Map Projections for Geospatial Applications
1. The orthographic case results from a per-
spective projection from an innite distance,
which gives a globe-like shape. Only one
hemisphere can be mapped at a time, and
distortions are greatest along the rim of the
hemisphere, where distances and landmasses
tend to be compressed.
2
. The

stereographic case is a true perspective
projection with the globe being projected onto
the plane from the point on the globe dia-
metrically opposite to the point of tangency,
also called nadir. The stereographic case
preserves angles.
3
. A gn
omonic projection is obtained by projec-
tion on the plane from the center of the globe.
The shape of the countries is dramatically
distorted away from the center of the plane.
Straight lines on a gnomonic projection depict
great circles. Unfortunately, the gnomonic
projection excessively distorts shapes. Its
use is recommended for comparison with the
Mercator and plotting long-distance courses
of ships and airplanes (see Figure 4).
Pseudoconic and Polyconic
projections
The pseudoconic projection, such as the Boone’s
equal-area, has its parallels represented as con-
centric circular arcs, and meridians as concurrent
curves. A polyconic projection results from project-
ing the Earth on different cones tangent to each
parallel of latitude. Both meridians are parallels
are represented by concurrent curves. The Van Der
Grinten and Lagrange are polyconic projections.
(Snyder and Voxland, 1994).
Pseudocylindrical Projection

This projection is characterized by straight lines
of latitude and concurrent curved meridians.
Robinson’s projection, adopted by the National
Geographic Society is a key example (Robinson,
1974), and so is the sinusoidal equal-area (Figure
5).
dIst or t Ion gener At ed dur Ing
t he pr oJect Ion pr ocess
Projections generate distortion from the original
shape of the globe by shearing, compression and
tearing of continental areas. On world maps, conti-
nental areas may severely be altered, increasingly
away from the central meridian.
distortion Indexes
The scale distortion m is dened by the ratio of a
projected length ds determined by two points over
the original length DS on the generation globe. The


Figure 4. From left to right: the Mercator projection centered 60°N, 35°W, and the gnomonic projection
centered 60°N, 47°W. Great circles from Oslo to Anchorage and San Diego are represented as straight lines
on the gnomonic projection and are curved on the Mercator projection.