[QGIS Commit] r11056 - docs/trunk/english_us/gis_introduction
svn_qgis at osgeo.org
svn_qgis at osgeo.org
Mon Jul 13 10:17:51 EDT 2009
Author: dassau
Date: 2009-07-13 10:17:50 -0400 (Mon, 13 Jul 2009)
New Revision: 11056
Modified:
docs/trunk/english_us/gis_introduction/crs.tex
docs/trunk/english_us/gis_introduction/rasterdata.tex
docs/trunk/english_us/gis_introduction/topology.tex
Log:
finished sections 5-7
Modified: docs/trunk/english_us/gis_introduction/crs.tex
===================================================================
--- docs/trunk/english_us/gis_introduction/crs.tex 2009-07-13 12:31:21 UTC (rev 11055)
+++ docs/trunk/english_us/gis_introduction/crs.tex 2009-07-13 14:17:50 UTC (rev 11056)
@@ -17,4 +17,503 @@
\subsection{Overview}\label{subsec:overview}
+\textbf{Map projections} try to portray the surface of the earth or a portion of the
+earth on a flat piece of paper or computer screen. A \textbf{coordinate reference
+system} (CRS) then defines, with the help of coordinates, how the
+two-dimensional, projected map in your GIS is related to real places on the
+earth. The decision as to which map projection and coordinate reference
+system to use, depends on the regional extent of the area you want to work
+in, on the analysis you want to do and often on the availability of data.
+\subsection{Map Projection in detail}
+
+A traditional method of representing the earth's shape is the use of globes.
+There is, however, a problem with this approach. Although globes preserve the
+majority of the earth's shape and illustrate the spatial configuration of
+continent-sized features, they are very difficult to carry in one's pocket.
+They are also only convenient to use at extremely small scales (e.g. 1 : 100
+million).
+
+Most of the thematic map data commonly used in GIS applications are of
+considerably larger scale. Typical GIS datasets have scales of 1:250 000 or
+greater, depending on the level of detail. A globe of this size would be
+difficult and expensive to produce and even more difficult to carry around.
+As a result, cartographers have developed a set of techniques called
+\textbf{map projections} designed to show, with reasonable accuracy, the
+spherical earth in two-dimensions.
+
+When viewed at close range the earth appears to be relatively flat. However
+when viewed from space, we can see that the earth is relatively spherical.
+Maps, as we will see in the upcoming map production topic, are
+representations of reality. They are designed to not only represent features,
+but also their shape and spatial arrangement. Each map projection has
+\textbf{advantages} and \textbf{disadvantages}. The best projection for a map
+depends on the
+scale of the map, and on the purposes for which it will be used. For example,
+a projection may have unacceptable distortions if used to map the entire
+African continent, but may be an excellent choice for a \textbf{large-scale
+(detailed) map} of your country. The properties of a map projection may also
+influence some of the design features of the map. Some projections are good
+for small areas, some are good for mapping areas with a large East-West
+extent, and some are better for mapping areas with a large North-South
+extent.
+
+\subsection{The three families of map projections}
+
+The process of creating map projections can be visualised by positioning a
+light source inside a transparent globe on which opaque earth features are
+placed. Then project the feature outlines onto a two-dimensional flat piece
+of paper. Different ways of projecting can be produced by surrounding the
+globe in a \textbf{cylindrical} fashion, as a \textbf{cone}, or even as a
+\textbf{flat surface}. Each of
+these methods produces what is called a map \textbf{projection family}.
+Therefore, there is a family of \textbf{planar projections}, a family of
+\textbf{cylindrical projections}, and another called \textbf{conical
+projections} (see Figure \ref{fig:projfamilies})
+
+\begin{figure}[ht]
+ \begin{center}
+ \caption{The three families of map projections. They can be represented by
+a) cylindrical projections, b) conical projections or c) planar projections.}
+\label{fig:projfamilies}\smallskip
+ \includegraphics[clip=true, width=\textwidth]{projection-family}
+\end{center}
+\end{figure}
+
+\subsection{Accuracy of map projections}
+
+Map projections are never absolutely accurate representations of the
+spherical earth. As a result of the map projection process, every map shows
+\textbf{distortions of angular conformity, distance and area}. A map
+projection may
+combine several of these characteristics, or may be a compromise that
+distorts all the properties of area, distance and angular conformity, within
+some acceptable limit. Examples of compromise projections are the
+\textbf{Winkel Tripel projection} and the \textbf{Robinson projection} (see
+Figure \ref{fig:robinson}), which are often used for world maps.
+
+\begin{figure}[ht]
+ \begin{center}
+ \caption{The Robinson projection is a compromise where distortions of
+area, angular conformity and distance are acceptable.}
+\label{fig:robinson}\smallskip
+ \includegraphics[clip=true, width=0.7\textwidth]{robinson-projection}
+\end{center}
+\end{figure}
+
+It is usually impossible to preserve all characteristics at the same time in
+a map projection. This means that when you want to carry out accurate
+analytical operations, you need to use a map projection that provides the
+best characteristics for your analyses. For example, if you need to measure
+distances on your map, you should try to use a map projection for your data
+that provides high accuracy for distances.
+
+\subsection{Map projections with angular conformity}
+
+When working with a globe, the main directions of the compass rose (North,
+East, South and West) will always occur at 90 degrees to one another. In
+other words, East will always occur at a 90 degree angle to North.
+Maintaining correct \textbf{angular properties} can be preserved on a map
+projection as well. A map projection that retains this property of angular
+conformity is called a \textbf{conformal or orthomorphic projection}.
+
+\begin{figure}[ht]
+ \begin{center}
+ \caption{The Mercator projection, for example, is used where angular
+relationships are important, but the relationship of areas are distorted.}
+\label{fig:mercator}\smallskip
+ \includegraphics[clip=true, width=0.7\textwidth]{mercator-projection}
+\end{center}
+\end{figure}
+
+These projections are used when the \textbf{preservation of angular
+relationships} is
+important. They are commonly used for navigational or meteorological tasks.
+It is important to remember that maintaining true angles on a map is
+difficult for large areas and should be attempted only for small portions of
+the earth. The conformal type of projection results in distortions of areas,
+meaning that if area measurements are made on the map, they will be
+incorrect. The larger the area the less accurate the area measurements will
+be. Examples are the \textbf{Mercator projection} (as shown in Figure
+ref{fig:mercator}) and the \textbf{Lambert Conformal Conic projection}. The
+U.S. Geological Survey uses a conformal projection for many of its
+topographic maps.
+
+\subsection{Map projections with equal distance}
+
+If your goal in projecting a map is to accurately measure distances, you
+should select a projection that is designed to preserve distances well. Such
+projections, called \textbf{equidistant projections}, require that the
+\textbf{scale} of the map is \textbf{kept constant}. A map is equidistant
+when it correctly represents
+distances from the centre of the projection to any other place on the map.
+\textbf{Equidistant projections} maintain accurate distances from the centre of the
+projection or along given lines. These projections are used for radio and
+seismic mapping, and for navigation. The \textbf{Plate Carree Equidistant
+Cylindrical} (see Figure \ref{fig:platte}) and the \textbf{Equirectangular
+projection} are two good examples of equidistant projections. The
+\textbf{Azimuthal Equidistant projection} is
+the projection used for the emblem of the United Nations (see Figure
+\ref{fig:uno}).
+
+\begin{figure}[ht]
+ \begin{center}
+ \caption{The United Nations Logo uses the Azimuthal Equidistant
+projection.}
+\label{fig:uno}\smallskip
+ \includegraphics[clip=true, width=0.3\textwidth]{unlogo}
+\end{center}
+\end{figure}
+
+\begin{figure}[ht]
+ \begin{center}
+ \caption{The Plate Carree Equidistant Cylindrical projection, for example,
+is used when accurate distance measurement is important.}
+\label{fig:platte}\smallskip
+ \includegraphics[clip=true, width=0.8\textwidth]{platte-carree-projection}
+\end{center}
+\end{figure}
+
+\subsection{Projections with equal areas}
+
+When a map portrays areas over the entire map, so that all mapped areas have
+the same proportional relationship to the areas on the Earth that they
+represent, the map is an \textbf{equal area map}. In practice, general reference and
+educational maps most often require the use of \textbf{equal area
+projections}. As the
+name implies, these maps are best used when calculations of area are the
+dominant calculations you will perform. If, for example, you are trying to
+analyse a particular area in your town to find out whether it is large enough
+for a new shopping mall, equal area projections are the best choice. On the
+one hand, the larger the area you are analysing, the more precise your area
+measures will be, if you use an equal area projection rather than another
+type. On the other hand, an equal area projection results in
+\textbf{distortions of angular conformity} when dealing with large areas.
+Small areas will be far
+less prone to having their angles distorted when you use an equal area
+projection. \textbf{Alber's Equal Area, Lambert's Equal Area and Mollweide
+Equal Area Cylindrical projections} (shown in Figure \ref{fig:mollweide}) are
+types of equal area projections that are often encountered in GIS work.
+
+Keep in mind that map projection is a very complex topic. There are hundreds
+of different projections available world wide each trying to portray a
+certain portion of the earth's surface as faithfully as possible on a flat
+piece of paper. In reality, the choice of which projection to use, will often
+be made for you. Most countries have commonly used projections and when data
+is exchanged people will follow the \textbf{national trend}.
+
+\begin{figure}[ht]
+ \begin{center}
+ \caption{The Mollweide Equal Area Cylindrical projection, for example,
+ensures that all mapped areas have the same proportional relationship to the
+areas on the Earth.}
+\label{fig:mollweide}\smallskip
+ \includegraphics[clip=true, width=0.8\textwidth]{mollweide_equal_area_projection}
+\end{center}
+\end{figure}
+
+\subsection{Coordinate Reference System (CRS) in detail}
+
+With the help of coordinate reference systems (CRS) every place on the earth
+can be specified by a set of three numbers, called coordinates. In general
+CRS can be divided into \textbf{projected coordinate reference systems} (also
+called Cartesian or rectangular coordinate reference systems) and
+\textbf{geographic coordinate reference systems}.
+
+\subsection{Geographic Coordinate Systems}
+
+The use of Geographic Coordinate Reference Systems is very common. They use
+degrees of latitude and longitude and sometimes also a height value to
+describe a location on the earth's surface. The most popular is called
+\textbf{WGS 84}.
+
+\textbf{Lines of latitude} run parallel to the equator and divide the earth into 180
+equally spaced sections from North to South (or South to North). The
+reference line for latitude is the equator and each \textbf{hemisphere} is
+divided
+into ninety sections, each representing one degree of latitude. In the
+northern hemisphere, degrees of latitude are measured from zero at the
+equator to ninety at the north pole. In the southern hemisphere, degrees of
+latitude are measured from zero at the equator to ninety degrees at the south
+pole. To simplify the digitisation of maps, degrees of latitude in the
+southern hemisphere are often assigned negative values (0 to -90$^\circ$). Wherever
+you are on the earth's surface, the distance between the lines of latitude is
+the same (60 nautical miles). See Figure \ref{fig:latlon} for a pictorial view.
+
+\begin{figure}[ht]
+ \begin{center}
+ \caption{Geographic coordinate system with lines of latitude parallel to
+the equator and lines of longitude with the prime meridian through Greenwich.}
+\label{fig:latlon}\smallskip
+ \includegraphics[clip=true, width=0.8\textwidth]{latlon}
+\end{center}
+\end{figure}
+
+\textbf{Lines of longitude}, on the other hand, do not stand up so well to the
+standard of uniformity. Lines of longitude run perpendicular to the equator
+and converge at the poles. The reference line for longitude (the prime
+meridian) runs from the North pole to the South pole through Greenwich,
+England. Subsequent lines of longitude are measured from zero to 180 degrees
+East or West of the prime meridian. Note that values West of the prime
+meridian are assigned negative values for use in digital mapping
+applications. See Figure \ref{fig:latlon} for a pictorial view.
+
+At the equator, and only at the equator, the distance represented by one line
+of longitude is equal to the distance represented by one degree of latitude.
+As you move towards the poles, the distance between lines of longitude
+becomes progressively less, until, at the exact location of the pole, all
+360$^\circ$ of longitude are represented by a single point that you could put your
+finger on (you probably would want to wear gloves though). Using the
+geographic coordinate system, we have a grid of lines dividing the earth into
+squares that cover approximately 12363.365 square kilometres at the equator -
+a good start, but not very useful for determining the location of anything
+within that square.
+
+To be truly useful, a map grid must be divided into small enough sections so
+that they can be used to describe (with an acceptable level of accuracy) the
+location of a point on the map. To accomplish this, degrees are divided into
+\textbf{minutes (')} and \textbf{seconds (")}. There are sixty minutes in a
+degree, and sixty
+seconds in a minute (3600 seconds in a degree). So, at the equator, one
+second of latitude or longitude = 30.87624 meters.
+
+\subsection{Projected coordinate reference systems}
+
+A two-dimensional coordinate reference system is commonly defined by two
+axes. At right angles to each other, they form a so called \textbf{XY}-plane
+(see Figure \ref{fig:crsaxes} on the left side). The horizontal axis is normally
+labelled \textbf{X}, and the vertical axis is normally labelled \textbf{Y}.
+In a three-dimensional coordinate reference system, another axis, normally
+labelled \textbf{Z}, is added. It
+is also at right angles to the \textbf{X} and \textbf{Y} axes. The Z axis
+provides the third
+dimension of space (see Figure \ref{fig:crsaxes} on the right side). Every
+point that
+is expressed in spherical coordinates can be expressed as an \textbf{X Y Z}
+coordinate.
+
+\begin{figure}[ht]
+ \begin{center}
+ \caption{Two and three dimensional coordinate reference systems}
+\label{fig:crsaxes}\smallskip
+ \includegraphics[clip=true, width=\textwidth]{cartesian-system}
+\end{center}
+\end{figure}
+
+A projected coordinate reference system in the southern hemisphere (south of
+the equator) normally has its origin on the equator at a specific
+\textbf{Longitude}.
+This means that the Y-values increase southwards and the X-values increase to
+the West. In the northern hemisphere (north of the equator) the origin is
+also the equator at a specific \textbf{Longitude}. However, now the Y-values
+increase
+northwards and the X-values increase to the East. In the following section,
+we describe a projected coordinate reference system, called \textbf{Universal
+Transverse Mercator} (UTM) often used for South Africa.
+
+\subsubsection{Universal Transverse Mercator (UTM) CRS in detail}
+
+The Universal Transverse Mercator (UTM) coordinate reference system has its
+origin on the \textbf{equator} at a specific \textbf{Longitude}. Now the
+Y-values increase
+Southwards and the X-values increase to the West. The UTM CRS is a global map
+projection. This means, it is generally used all over the world. But as
+already described in the section 'accuracy of map projections' above, the
+larger the area (for example South Africa) the more distortion of angular
+conformity, distance and area occur. To avoid too much distortion, the world
+is divided into \textbf{60 equal zones} that are all \textbf{6 degrees} wide
+in longitude from
+East to West. The \textbf{UTM zones} are numbered \textbf{1 to 60}, starting
+at the \textbf{international date line} (\textbf{zone 1} at 180 degrees West
+longitude) and progressing East back to the \textbf{international date line}
+(\textbf{zone 60} at 180 degrees East longitude) as shown in Figure
+\ref{fig:utmzones}.
+
+\begin{figure}[ht]
+ \begin{center}
+ \caption{The Universal Transverse Mercator zones. For South Africa UTM
+zones 33S, 34S, 35S, and 36S are used.}
+\label{fig:utmzones}\smallskip
+ \includegraphics[clip=true, width=\textwidth]{utmzones}
+\end{center}
+\end{figure}
+
+As you can see in Figure \ref{fig:utmzones} and Figure \ref{fig:zautmzones},
+South Africa is covered by four \textbf{UTM zones} to minimize distortion.
+The \textbf{zones} are called \textbf{UTM 33S, UTM 34S, UTM 35S} and
+\textbf{UTM 36S}. The \textbf{S} after the zone means that
+the UTM zones are located \textbf{south of the equator}.
+
+\begin{figure}[ht]
+ \begin{center}
+ \caption{UTM zones 33S, 34S, 35S, and 36S with their central longitudes
+(meridians) used to project South Africa with high accuracy. The red cross
+shows an Area of Interest (AOI).}
+\label{fig:zautmzones}\smallskip
+ \includegraphics[clip=true, width=0.8\textwidth]{za_utmzones}
+\end{center}
+\end{figure}
+
+Say, for example, that we want to define a two-dimensional coordinate within
+the \textbf{Area of Interest (AOI)} marked with a red cross in Figure
+\ref{fig:zautmzones}.
+You can see, that the area is located within the \textbf{UTM zone 35S}. This
+means, to
+minimize distortion and to get accurate analysis results, we should use
+\textbf{UTM zone 35S} as the coordinate reference system.
+
+The position of a coordinate in UTM south of the equator must be indicated
+with the \textbf{zone number} (35) and with its \textbf{northing (y) value}
+and \textbf{easting (x) value} in meters. The \textbf{northing value} is the
+distance of the position from the \textbf{equator} in meters. The
+\textbf{easting value} is the distance from the \textbf{central
+meridian} (longitude) of the used UTM zone. For UTM zone 35S it is \textbf{27
+degrees East} as shown in Figure \ref{fig:zautmzones}. Furthermore, because
+we are south of
+the equator and negative values are not allowed in the UTM coordinate
+reference system, we have to add a so called \textbf{false northing value} of
+10,000,000m to the northing (y) value and a false easting value of 500,000m
+to the easting (x) value.
+
+This sounds difficult, so, we will do an example that shows you how to find
+the correct \textbf{UTM 35S} coordinate for the \textbf{Area of Interest}.
+
+\minisec{The northing (y) value}
+
+The place we are looking for is 3,550,000 meters south of the equator, so the
+northing (y) value gets a \textbf{negative sign} and is -3,550,000m.
+According to the
+UTM definitions we have to add a \textbf{false northing value} of
+10,000,000m. This
+means the northing (y) value of our coordinate is 6,450,000m (-3,550,000m +
+10,000,000m).
+
+\minisec{The easting (x) value}
+
+First we have to find the \textbf{central meridian} (longitude) for the
+\textbf{UTM zone 35S}.
+As we can see in ***71*** it is \textbf{27 degrees East}. The place we are
+looking for
+is \textbf{85,000 meters West} from the central meridian. Just like the northing
+value, the easting (x) value gets a negative sign, giving a result of
+\textbf{-85,000m}. According to the UTM definitions we have to add a
+\textbf{false easting value} of 500,000m. This means the easting (x) value of
+our coordinate is
+415,000m (-85,000m + 500,000m). Finally, we have to add the \textbf{zone
+number} to the easting value to get the correct value.
+
+As a result, the coordinate for our \textbf{Point of Interest}, projected in
+\textbf{UTM zone 35S} would be written as: \textbf{35 415,000mE /
+6,450,000mN}. In some GIS, when the
+correct UTM zone 35S is defined and the units are set to meters within the
+system, the coordinate could also simply appear as \textbf{415,000 6,450,000}.
+
+\subsection{On-The-Fly Projection}
+
+As you can probably imagine, there might be a situation where the data you
+want to use in a GIS are projected in different coordinate reference systems.
+For example, you might get a vector layer showing the boundaries of South
+Africa projected in UTM 35S and another vector layer with point information
+about rainfall provided in the geographic coordinate system WGS 84. In GIS
+these two vector layers are placed in totally different areas of the map
+window, because they have different projections.
+
+To solve this problem, many GIS include a functionality called
+\textbf{On-the-fly} projection. It means, that you can \textbf{define} a
+certain projection when you start
+the GIS and all layers that you then load, no matter what coordinate
+reference system they have, will be automatically displayed in the projection
+you defined. This functionality allows you to overlay layers within the map
+window of your GIS, even though they may be in \textbf{different} reference
+systems.
+
+\subsection{Common problems / things to be aware of}
+
+The topic \textbf{map projection} is very complex and even professionals who have
+studied geography, geodetics or any other GIS related science, often have
+problems with the correct definition of map projections and coordinate
+reference systems. Usually when you work with GIS, you already have projected
+data to start with. In most cases these data will be projected in a certain
+CRS, so you don't have to create a new CRS or even re project the data from
+one CRS to another. That said, it is always useful to have an idea about what
+map projection and CRS means.
+
+\subsection{What have we learned?}
+
+Let's wrap up what we covered in this worksheet:
+
+\begin{itemize}
+\item \textbf{Map projections} portray the surface of the earth on a two-dimensional, flat
+piece of paper or computer screen.
+\item There are global map projections, but most map projections are created and
+\textbf{optimized to project smaller areas} of the earth's surface.
+\item Map projections are never absolutely accurate representations of the
+spherical earth. They show \textbf{distortions of angular conformity, distance and
+area}. It is impossible to preserve all these characteristics at the same time
+in a map projection.
+\item \textbf{A Coordinate reference system} (CRS) defines, with the help of
+coordinates,
+how the two-dimensional, projected map is related to real locations on the
+earth.
+\item There are two different types of coordinate reference systems:
+\textbf{Geographic Coordinate Systems} and \textbf{Projected Coordinate
+Systems}.
+\item \textbf{On the Fly projection} is a functionality in GIS that allows us
+to overlay
+layers, even if they are projected in different coordinate reference systems.
+\end{itemize}
+
+\subsection{Now you try!}
+
+Here are some ideas for you to try with your learners:
+
+\begin{itemize}
+\item Start QGIS and load two layers of the same area but with different
+projections and let your pupils find the coordinates of several places on the
+two layers. You can show them that it is not possible to overlay the two
+layers. Then define the coordinate reference system as Geographic/ WGS 84
+inside the Project Properties Dialog and activate the check box 'enable
+On-the-fly CRS transformation'. Load the two layers of the same area again
+and let your pupils see how On-the-fly projection works.
+\item You can open the Project Properties Dialog in QGIS and show your pupils the
+many different Coordinate Reference Systems so they get an idea of the
+complexity of this topic. With 'On-the-fly CRS transformation' enabled you
+can select different CRS to display the same layer in different projections.
+\end{itemize}
+
+\subsection{Something to think about}
+
+If you don't have a computer available, you can show your pupils the
+principles of the three map projection families. Get a globe and paper and
+demonstrate how cylindrical, conical and planar projections work in general.
+With the help of a transparency sheet you can draw a two-dimensional
+coordinate reference system showing X axes and Y axes. Then, let your pupils
+define coordinates (x and y values) for different places.
+
+\subsection{Further reading}
+
+\textbf{Books}:
+
+\begin{itemize}
+\item Chang, Kang-Tsung (2006): Introduction to Geographic Information Systems. 3rd
+Edition. McGraw Hill. (ISBN 0070658986)
+\item DeMers, Michael N. (2005): Fundamentals of Geographic Information Systems.
+3rd Edition. Wiley. (ISBN 9814126195)
+\item Galati, Stephen R. (2006): Geographic Information Systems Demystified. Artech
+House Inc. (ISBN 158053533X)
+\end{itemize}
+
+\textbf{Websites}:
+
+\url{http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html}
+\\
+\url{http://geology.isu.edu/geostac/Field_Exercise/topomaps/index.htm}
+
+The QGIS User Guide also has more detailed information on working with map
+projections in QGIS.
+
+\subsection{What's next?}
+
+In the section that follows we will take a closer look at \textbf{Map Production}.
+
+
Modified: docs/trunk/english_us/gis_introduction/rasterdata.tex
===================================================================
--- docs/trunk/english_us/gis_introduction/rasterdata.tex 2009-07-13 12:31:21 UTC (rev 11055)
+++ docs/trunk/english_us/gis_introduction/rasterdata.tex 2009-07-13 14:17:50 UTC (rev 11056)
@@ -16,7 +16,356 @@
\subsection{Overview}\label{subsec:overview}
+In the previous topics we have taken a closer look at vector data. While
+vector features use geometry (points, polylines and polygons) to represent
+the real world, raster data takes a different approach. Rasters are made up
+of a matrix of pixels (also called cells), each containing a value that
+represents the conditions for the area covered by that cell (see
+Figure \ref{fig:rastergrid}). In this topic we are going to take a closer
+look at raster data, when it is useful and when it makes more sense to use
+vector data.
+\begin{figure}[ht]
+ \begin{center}
+ \caption{A raster dataset is composed of rows (running across) and columns
+(running down) of pixels (also know as cells). Each pixel represents a
+geographical region, and the value in that pixel represents some
+characteristic of that region.}
+\label{fig:rastergrid}\smallskip
+ \includegraphics[clip=true, width=0.5\textwidth]{raster_basics}
+\end{center}
+\end{figure}
+\subsection{Raster data in detail}
+Raster data is used in a GIS application when we want to display information
+that is continuous across an area and cannot easily be divided into vector
+features. When we introduced you to vector data we showed you the image in
+Figure \ref{fig:landfeatures}. Point, polyline and polygon features work well for
+representing some features on this landscape, such as trees, roads and
+building footprints. Other features on a landscape can be more difficult to
+represent using vector features. For example the grasslands shown have many
+variations in colour and density of cover. It would be easy enough to make a
+single polygon around each grassland area, but a lot of the information about
+the grassland would be lost in the process of simplifying the features to a
+single polygon. This is because when you give a vector feature attribute
+values, they apply to the whole feature, so vectors aren't very good at
+representing features that are not homogeneous (entirely the same) all over.
+Another approach you could take is to digitise every small variation of grass
+colour and cover as a separate polygon. The problem with that approach is
+that it will take a huge amount of work in order to create a good vector
+dataset.
+\begin{figure}[ht]
+ \begin{center}
+ \caption{Some features on a landscape are easy to represent as points,
+polylines and polygons (e.g. trees, roads, houses). In other cases it can be
+difficult. For example how would you represent the grasslands? As polygons?
+What about the variations in colour you can see in the grass? When you are
+trying to represent large areas with continuously changing values, raster
+data can be a better choice.}
+\label{fig:landfeatures}\smallskip
+ \includegraphics[clip=true, width=\textwidth]{Landscape}
+\end{center}
+\end{figure}
+
+Using raster data is a solution to these problems. Many people use raster
+data as a backdrop to be used behind vector layers in order to provide more
+meaning to the vector information. The human eye is very good at interpreting
+images and so using an image behind vector layers, results in maps with a lot
+more meaning. Raster data is not only good for images that depict the real
+world surface (e.g. satellite images and aerial photographs), they are also
+good for representing more abstract ideas. For example, rasters can be used
+to show rainfall trends over an area, or to depict the fire risk on a
+landscape. In these kinds of applications, each cell in the raster represents
+a different value. e.g. risk of fire on a scale of one to ten.
+
+An example that shows the difference between an image obtained from a
+satellite and one that shows calculated values can be seen in Figure
+\ref{fig:imgcomp}.
+
+\begin{figure}[ht]
+ \begin{center}
+ \caption{True colour raster images (left) are useful as they provide a lot
+of detail that is hard to capture as vector features but easy to see when
+looking at the raster image. Raster data can also be non-photographic data
+such as the raster layer shown on the right which shows the calculated
+average minimum temperature in the Western Cape for the month of March.}
+\label{fig:imgcomp}\smallskip
+ \includegraphics[clip=true, width=\textwidth]{image_vs_computed}
+\end{center}
+\end{figure}
+
+\subsection{Georeferencing}
+
+Georeferencing is the process of defining exactly where on the earth's
+surface an image or raster dataset was created. This positional information
+is stored with the digital version of the aerial photo. When the GIS
+application opens the photo, it uses the positional information to ensure
+that the photo appears in the correct place on the map. Normally this
+positional information consists of a coordinate for the top left pixel in the
+image, the size of each pixel in the X direction, the size of each pixel in
+the Y direction, and the amount (if any) by which the image is rotated. With
+these few pieces of information, the GIS application can ensure that raster
+data are displayed in the correct place. The georeferencing information for a
+raster is often provided in a small text file accompanying the raster.
+
+\subsection{Sources of raster data}
+
+Raster data can be obtained in a number of ways. Two of the most common ways
+are aerial photography and satellite imagery. In aerial photography, an
+aeroplane flies over an area with a camera mounted underneath it. The
+photographs are then imported into a computer and georeferenced. Satellite
+imagery is created when satellites orbiting the earth point special digital
+cameras towards the earth and then take an image of the area on earth they
+are passing over. Once the image has been taken it is sent back to earth
+using radio signals to special receiving stations such as the one shown in
+Figure \ref{fig:csir}. The process of capturing raster data from an aeroplane
+or satellite is called remote sensing.
+
+\begin{figure}[ht]
+ \begin{center}
+ \caption{The CSIR Satellite Applications Center at Hartebeeshoek near
+Johannesburg. Special antennae track satellites as they pass overhead and
+download images using radio waves.}
+\label{fig:csir}\smallskip
+ \includegraphics[clip=true, width=\textwidth]{hartebeeshoek}
+\end{center}
+\end{figure}
+
+In other cases, raster data can be computed. For example an insurance company
+may take police crime incident reports and create a country wide raster map
+showing how high the incidence of crime is likely to be in each area.
+Meteorologists (people who study weather patterns) might generate a province
+level raster showing average temperature, rainfall and wind direction using
+data collected from weather stations (see Figure \ref{fig:csir}). In these
+cases, they will often use raster analysis techniques such as interpolation
+(which we describe in Topic \ref{sec:interpolation}).
+
+Sometimes raster data are created from vector data because the data owners
+want to share the data in an easy to use format. For example, a company with
+road, rail, cadastral and other vector datasets may choose to generate a
+raster version of these datasets so that employees can view these datasets in
+a web browser. This is normally only useful if the attributes, that users
+need to be aware of, can be represented on the map with labels or symbology.
+If the user needs to look at the attribute table for the data, providing it
+in raster format could be a bad choice because raster layers do not usually
+have any attribute data associated with them.
+
+\subsection{Spatial Resolution}
+
+Every raster layer in a GIS has pixels (cells) of a fixed size that determine
+its spatial resolution. This becomes apparent when you look at an image at a
+small scale (see Illustration 5 below) and then zoom in to a large scale (see
+Illustration 6 below).
+
+%% Minipage to put both figures on one page
+\begin{figure}[htpb]
+ \begin{minipage}[h]{\textwidth}
+ \begin{center}
+ \caption{This satellite image looks good when using a small scale...}
+ \label{fig:smallscale}\smallskip
+ \includegraphics[clip=true, width=0.6\textwidth]{raster_zoomed_out}
+ \end{center}
+ \end{minipage} \\
+ \vspace{1cm}
+ \begin{minipage}[h]{\textwidth}
+ \begin{center}
+ \caption{...but when viewed at a large scale you can see the individual
+pixels that the image is composed of.}
+ \label{fig:largescale}\smallskip
+ \includegraphics[clip=true, width=0.6\textwidth]{raster_zoomed_in}
+ \end{center}
+ \end{minipage}
+\end{figure}
+
+Several factors determine the spatial resolution of an image. For remote
+sensing data, spatial resolution is usually determined by the capabilities of
+the sensor used to take an image. For example SPOT5 satellites can take
+images where each pixel is 10m x 10m. Other satellites, for example MODIS
+take images only at 500m x 500m per pixel. In aerial photography, pixel sizes
+of 50cm x 50cm are not uncommon. Images with a pixel size covering a small
+area are called \textbf{'high resolution'} images because it is possible to
+make out a high degree of detail in the image. Images with a pixel size
+covering a large area are called \textbf{'low resolution'} images because the
+amount of detail the images show is low.
+
+In raster data that is computed by spatial analysis (such as the rainfall map
+we mentioned earlier), the spatial density of information used to create the
+raster will usually determine the spatial resolution. For example if you want
+to create a high resolution average rainfall map, you would ideally need many
+weather stations in close proximity to each other.
+
+One of the main things to be aware of with rasters captured at a high spatial
+resolution is storage requirements. Think of a raster that is 3x3 pixels,
+each of which contains a number representing average rainfall. To store all
+the information contained in the raster, you will need to store 9 numbers in
+the computer's memory. Now imagine you want to have a raster layer for the
+whole of South Africa with pixels of 1km x 1km. South Africa is around
+1,219,090 km2. Which means your computer would need to store over a million
+numbers on its hard disk in order to hold all of the information. Making the
+pixel size smaller would greatly increase the amount of storage needed.
+
+Sometimes using a low spatial resolution is useful when you want to work with
+a large area and are not interested in looking at any one area in a lot of
+detail. The cloud maps you see on the weather report, are an example of this
+- it's useful to see the clouds across the whole country. Zooming in to one
+particular cloud in high resolution will not tell you very much about the
+upcoming weather!
+
+On the other hand, using low resolution raster data can be problematic if you
+are interested in a small region because you probably won't be able to make
+out any individual features from the image.
+
+\subsection{Spectral resolution}
+
+If you take a colour photograph with a digital camera or camera on a
+cellphone, the camera uses electronic sensors to detect red, green and blue
+light. When the picture is displayed on a screen or printed out, the red,
+green and blue (RGB) information is combined to show you an image that your
+eyes can interpret. While the information is still in digital format though,
+this RGB information is stored in separate colour \textbf{bands}.
+
+Whilst our eyes can only see RGB wavelengths, the electronic sensors in
+cameras are able to detect wavelengths that our eyes cannot. Of course in a
+hand held camera it probably doesn't make sense to record information from
+the \textbf{non-visible} parts of the spectrum since most people just want to
+look at
+pictures of their dog or what have you. Raster images that include data for
+non-visible parts of the light spectrum are often referred to as
+multi-spectral images. In GIS recording the non-visible parts of the spectrum
+can be very useful. For example, measuring infra-red light can be useful in
+identifying water bodies.
+
+Because having images containing multiple bands of light is so useful in GIS,
+raster data are often provided as multi-band images. Each band in the image
+is like a separate layer. The GIS will combine three of the bands and show
+them as red, green and blue so that the human eye can see them. The number of
+bands in a raster image is referred to as its \textbf{spectral resolution}.
+
+If an image consists of only one band, it is often called a grayscale image.
+With grayscale images, you can apply false colouring to make the differences
+in values in the pixels more obvious. Images with false colouring applied are
+often referred to as \textbf{pseudocolour images}.
+
+\subsection{Raster to vector conversion}
+
+In our discussion of vector data, we explained that often raster data are
+used as a backdrop layer, which is then used as a base from which vector
+features can be digitised.
+
+Another approach is to use advanced computer programs to automatically
+extract vector features from images. Some features such as roads show in an
+image as a sudden change of colour from neighbouring pixels. The computer
+program looks for such colour changes and creates vector features as a
+result. This kind of functionality is normally only available in very
+specialised (and often expensive) GIS software.
+
+\subsection{Vector to raster conversion}
+
+Sometimes it is useful to convert vector data into raster data. One side
+effect of this is that attribute data (that is attributes associated with the
+original vector data) will be lost when the conversion takes place. Having
+vectors converted to raster format can be useful though when you want to give
+GIS data to non GIS users. With the simpler raster formats, the person you
+give the raster image to can simply view it as an image on their computer
+without needing any special GIS software.
+
+\subsection{Raster analysis}
+
+There are a great many analytical tools that can be run on raster data which
+cannot be used with vector data. For example, rasters can be used to model
+water flow over the land surface. This information can be used to calculate
+where watersheds and stream networks exist, based on the terrain.
+
+Raster data are also often used in agriculture and forestry to manage crop
+production. For example with a satellite image of a farmer's lands, you can
+identify areas where the plants are growing poorly and then use that
+information to apply more fertilizer on the affected areas only. Foresters
+use raster data to estimate how much timber can be harvested from an area.
+
+Raster data is also very important for disaster management. Analysis of
+Digital Elevation Models (a kind of raster where each pixel contains the
+height above sea level) can then be used to identify areas that are likely to
+be flooded. This can then be used to target rescue and relief efforts to
+areas where it is needed the most.
+
+\subsection{Common problems / things to be aware of}
+
+As we have already mentioned, high resolution raster data can require large
+amounts of computer storage.
+
+\subsection{What have we learned?}
+
+Let's wrap up what we covered in this worksheet:
+
+\begin{itemize}
+\item Raster data are a grid of regularly sized \textbf{pixels}.
+\item Raster data are good for showing \textbf{continually varying
+information}.
+\item The size of pixels in a raster determines its \textbf{spatial
+resolution}.
+\item Raster images can contain one or more \textbf{bands}, each covering the
+same spatial area, but containing different information.
+\item When raster data contains bands from different parts of the electromagnetic
+spectrum, they are called \textbf{multi-spectral images}.
+\item Three of the bands of a multi-spectral image can be shown in the colours Red,
+Green and Blue so that we can see them.
+\item Images with a single band are called grayscale images.
+\item Single band, grayscale images can be shown in pseudocolour by the GIS.
+\item Raster images can consume a large amount of storage space.
+\end{itemize}
+
+\subsection{Now you try!}
+
+Here are some ideas for you to try with your learners:
+
+\begin{itemize}
+\item Discuss with your learners in which situations you would use raster
+data and in which you would use vector data.
+\item Get your learners to create a raster map of your school by using A4
+transparency sheets with grid lines drawn on them. Overlay the transparencies
+onto a toposheet or aerial photograph of your school. Now let each learner or
+group of learners colour in cells that represent a certain type of feature.
+e.g. building, playground, sports field, trees, footpaths etc. When they are
+all finished, overlay all the sheets together and see if it makes a good
+raster map representation of your school. Which types of features worked well
+when represented as rasters? How did your choice in cell size affect your
+ability to represent different feature types?
+\end{itemize}
+
+\subsection{Something to think about}
+
+If you don't have a computer available, you can understand raster data using
+pen and paper. Draw a grid of squares onto a sheet of paper to represent your
+soccer field. Fill the grid in with numbers representing values for grass
+cover on your soccer field. If a patch is bare give the cell a value of 0. If
+the patch is mixed bare and covered, give it a value of 1. If an area is
+completely covered with grass, give it a value of 2. Now use pencil crayons
+to colour the cells based on their values. Colour cells with value 2 dark
+green. Value 1 should get coloured light green, and value 0 coloured in
+brown. When you finish, you should have a raster map of your soccer field!
+
+
+\subsection{Further reading}
+
+\textbf{Book}:
+
+Chang, Kang-Tsung (2006): Introduction to Geographic Information Systems. 3rd
+Edition. McGraw Hill. (ISBN 0070658986)
+DeMers, Michael N. (2005): Fundamentals of Geographic Information Systems.
+3rd Edition. Wiley. (ISBN 9814126195)
+
+\textbf{Website}: \url{http://en.wikipedia.org/wiki/GIS#Raster}
+
+
+The QGIS User Guide also has more detailed information on working with raster
+data in QGIS.
+
+\subsection{What's next?}
+
+In the section that follows we will take a closer look at topology to see how
+the relationship between vector features can be used to ensure the best data
+quality.
+
+
Modified: docs/trunk/english_us/gis_introduction/topology.tex
===================================================================
--- docs/trunk/english_us/gis_introduction/topology.tex 2009-07-13 12:31:21 UTC (rev 11055)
+++ docs/trunk/english_us/gis_introduction/topology.tex 2009-07-13 14:17:50 UTC (rev 11056)
@@ -17,7 +17,226 @@
\subsection{Overview}\label{subsec:overview}
+\textbf{Topology} expresses the spatial relationships between connecting or
+adjacent
+vector features (points, polylines and polygons) in a GIS. Topological or
+topology-based data are useful for detecting and correcting digitising errors
+(e.g. two lines in a roads vector layer that do not meet perfectly at an
+intersection). Topology is necessary for carrying out some types of spatial
+analysis, such as network analysis.
+Imagine you travel to London. On a sightseeing tour you plan to visit St.
+Paul's Cathedral first and in the afternoon Covent Garden Market for some
+souvenirs. Looking at the Underground map of London (see Figure
+\ref{fig:londontube}) you have to find connecting trains to get from Covent
+Garden to St. Paul's. This requires topological information (data) about
+where it is
+possible to change trains. Looking at a map of the underground, the
+topological relationships are illustrated by circles that show connectivity.
+Changing trains at stations allows you to move from one connected part of the
+network to another.
+\begin{figure}[ht]
+ \begin{center}
+ \caption{Topology of London Underground Network.}
+\label{fig:londontube}\smallskip
+ \includegraphics[clip=true, width=0.8\textwidth]{London_Underground_Zone_1_Small}
+\end{center}
+\end{figure}
+\subsection{Topology errors}
+There are different types of topological errors and they can be grouped
+according to whether the vector feature types are polygons or polylines.
+Topological errors with \textbf{polygon} features can include unclosed
+polygons, gaps
+between polygon borders or overlapping polygon borders. A common topological
+error with \textbf{polyline} features is that they do not meet perfectly at a
+point (node). This type of error is called an \textbf{undershoot} if a gap
+exists between the lines, and an \textbf{overshoot} if a line ends beyond the
+line it should connect to (see Figure \ref{fig:underovershoot}).
+\begin{figure}[ht]
+ \begin{center}
+ \caption{Undershoots (1) occur when digitised vector lines that should
+connect to each other don't quite touch. Overshoots (2) happen if a line ends
+beyond the line it should connect to. Slivers (3) occur when the vertices of
+two polygons do not match up on their borders.}
+\label{fig:underovershoot}\smallskip
+ \includegraphics[clip=true, width=\textwidth]{sliver-over-undershoot}
+\end{center}
+\end{figure}
+
+The result of overshoot and undershoot errors are so-called 'dangling nodes'
+at the end of the lines. Dangling nodes are acceptable in special cases, for
+example if they are attached to dead-end streets.
+Topological errors break the relationship between features. These errors need
+to be fixed in order to be able to analyse vector data with procedures like
+network analysis (e.g. finding the best route across a road network) or
+measurement (e.g. finding out the length of a river). In addition to topology
+being useful for network analysis and measurement, there are other reasons
+why it is important and useful to create or have vector data with correct
+topology. Just imagine you digitise a municipal boundaries map for your
+province and the polygons overlap or show slivers. If such errors were
+present, you would be able to use the measurement tools, but the results you
+get will be incorrect. You will not know the correct area for any
+municipality and you will not be able to define exactly, where the borders
+between the municipalities are.
+It is not only important for your own analysis to create and have
+topologically correct data, but also for people who you pass data on to. They
+will be expecting your data and analysis results to be correct!
+
+\subsection{Topology rules}
+
+Fortunately, many common errors that can occur when digitising vector
+features can be prevented by topology rules that are implemented in many GIS
+applications.
+Except for some special GIS data formats, topology is usually not enforced by
+default. Many common GIS, like QGIS, define topology as relationship rules
+and let the user choose the rules, if any, to be implemented in a vector
+layer.
+The following list shows some examples of where topology rules can be defined
+for real world features in a vector map.
+
+\begin{itemize}
+\item Area edges of a municipality map must not overlap.
+\item Area edges of a municipality map must not have gaps (slivers).
+\item Polygons showing property boundaries must be closed. Undershoots or
+overshoots of the border lines are not allowed.
+\item Contour lines in a vector line layer must not intersect (cross each other).
+\end{itemize}
+
+\subsection{Topological tools}
+
+Many GIS applications provide tools for topological editing. For example in
+QGIS you can \textbf{enable topological editing} to improve editing and maintaining
+common boundaries in polygon layers. A GIS such as QGIS 'detects' a shared
+boundary in a polygon map so you only have to move the edge vertex of one
+polygon boundary and QGIS will ensure the updating of the other polygon
+boundaries as shown in Figure \ref{}(1).
+
+Another topological option allows you to prevent \textbf{polygon overlaps}
+during
+digitising (see Figure \ref{}(2)). If you already have one polygon, it
+is possible with this option to digitise a second adjacent polygon so that
+both polygons overlap and QGIS then clips the second polygon to the common
+boundary.
+
+\begin{figure}[ht]
+ \begin{center}
+ \caption{(1)Topological editing to detect shared boundaries, when moving
+vertices. When moving a vertex, all features that share that vertex are
+updated. (2) To avoid polygon overlaps, when a new polygon is digitised
+(shown in red) it is clipped to avoid overlapping neighbouring areas.}
+\label{fig:topotools}\smallskip
+ \includegraphics[clip=true, width=\textwidth]{topoediting}
+\end{center}
+\end{figure}
+
+\subsection{Snapping distance}
+
+Snapping distance is the distance a GIS uses to search for the closest vertex
+and / or segment you are trying to connect when you digitise. A
+\textbf{segment} is a
+straight line formed between two vertices in a polygon or polyline geometry.
+If you aren't within the snapping distance, a GIS such as QGIS will leave the
+vertex where you release the mouse button, instead of snapping it to an
+existing vertex and / or segment (see Illustration 4 below).
+
+\begin{figure}[ht]
+ \begin{center}
+ \caption{The snapping distance (black circle) is defined in map units
+(e.g. decimal degrees) for snapping to either vertices or segments.}
+\label{fig:snapping}\smallskip
+ \includegraphics[clip=true, width=\textwidth]{snapping}
+\end{center}
+\end{figure}
+
+\subsection{Search Radius}
+
+Search radius is the distance a GIS uses to search for the closest vertex you
+are trying to move when you click on the map. If you aren't within the search
+radius, the GIS won't find and select any vertex of a feature for editing. In
+principle, it is quite similar to the snapping distance functionality.
+Snapping distance and search radius are both set in map units so you may
+need to experiment to get the distance value set right. If you specify a
+value that is too big, the GIS may snap to a wrong vertex, especially if you
+are dealing with a large number of vertices close together. If you specify
+the search radius too small the GIS application won't find any feature or
+vertex to move or edit.
+
+\subsection{Common problems / things to be aware of}
+
+Topology is a complex representation of vector data. True topological vector
+datasets are stored in special file formats that record all the relationships
+between features. Most commonly used vector data formats use something called
+'Simple Features' which also consists of point, line and polygon features.
+Simple feature datasets are mainly designed for simplicity and for fast
+rendering but not for data analysis that require topology (such as finding
+routes across a network). Many GIS applications are able to show topological
+and simple feature data together and some can also create, edit and analyse
+both.
+
+\subsection{What have we learned?}
+
+Let's wrap up what we covered in this worksheet:
+
+\begin{itemize}
+\item \textbf{Topology} shows the spatial relation of neighbouring vector features.
+\item Topology in GIS is provided by \textbf{topological tools}.
+\item Topology can be used to \textbf{detect and correct digitizing errors}.
+\item For some tools, such as \textbf{network analysis}, topological data is
+essential.
+\item \textbf{Snapping distance} and \textbf{search radius} help us to
+digitise topologically correct vector data.
+\item \textbf{Simple feature} data is not a true topological data format but
+it is commonly used by GIS applications.
+\end{itemize}
+
+\subsection{Now you try!}
+
+Here are some ideas for you to try with your learners:
+
+\begin{itemize}
+\item Mark your local bus stops on a toposheet map and then task your learners to
+find the shortest route between two stops.
+\item Think of how you would create vector features in a GIS to represent a
+topological road network of your town. What topological rules are important
+and what tools can your learners use in QGIS to make sure that the new road
+layer is topologically correct?
+\end{itemize}
+
+\subsection{Something to think about}
+
+If you don't have a computer available, you can use a map of a bus or railway
+network and discuss the spatial relationships and topology with your
+learners.
+
+\subsection{Further reading}
+
+\textbf{Books}:
+
+\begin{itemize}
+\item Chang, Kang-Tsung (2006): Introduction to Geographic Information Systems. 3rd
+Edition. McGraw Hill. (ISBN 0070658986)
+\item DeMers, Michael N. (2005): Fundamentals of Geographic Information Systems.
+3rd Edition. Wiley. (ISBN 9814126195)
+\end{itemize}
+
+\textbf{Websites}:
+
+\url{http://www.innovativegis.com/basis/primer/concepts.html} \\
+\url{http://en.wikipedia.org/wiki/Geospatial\_topology}
+
+The QGIS User Guide also has more detailed information on topological editing
+provided in QGIS.
+
+\subsection{What's next?}
+
+In the section that follows we will take a closer look at \textbf{Coordinate
+Reference Systems} to understand how we relate data from our spherical earth
+onto flat maps!
+
+
+
+
+
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