Introduction to GIS and Coordinate Systems

Introduction to GIS and Coordinate Systems


The Basics

A coordinate system is defined in geometry as a system that uses one or more numbers, coordinates, to determine the position of the points. Unique values will have unique positions. The simplest example of this is the identification of points on a line. 

The Origin

The origin is the reference point for all measurements within a coordinate system. In the example above, an arbitrary point 0 has been defined as the origin. The coordinate of any point on the line is defined as the distance between the origin to the point. 

Axes

Axes are lines that extend from the origin, providing direction and scale. In the example above, there is only one axis. Typically, the coordinate systems we will be operating with will have two or three axes. They will be the X-axis, Y-axis and the Z-axis.

If there is only two axes present, it will be the X and Y. The Z-axis will only be present in three dimensional systems.

Units of Measurement

Each axis should have a unit of measurement, the scale used to measure distances along each axis. This could be in terms of length, time, or any other relevant unit. In the example above, there is no defined unit of measurement. We could provide an arbitrary unit of measurement as 'Distance in Metres'. The value 6 (or -6) is located 6 metres from the origin. 

Coordinates

A coordinate is a point represented by ordered values. In a two-dimensional system it will be a pair of values (x,y) and in a three-dimensional system it will be a trio of values (x,y,z). 

We can conclude that the origin for a two-dimensional system will be (0,0) and for a three-dimensional system will be (0,0,0).

Quadrants (2D systems)

2D systems can be divided into four quadrants, each of potentially infinite extent. In the example below, the quadrants are denoted by Roman numerals. Every unique set of coordinates will have its own defined point within this system. 

Similarly, a three-dimensional system can be divided into eight regions, or octants. 


In the example above, we can see the concepts core to coordinate systems in use. We can see labelled the origin (0,0). We can see labelled the axes; the x-axis and y-axis. We can see labelled the units of measurement along the axis (although they are missing definition, e.g. metres or time). We an see labelled coordinates and their position within this coordinate system, P(3,5).

Grid Lines

Grid lines are lines parallel to the axes. They help visualise and locate points in the coordinate system. An example of these would be lines of latitude. The most famous line of latitude, the equator, is an imaginary line located at 0 degrees latitude (halfway between the North and South poles).

Orientation

Background reading, only relevant to photogrammetry and the orientation of the drone.

Orientation can be described in various ways. In kinematics, coordinate systems are used to describe the position of points. A second 'local' coordinate system, fixed to the point, can be defined based on the first and be called the orientation. In photogrammetry, this will be described using yaw, pitch and roll. 
  1. Yaw is the rotation around the Vertical Z-axis. Imagine a drone remaining stationary in the air but rotating in a circle. It starts by facing North, and ends facing South. This would be changing the yaw.
  2. Pitch is the rotation around the Lateral Y-axis. Imagine a drone remaining stationary, but tipping its nose forward. This would be changing the pitch.
  3. Roll is the rotation around the Longitudinal X-axis. Imagine a drone remaining stationary, but 'tilting' from side to side. This would be changing the roll.

Coordinate Reference Systems

A coordinate reference system (CRS), sometimes referred to as a spatial reference system (SRS), is a framework used to specify locations on the surface of the Earth. It involves using a coordinate system (and the concepts explained in 'The Basics', a datum (a reference model of the Earth) and a map projection (a method for representing the Earth's curved surface on a flat map).

Coordinate reference systems can be incredibly useful to society, the most common usage being by GPS, the Global Positioning System. GPS uses the coordinate reference system known as WGS 84 (world geodetic system). This system can be considered accurate to within a couple of metres globally. For many applications, being within a couple of metres would be sufficient. If I'm just tracking my walk or run, I would not be disheartened by losing two metres! However, when it comes to the design and construction of solar farms, a deviation of even a metre can have significant impacts on the yield. Therefore, it is important that we can achieve far greater levels of accuracy so we can be useful to our clients.

Datums

A datum serves as the starting point for measuring distances on Earth. Consisting of several key elements, datums provide a consistent and standardised way to represent locations on the Earth. Key elements are:
  1. Origin: The starting point or reference point for measuring coordinates.
  2. Coordinate system: The set of rules and parameters used to define how coordinates are measured and where the axes are oriented.
  3. Reference surface: The shape used to model the Earth's surface e.g. which ellipsoid or geoid used.
  4. Orientation: How the coordinate system is aligned or oriented in relation to the Earth.
One of the simplest ways to imagine a datum is by imaging a game of 'Where's Wally?' on a giant globe. To locate Wally, you and the other participants would need a common starting point and a way to describe where Wally is. The starting point would be like a 'datum' in the game. Just as within 'Where's Wally?' you might have different starting points or 'datums', the same can be said about coordinate reference systems. 

Map Projections

A map projection is a way to portray the surface of the Earth onto a flat piece of paper. By its very nature, every map projection will be subject to some distortion. Some projections will focus on preserving angles whilst others will focus on preserving distances. No projection will be perfect, so there will always be a trade-off that users of a map projection must consider. 

Ellipsoid vs Geoid Simplified

The Earth is a complex and irregular shape. Trying to map the Earth accurately inclusive of all hills, valleys, bumps, ditches and dips would be impossible. Not only is it incredibly complex and irregular, it is also changing constantly. To map regions on Earth effectively, we must use a simplified model of Earth.

Measuring heights requires an imaginary surface of 'zero height'. The height of any point is the vertical distance above this imaginary surface. 

Ellipsoid

The closest approximate shape to the Earth is an ellipsoid. Because the ellipsoid shape doesn't perfectly fit the Earth, there are lots of different ellipsoids in use. Some are designed to best fit the whole Earth, whilst others might be designed to best fit one region. The elevation data provided when using an ellipsoid will be the vertical distance between the point and the closest point on the ellipsoid being used. 

In GPS, the coordinate reference system best known globally uses the ellipsoid called GRS80 (Geodetic Reference System 1980) which is designed to best fit the whole Earth. 

There is an ellipsoid specifically used for mapping in Britain, the Airy 1830 ellipsoid. For use in Britain, it is more accurate than GRS80. In other parts of the world it would not be practical to use the Airy 1830 ellipsoid, since the ellipsoid was created with a region of best fit in mind, compromising the shape and accuracy in other regions. 

For reasons of global compatibility, it is becoming common place to use the GRS80 ellipsoid everywhere. The best local fitting ellipsoid is becoming outdated, but are often built into national coordinate systems. 

Geoid

In geometry, level surfaces are not defined as simple shapes. 

World Files for JPEGs/TIFFs

World files are used to describe the location, scale and rotation of the map used to project an image to its real world location.

World files will have the same name as the image with a different file extension format. The first and last letter of the corresponding image file's format, with a w added at the end. For example, a .tif turns into a .tfw.

A world file has been standardised to always contain the same 6 lines.
  1. Pixel size in the x-direction in map units/pixel
  2. Rotation about the y-axis
  3. Rotation about the x-axis
  4. Pixel size in the y-direction in map units (almost always negative)
  5. X-coordinate of the centre of the upper left pixel
  6. Y-coordinate of the centre of the upper left pixel
Using these 6 bits of information, an image can be projected to its real world location using software like AutoCAD, QGIS and ArcGIS.

We use an AutoCAD plugin called Plex-Earth to automatically import georeferenced images into our topographical mapping projects. Using the Plex-Earth plugin we can define a coordinate system and force AutoCAD to read the lines in the world file to automatically geolocate the image. This will ensure our linework and deliverables are within our promised accuracy of 6cm in the x and y axis.

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