Czech Technical University in Prague Faculty of Transportation Sciences Department of Transport Telematics Doc. Ing. Pavel Hrubeš, Ph.D. Geographical Information Systems

Rehearsal  Vector data models  Spaghetti model  Topological model Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

České vysoké učení technick é v Praze - Fakulta dopravní Katedra řídící techniky a telematik y Model of the Earth  Sphere  Big scales  Elipsoid/Spheroid  Closer to reality  Geoid  The closest to reality  Model of elevation Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Parameters for Mapping  A mathematical model of the earth must be selected. Spheroid  The mathematical model must be related to real-world features. Datum  Real-world features must be projected with minimum distortion from a round earth to a flat map; and given a grid system of coordinates. Projection Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Spheroid  A mathematical model of the earth must be selected.  Simplistic - A round ball having a radius big enough to approximate the size of the earth.  Reality - Spinning planets bulge at the equator with reciprocal flattening at the poles. e.g. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Different Spheroids GRS80 (North America) Clark 1866 (North America) WGS84 (GPS World-wide) International 1924 (Europe) Bessel 1841 (Europe) Name Equatorial axis (m)m Polar axis (m) Inverse flattening, AiryAiry Clarke Bessel International Krasovsky GRS WGS Sphere (6371 km) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Why use different spheroids?  The earth's surface is not perfectly symmetrical, so the semi-major and semi-minor axes that fit one geographical region do not necessarily fit another.  Satellite technology has revealed several elliptical deviations. For one thing, the most southerly point on the minor axis (the South Pole) is closer to the major axis (the equator) than is the most northerly point on the minor axis (the North Pole).  The earth's spheroid deviates slightly for different regions of the earth.  Ignoring deviations and using the same spheroid for all locations on the earth could lead to errors of several meters, or in extreme cases hundreds of meters, in measurements on a regional scale. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Datum  A mathematical model must be related to real-world features.  A smooth mathematical surface that fits closely to the mean sea level surface throughout the area of interest. The surface to which the ground control measurements are referred.  Provides a frame of reference for measuring locations on the surface of the earth.  Changes to the values of any datum parameters can result in changes to coordinate values of points.  If you have two different datums, in practice you have two different geographic coordinate systems. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

How do I get a Datum?  To determine latitude and longitude, surveyors level their measurements down to a surface called a geoid. The geoid is the shape that the earth would have if all its topography were removed.  Or more accurately, the shape the earth would have if every point on the earth's surface had the value of mean sea level. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Model of the Earth Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Model of the Earth Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Geoid vs Spheroid  Coordinate systems are applied to the simpler model of a spheroid. The problem is that actual measurements of location conform to the geoid surface and have to be mathematically recalculated to positions on the spheroid. This process changes the measured positions of many point. Sometimes by a few meters, sometimes by hundreds of meters.  Different datums use a different orientation of the spheroid to the geoid to determine which parts of the world keep accurate coordinates on the spheroid.  For an area of interest, the surface of the spheroid can arbitrarily be made to coincide with the surface of the geoid; for this area, measurements can be accurately transferred from the geoid to the spheroid. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Earth Centered Datums  Satellite technology has made earth-centered datums possible.  In an earth-centered datum, the spheroid is no longer aligned with the geoid at a point on the earth's surface. Instead, the center of the spheroid is aligned with the center of mass of the earth—a location that satellite technology has made it possible to determine.  In an earth-centered datum, the spheroid and geoid still don't match up perfectly, but the separations are more evenly distributed.

North American Datum – 1927 NAD 27 North American Datum – 1983 NAD 83 Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Horizontal vs Vertical Datums  Horizontal datums are the reference values for a system of location measurements.  Vertical datums are the reference values for a system of elevation measurements.  The job of a vertical datum is to define where zero elevation is, this is usually done by determining mean sea level, a project that involves measuring tides over a cycle of many years.

Graticules  Also called parallels and meridians.  Latitude lines are parallel, run east and west around the earth's surface, and measure distances north and south of the equator. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics Latitude/Longitude Lines of latitude Longitude lines N or S of Equator E or W of Prime Meridian

Location on the Earth Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics  Longitude lines run north and south around the earth's surface, intersect at the poles, and measure distances east and west of the prime meridian.  Based on 360 degrees. Each degree is divided into 60 minutes and each minute into 60 seconds.

Projection  Real-world features must be projected with minimum distortion from a round earth to a flat map; and given a grid system of coordinates.  A map projection transforms latitude and longitude locations to x,y coordinates. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Projection  Plane  Cylinder  Cone   Sphere  Elipsoid Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

What is a Projection?  If you could project light from a source through the earth's surface onto a two-dimensional surface, you could then trace the shapes of the surface features onto the two-dimensional surface.  This two-dimensional surface would be the basis for your map. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Why use a Projection?  Can only see half the earth’s surface at a time.  Unless a globe is very large it will lack detail and accuracy.  Harder to represent features on a flat computer screen.  Doesn’t fold, roll or transport easily.  Converting a sphere to a flat surface results in distortion. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Map Projection & Distortion  Shape (conformal) - If a map preserves shape, then feature outlines (like county boundaries) look the same on the map as they do on the earth.  Area (equal-area) - If a map preserves area, then the size of a feature on a map is the same relative to its size on the earth. On an equal-area map each county would take up the same percentage of map space that actual county takes up on the earth.  Distance (equidistant) - An equidistant map is one that preserves true scale for all straight lines passing through a single, specified point. If a line from a to b on a map is the same distance that it is on the earth, then the map line has true scale. No map has true scale everywhere. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Map projection - Azimuthal (projections onto a plane) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Map projection - Azimuthal Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Map projection - Cylindrical Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Map projection – Conical Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Map projections Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Křovak’s projection Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Planar Coordinate Systems  Coordinate systems identify locations by making measurements on a framework of intersecting lines that resemble a net.  On a map, the lines are straight and the measurements are made in terms of distance.  On a round surface (like the earth) the lines become circles and the measurements are made in terms of angle.

Cartesian Coordinate System Planar coordinate systems are based on Cartesian coordinates.

 The origin of the coordinate system is made to coincide with the intersection of the central meridian and central parallel of the map.  But this conflicts with the desire to keep all their map coordinates positive (within the first quadrant) and unique numbers.  This conflict can be resolved with false easting and false northing. Adding a number to the Y axis origin (false easting) and another number to the X axis origin (false northing) is equivalent to moving the origin of the system.

 The projected coordinate system is a Cartesian coordinate system with an origin, a unit of measure (map unit), and usually a false easting or false northing.  The main value of Cartesian coordinates is for making measurements on maps. Before the age of computers formulas for converting latitude and longitude were too cumbersome to be done quickly, but Cartesian coordinates offered a satisfactory solution.