ProjectionsReviewSlide 3Slide 4Common types of projectionsViews of projected surfacesAzimuthal ProjectionsCylindrical projectionsCylindrical projections (Cont.)Conic ProjectionsStandard Lines and PointsAdditional Projection FeaturesSlide 13Light source optionsChange where the paper touches the globeExample of tangent and secant azimuthal projectionsSlide 17Map projections distortionPreservation of propertiesSlide 20A Few Common Map Projections Used For DisplayMap Projections Commonly Used For GIS ApplicationsSlide 23True Direction & DistanceTissot’s IndicatrixSlide 26Slide 27Examples of projectionsEquidistant exampleSlide 30Example: What projection might this map be in?Compromise projectionsWrap-UpOdds and endsProjectionsProjectionsReviewReview•The Earth is a complex shape called a geoid •Ellipsoids are models that approximate the shape of the Earth•Ellipsoids are used in place of the geoid because they are much simpler mathematically•Datums link the geoid (real shape) to the ellipsoid (modeled shape)Map Projections•The systematic transformation of points on the Earth’s surface to corresponding points on a plane surface•In other words: Translating the Earth (3D) to a flat map (2D)•All projections distort the Earth in one or more way(s)•Selection of a projection is done to minimize distortion for the particular applicationCreating maps–we must choose an appropriate projection for the map to communicate effectively–part of good cartographic designAnalyzing geographic data–along with the datum (and the associated ellipsoid) and the coordinate system we must know the map projection in which the data are stored–identical projections are required for data to overlay correctlyWhy do we need a projection?Common types of projectionsCommon types of projections (a) Azimuthal (b) Cylindrical (c) ConicViews of projected surfacesViews of projected surfacesAzimuthal ProjectionsAzimuthal ProjectionsCylindrical projectionsCylindrical projections You cut the cylinder along any meridian and unroll it to produce your base map. The meridian opposite the cut is called the central meridian (the red line). (ESRI Press.)Cylindrical projections (Cont.)Cylindrical projections (Cont.) The light source's origin for the map projection is also the origin of the spherical coordinate system, so simply extending the degree lines until they reach the cylinder creates the map projection. The poles cannot be displayed on the map projection because the projected 90 degree latitude will never contact the cylinder. (ESRI Press)Conic ProjectionsConic ProjectionsStandard Lines and PointsStandard Lines and Points•Location(s) on a projected map at the exact point or line where the surface (cylinder, cone, plane) touches the globe•Standard lines and points are free of all distortion•Distortion becomes more pronounced with increased distance from the standard line or pointAdditional Projection FeaturesAdditional Projection Features•Projections get a lot more complicated because we can:•1) Change the aspect•2) Move the light source •3) Change where the paper touches the globeProjection AspectscylindricalconicalplanarLight source optionsLight source options–Orthographic (light source infinitely far away – think of the sun)–Stereographic (the point opposite of the point of tangency of the projection)–Vertical (how the earth would look from space)–Gnomonic (center of earth)Change where the paper touches Change where the paper touches the globethe globe–Tangent case – the paper rests against the surface of the globe–Secant case – the paper goes into and back out of the globe (intersecting at 2 standard lines)Standard lineStandard lineStandard lineExample of tangent and secant Example of tangent and secant azimuthal projectionsazimuthal projectionsPreservation of Properties•Map projections always introduce some sort of distortion. How to deal with it?•Choose a map projection that preserves the globe properties appropriate for the application•Note: The preservation of properties offers an alternative -- perhaps more meaningful -- way to categorize projectionsMap projections distortionMap projections distortionProjections cause distortion. The projection process will distort one or more of the four spatial properties listed below. Distortion of these spatial properties is inherent in any map.ShapeAreaDistanceDirectionConformal projections•-preserve shape •shape preserved for local (small) areas(angular relationships are preserved at each point)•sacrifices preservation of area away from standard point/linesEquivalent/Equal-Area projections•-preserve area •all areas are correctly sized relative to one another •sacrifices preservation of shape away from standard point/lines Preservation of propertiesPreservation of propertiesEquidistant projections•-preserve distance •scale is correct from one to all other points on the map, or along all meridians •however, between other points on map, scale is incorrect Azimuthal projections•-preserve direction •azimuths (lines of true direction) from the center point of the projection to all other points are correctA Few Common Map Projections Used For DisplayA Few Common Map Projections Used For DisplayMap Projections Commonly Used For GIS Map Projections Commonly Used For GIS ApplicationsApplications•Mercator: True compass directions are maintained (lines of latitude and longitude are at right angles to each other), but area is distorted toward the poles•This is a cylindrical projection•We often use Universal Transverse Mercator (UTM), which is a coordinate system applied to a Mercator projectionMap Projections Commonly Used For GIS Map Projections Commonly Used For GIS ApplicationsApplications•In the US these are also common projections–Lambert Conformal Conic – a conic projection that preserves shape–Albers Equal Area – a conic projection that preserves area•Remember that these projections (including UTM) can be associated with the same datum (e.g., NAD 1983, NAD 1927, etc.), which is in turn associated with a corresponding ellipsoid (e.g., NAD 1983 uses the GRS 1980 ellipsoid)True Direction & DistanceTrue Direction & DistanceTissot’s IndicatrixThe