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UNC-Chapel Hill GEOG 070 - Georeferencing

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GeoreferencingUsing Projections to Map the EarthWhy Use Projections at All?What is a Projection?Projections DistortThree Families of ProjectionsDevelopable SurfacesStandard Points and LinesTangent ProjectionsSecant ProjectionsThe GraticuleThe GraticuleThe Graticule, ProjectedCylindrical ProjectionsCylindrical Projection DistortionMercator ProjectionTransverse Mercator ProjectionPlate Carrée (or Cylindrical Equidistant) ProjectionConical ProjectionsConical Projection DistortionLambert Conformal Conic ProjectionAlbers Equal Area Conic ProjectionPlanar ProjectionsPlanar Projection DistortionPlanar ProjectionsLambert Azimuthal ProjectionPlanar ProjectionsPreservation of PropertiesPreservation of Properties - ShapePreservation of Properties - AreaPreservation Properties - DistancePreservation Properties - DirectionTissot’s IndicatrixTissot’s IndicatrixDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Georeferencing• GOAL: To assign a location to all the features represented in our geographic information data• In order to do so, we need to make use of the following elements:– ellipsoid/geoid–datum– projection– coordinate system– scale• The next few lectures will introduce you to these elementsTo determine a position on the Earth, you’ll need to understand how these elements relate to each other in order to specify a positionDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Using Projections to Map the EarthmapEarth surface Paper map or GIS•We have discussed geodesy, and we now know about modeling the shape of Earth as an ellipsoid and geoid•We are ready to tackle the problem of transforming the 3-dimensional Earth Æ 2-dimensional representation that suits our purposes:David Tenenbaum – GEOG 070 – UNC-CH Spring 2005Why Use Projections at All?•There are many reasons for wanting to project the Earth’s surface onto a plane, rather than deal with the curved surface:•The paper used to output GIS maps is flat, and paper maps are more convenient than 3D models like globes for most large-scale applications•Scanning and digitizing flat maps is a significant source of spatial data that is used in a GIS•The raster spatial data model representation of the Earth’s surface is flat, and it is impossible to create a raster on a curved surface•The Earth has to be projected to see all of it at once•It is much easier to measure distance on a planeDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005What is a Projection?•Map projection - The systematic transformation of points on the Earth’s surface to corresponding points on a planar surface•The easiest way to imagine this is to think of a light bulb inside of a semi-transparent globe, shining features from the Earth’s surfaceonto the planar surfaceDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Projections Distort• Because we are going from the 3D Earth Æ 2D planar surface, projections alwaysintroduce some type of distortion• When we select a map projection, we choose a particular projection to minimize the distortionsthat are important to a particular applicationDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Three Families of Projections•There are three major families of projections, each tends to introduce certain kinds of distortions, or conversely each has certain properties that it used to preserve (i.e. spatial characteristics that it does not distort):• Three families:1. Cylindrical projections2. Conical projections3. Planar projections312David Tenenbaum – GEOG 070 – UNC-CH Spring 2005Developable Surfaces• We refer to the 2-dimensional surface upon which the map information is projected as a developable surface• The developable surface is a geometric surface that can be unrolled without distortion, although the projected information will contain distortionsDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Standard Points and Lines• We can identify the locations where the developable surface contacts the ellipsoid’s surface Æ these locations are standard points and lines• Standard point/lines: On a projected map, these are location(s) free of all distortion at the exact point or lines where the developable surface (cylinder, cone, plane) touches the globeDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Tangent Projections•Tangent projections have a single standard point (in the case of planar projection surfaces) or a standard line (for conical and cylindrical projection surfaces) of contact between the developable surface and globeDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Secant Projections •Secant projections have a single standard line (in the case of planar projection surfaces) or multiple standard lines (for conical and cylindrical projection surfaces) of contact between the developable surface and the globeDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005The Graticule•The parallels and meridians of latitude and longitude form a graticule on a globe, a grid of orthogonal linesDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005The Graticule• Picture a light source projecting the shadows of the graticule lines on the surface of a transparent globe onto the developable surface …David Tenenbaum – GEOG 070 – UNC-CH Spring 2005The Graticule, ProjectedDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Cylindrical Projections• To create a cylindrical projection, the meridiansare projected geometricallywhile the parallels are projected mathematicallyto produce 90° intersections throughout the graticule•The meridians are equally spaced on a regular cylindrical projection, while the parallels are not•The distortions have a linear pattern moving away from the standard linesDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Cylindrical Projection DistortionTangent SecantStandardLineStandardLinesIncreasingDistortionDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Mercator Projection•The Mercator projection is a well known cylindrical projection (commonly used for world maps)•The Equator is the standard line•The spacing between parallels increases towards poles• True-direction along graticule lines• Great circles are not straight lines on this map projectionDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Transverse Mercator Projection• You are likely less familiar with the transverse Mercator projection, although it is one of the most popularprojections in current use•It uses a cylindrical developable surface,


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UNC-Chapel Hill GEOG 070 - Georeferencing

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