Lecture_4_notes_Georeferencing_II.pdf - 4 Georeferencing II � What is a map Types of maps Map scale Mapping the Earth Map datums Map projections GIS

Lecture_4_notes_Georeferencing_II.pdf - 4 Georeferencing II...

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Geog/Plan 281 (Spring 2010) Lecture 4 Dr. Su-Yin Tan 1 4. Georeferencing II What is a map? Types of maps Map scale Mapping the Earth Map datums » Map projections GIS compared to maps Geography / Planning 281 Geography / Planning 281 Flatten the earth’s curved surface… Peel and flatten the earth…like an orange peel Map projections are an important aspect of all mapping All maps require the transformation of the surface of the spherical earth to a flat surface Introduction to GIS - 2
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Geog/Plan 281 (Spring 2010) Lecture 4 Dr. Su-Yin Tan 2 Geography / Planning 281 Map Projections (cont.) Transformation sequence: Model geoid as ellipsoid or sphere Reduce scale --> Generating globe Project from globe to developable surface Distortion is inevitable Least for maps of small areas Greatest when map attempts to show entire surface of the Earth Introduction to GIS - 3 Geography / Planning 281 A system in which locations on the curved surface of the Earth are displayed on a flat sheet or surface according to some set of rules Mathematically, it is a process of transforming geographical location ( ,  to Cartesian (X,Y) co-ordinates on a flat map – Why necessary? For calculating distance, direction, and area Cartesian coordinates can be used directly to calculate distance between two points Euclidean distance – Pythagoras’ theorem Distance defined in a straight line from point (x1,y1) to point (x2,y2): D 2 = (x1 - x2) 2 + (y1 - y2) 2 Map Projections y x x1,y1 x2,y2
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Geog/Plan 281 (Spring 2010) Lecture 4 Dr. Su-Yin Tan 3 Geography / Planning 281 Map Projections – How? Perspective projections can be constructed geometrically Ray tracing All projections can be represented by mathematical equations Computer generation! Introduction to GIS - 5 Geography / Planning 281 Perspective Projections Transparent Globe Light Source Shadows cast on projection surface Light Rays Introduction to GIS - 6
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Geog/Plan 281 (Spring 2010) Lecture 4 Dr. Su-Yin Tan 4 Geography / Planning 281 Create different projections by changing position of light source Perspective Projections Gnomonic Stereographic Orthographic Introduction to GIS - 7 Geography / Planning 281 Projection Parameters Map projection equations have many parameters, including: radius of the sphere (R) or equatorial (a) and polar radius (b) of the reference ellipsoid geodetic datum origin of the coordinate system false easting and northings central meridian ( λ o ), standard parallels ( φ 1, φ 2 ) or centre of projection ( φ 1, λ o ) scale factor at the central meridian or standard parallels Information about the projection parameters is required to define a country’s spatial reference system Introduction to GIS - 8
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Geog/Plan 281 (Spring 2010) Lecture 4 Dr. Su-Yin Tan 5 Geography / Planning 281 Projection Properties ALL projections have distortions It is impossible to represent all geometric relationships among locations on the Earth’s surface accurately on a flat 2-D map How to assess the amount of distortion?
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