Coordinate_Systems - Coordinate Systems presentedby: Tim...

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presented by: Tim Haithcoat University of Missouri Columbia Coordinate Systems
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2 Introduction Coordinates are used to identify locations on the earth’s surface Are based on measurements of displacement from a given location Two types: Plane global
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3 Plane Coordinate Systems Cartesian Coordinates: Determining Coordinates Cartesian coordinates are determined as follows: Locate an origin Set two axes through origin in fixed direction, at right angles to each other By convention these are usually: Identified as x (horizontal) and y (vertical) i.e., y is anti-clockwise from x X is east, y is north Measure linear displacement from the origin in directions defined by the two axes Produce an ordered pair (x,y) x y
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4 Plane Coordinate System Cartesian Coordinates: Measuring Distance Euclidean (Pythagorean) Distance Distance defined in a straight line from point (x 1 ,y 1 ) to point (x 2 ,y 2 ): D 2 = (x 1 - x 2 ) 2 + (y 1 - y 2 ) 2 Cartesian coordinates can be used directly to calculate distance between two points. x y D (x 1 ,y 1 ) (x 2 ,y 2 )
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5 Plane Coordinate System Cartesian Coordinates: Measuring Distance Manhattan Metric Assumes a rectilinear route paralleling the x and y axes: D = |x 1 - x 2 | + |y 1 - Y 2 | Alternate routes all have the same length Assumes travel is parallel to the axes If not parallel, error in distance can be as much as 41% (√2-1) D (0,0) (0.7,0.7)
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6 Plane Coordinate System Cartesian Coordinates: Measuring Distance Distance with Barriers In this case, distance is calculated assuming there are barriers to go around Barrier may be areal (i.e. lake) or linear (river) Is difficult to solve if there are many barriers and may alternate routes B A Lake River Bridge
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7 Storing Coordinates Since in a GIS, coordinates must be stored in the computer as numbers, there are two important concepts that need to be considered: Integer vs. real number Questions of precision
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8 Integer vs. Real Numbers Integers are whole numbers, optionally preceded by “-” to indicate negation Are discrete since mathematically there is a distance of 1 between consecutive numbers Real numbers can be expressed as decimals
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Coordinate_Systems - Coordinate Systems presentedby: Tim...

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