Boolean Operators and Topological OVERLAY FUNCTIONS IN GIS

Transcription

1 Boolean Operators and Topological OVERLAY FUNCTIONS IN GIS Query asking a question of the attribute data Standard Query Language (SQL) is used to query the data There are 4 basic statements used to get information from 2 (or more) datasets AND if you are desiring the subset of each dataset that is true of both datasets OR if you are desiring the subset of each dataset that is true of either one or both datasets NOT if you are desiring the subset of one dataset that is only true of one dataset OR, BUT NOT BOTH (XOR) if you are seeking the subset of data that is true of one and another dataset, but not both datasets 1

2 Conceptual Design: Overlay Operations In this design, each data set is represented by a circle: A B Topological Overlay Operations Querying the dataset databases can be done several different ways, but they always use the same type of query language. A AND OR NOT XOR B 2

3 Boolean Operators: AND A AND B = True if Both A B Boolean Operators: AND A AND B = True if Both 3

4 Topological Overlay Operations Querying the dataset databases can be done several different ways, but they always use the same type of query language. A AND OR NOT XOR B Boolean Operators: OR A OR B = True if one or other A A B 4

5 Boolean Operators: OR A OR B = True if one or other A Topological Overlay Operations Querying the dataset databases can be done several different ways, but they always use the same type of query language. A AND OR NOT XOR B 5

6 Boolean Operators: NOT A NOT B = True if Neither A B Boolean Operators: NOT A NOT B = True if Neither A 6

7 Topological Overlay Operations Querying the dataset databases can be done several different ways, but they always use the same type of query language. A AND OR NOT XOR B Boolean Operators: A XOR B A OR B, but not both (XOR) A B 7

8 Boolean Operators: A XOR B A OR B, but not both (XOR) Union is an AND operation that produces a 3 rd output dataset A C B 8

9 Polygon on Polygon Vector Overlay Operations INPUT LAYER 1 INPUT LAYER 2 OUTPUT LAYER CLIP SELECT (NOT) Cuts out a piece of layer 1 using layer 2 as cookie cutter [1 AND 2] Erases (deletes) part of layer 1 using layer 2 [1 NOT 2] SPLIT Splits 1 into many layers based on 2 XOR Layer 1 or 2, but not both [1 XOR 2] UNION INTERSECT Overlays polygons and keeps all of both [1 OR 2] Overlays but keeps only portions of layer 1that fall within layer 2 [1 AND 2] Dissolve Operation Change in geometry based on common attribute values 9

10 Clip Operation The Clip feature is used as a cookie cutter Buffer Operation Proximity is measured from target features 10

11 Union and Intersect Union 11

12 Union Point in Polygon Vector Overlay Operations Also called the even-odd rule algorithm Line in Polygon Vector Overlay Operations INPUT LAYER 1 INPUT LAYER 2 INPUT LAYER 1 INPUT LAYER 2 Minimum Bounding Box Minimum Bounding Box OUTPU T LAYER Even or Zero intersects to each side = NO OUTPU T LAYER Even or Zero intersects to each side = NO Odd intersects to each side = YES Odd intersects to each side = YES 12

13 Representing The Shape of the Earth Geoids Ellipsoids Datums Coordinate Systems Projections The Shape of the Earth 3 ways to model it Topographic surface the land/air interface complex (rivers, valleys, etc) and difficult to model Geoid a theoretical, continuous surface for the earth which is perpendicular at every point to the direction of gravity (surface to which plumb line is perpendicular) approximates mean sea level in open ocean without tides, waves or swell satellite observation (after 1957) showed it to be quite irregular because of local variations in gravity. Spheres and spheroids (3 dimensional circle and ellipse) mathematical models which can be used to approximate the geoid and provide the basis for accurate location (horizontal) and elevation (vertical) measurement sphere (3 dimensional circle) with radius of 6,370,997m considered close enough for small scale maps (1:5,000,000 and below e.g. 1:7,500,000) spheroid (3 dimensional ellipse) should be used for larger scale maps of 1:1,000,000 or more (e.g. 1:24,000) 13

14 Spheroid, Ellipsoid, and Geoid Spheroid is a solid generated by rotating an ellipse about either the major or minor axis Ellipsoid is a solid for which all plane sections through one axis are ellipses and through the other are ellipses or circles If any two of the three axes of that ellipsoid are equal, the figure becomes a spheroid (ellipsoid of revolution) If all three are equal, it becomes a sphere Geoid is the equipotential gravity surface of the earth at mean sea level. At any point it is perpendicular to the direction of gravity Reference: Smith, James R., Introduction to Geodesy: The history and concepts of modern geodesy. John Wiley & Sons, 1997 What is an Oblate Ellipsoid (Spheroid)? 14

15 Which Spheroid to use? Hundreds have been defined depending upon: Available measurement technology Area of the globe Most commonly encountered are: e.g North America, Africa Map extent country, continent or global Political issues e.g Warsaw pact versus NATO ArcGIS supports 26 different spheroids! conversions via math formulae Clarke 1866 for North America basis for USGS 7.5 Quads a=6,378,206.4m b=6,356,583.8m GRS80 (Geodetic Ref. System, 1980) current North America mapping a=6,378,137m b=6,356, m WGS84 (World Geodetic Survey, 1984) current global choice a=6,378,137 b=6,356, Latitude and Longitude: location on the spheroid Lat / long coordinates for a location change depending on spheroid chosen! Longitude meridians Prime meridian is zero: Greenwich, U.K. International Date Line is 180 E&W 1 degree=69.17 mi at Equator mi at 40N/S 0 mi at 90N/S Latitude parallels equator is zero 1 degree=68.70 mi at equator mi at poles (1 mile= km=5280 feet) 15

16 Latitude and Longitude Graticule graticule: network of lines on globe or map representing latitude and longitude. Origin is at Equator/Prime Meridian intersection (0,0) grid: set of uniformly spaced straight lines intersecting at right angles. (XY Cartesian coordinate system) Latitude normally listed first (lat,long), the reverse of the convention for X,Y Cartesian coordinates Latitude and Longitude The most comprehensive and powerful method of georeferencing Metric, standard, stable, unique Uses a well defined and fixed reference frame Based on the Earth s rotation and center of mass, and the Greenwich Meridian 16

17 Definition of longitude. The Earth is seen here from above the North Pole, looking along the Axis, with the Equator forming the outer circle. The location of Greenwich defines the Prime Meridian. The longitude of the point at the center of the red cross is determined by drawing a plane through it and the axis, and measuring the angle between this plane and the Prime Meridian. Definition of Latitude Requires a model of the Earth s shape The Earth is somewhat elliptical The N S diameter is roughly 1/300 less than the E W diameter More accurately modeled as an ellipsoid than a sphere An ellipsoid is formed by rotating an ellipse about its shorter axis (the Earth s axis in this case) 17

18 The Public Land Survey System (PLSS) 18

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23 The (Brief) History of Ellipsoids Because the Earth is not shaped precisely as an ellipsoid, initially each country felt free to adopt its own as the most accurate approximation to its own part of the Earth Today an international standard has been adopted known as WGS 84 Its US implementation is the North American Datum of 1983 (NAD 83) Many US maps and data sets still use the North American Datum of 1927 (NAD 27) Differences can be as much as 200 m 23

24 Latitude and the Ellipsoid Latitude (of the red point) is the angle between a perpendicular to the surface and the plane of the Equator WGS 84 Radius of the Earth at the Equator km Flattening 1 part in Geoid A geoid is a representation of the Earth which would coincide exactly with the mean ocean surface of the Earth, if the oceans were to be extended through the continents A smooth but highly irregular surface that corresponds but to a surface which can only be known through extensive gravitational measurements and calculations, not to the actual surface of the Earth's crust 24

25 Geoid Geoid vs. an Ellipsoid 1. Ocean 2. Ellipsoid 3. Local plumb 4. Continent 5. Geoid 25

26 Datums: all location measurement is relative to a specific datum For the Geodesist a set of parameters defining a coordinate system, including: the spheroid (earth model) a point of origin (ties spheroid to earth) For the Local Surveyor a set of points whose precise location and /or elevation has been determined, which serve as reference points from which other point s locations can be determined (horizontal datum) a surface to which elevations are referenced, usually mean sea level (vertical datum) points usually marked with brass plates called survey markers or monuments whose identification codes and precise locations (usually in lat/long) are published North American Datums NAD27 NAD83 Clark 1866 spheroid Meades Ranch origin visual triangulation 25,000 stations (250,000 by 1970) NAVD29 (North American Vertical Datum, 1929) provided elevation basis for most USGS 7.5 minute quads satellite (since 1957) and laser distance data showed inaccuracy of NAD National Academy of Sciences report recommended new datum used GRS80 spheroid (functionally equivalent to WGS84) origin: Mass center of Earth 275,000 stations Helmert blocking least squares technique fitted 2.5 million other fed, state and local agency points. NAVD88 provides vertical datum points can differ up to 160m from NAD27, but seldom more than 30m, and data from digit. map more inaccurate than datum diff. no universal mathematical formulae for conversion from NAD27: See USGS Survey Bulletin # 1875 for conversion tables (in ARC/INFO). Transformations are preformed to local coordinates bin/nadcon.prl 26

27 NAD27 and NAD83 Ellipsoids (Canadian Spacial Reference System, 2006) Ground zero for Geo nerds everywhere The NGS data sheet is here: bin/ds2.prl?retrieval_type=by_pid&pid=kg0640 Meades Ranch, KS (12 miles north of Lucas, KS) is the designated geodedetic base point for the North American Datum 1927 (NAD 27) Owner of ranch is now Mr. Kyle Brant access with permission only ranch.html 27

28 State Plane & the NAD 27 Calculations for map projections are performed using the parameters of the ellipsoid Roadside Marker for the Geodetic Center of North America Meades Ranch, KS (12 miles north of Lucas, KS) is the designated geodedetic base point for the North American Datum 1927 (NAD 27) 28

29 Continuously Operating Reference Stations (CORS) data.html Each CORS site provides Global Navigation Satellite System (GNSS GPS and GLONASS) carrier phase and code range measurements in support of 3 dimensional positioning activities throughout the United States and its territories Surveyors, GIS/LIS professionals, engineers, scientists, and others can apply CORS data to position points at which GNNS data have been collected The CORS system enables positioning accuracies that approach a few centimeters relative to the National Spatial Reference System, both horizontally and vertically High Accuracy Reference Network (HARN) The generic acronym HARN is now used for both HARN and the High Precision Geodetic Network (HPGN) A HARN is a statewide or regional upgrade in accuracy of NAD 83 coordinates using Global Positioning System (GPS) observations HARNs were observed to support the use of GPS by Federal, state, and local surveyors, geodesists, and many other applications Horizontal relative accuracies range from 5mm± to 8mm± at 1:1,000,000 Of these 16,000 stations, NGS has committed to maintaining about 1,400 survey stations, named the Federal Base Network, and the various states will maintain the remainder 29

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31 Map Projections: the concept A method by which the curved 3 D surface of the earth is represented on a flat 2 D map surface a two dimensional representation, using a plane coordinate system, of the earth s three dimensional sphere/spheroid location on the 3 D earth is measured by latitude and longitude location on the 2 D map is measured by x,y Cartesian coordinates unlike choice of spheroid, choice of map projection does not change a location s lat/long coords, only its XY coords. Map projections Earth spherical maps flat! Thus all maps have distortions A good map has distortions that are predictable and systematic 31

32 Map projection Why is it called a projection? Because we project the earth s spherical surface on a flat surface As if we were shining a light from center of earth: Maps can be: 1. Conformal: Shape correct 2. Equivalent (Equal area): Area correct 3. Azimuthal: Direction correct 32

33 Physical Surface Use a physical surface to project the sphere 1. Plane 2. Cone 3. Cylinder Note differences between projections by comparing distortions of the lines of latitude and longitude. 1. Plane projection Hold plane against the surface of the globe (typically the pole) Lines of longitude straight, radiating Lines of latitudes are circles 33

34 1. Plane projection 4. Distortion increases away from the center ("principal point") 5. Good for polar regions 6. But can't show more than half the world. 2. Conic projection Hold cone over pole 34

35 2. Conic projection 2. Lines of latitude curve 3. Line of longitude are straight, and converge towards top 4. Distortion increases away from standard parallel 5. Good for Mid latitudes 3. Cylindrical projection 1. Wrap cylinder around the earth 2. Lines of latitude and longitude are straight, intersect at Distortion greatest at poles 35

36 3. Cylindrical projection 4. Good for lowlatitude areas 5. Poor representation of poles Good for navigation Mercator s Projection Other mathematical Condensed and interrupted projections. 36