1. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 1 Geographic Information Processing Vector Data Models - Points - Lines - TIGER ® Line Data - Areas Voronoi Tessellations, Wolfram Mathworld

2. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 2 Vector Data Comprised of points, lines, or areas, having geo- location Line vectors meet at nodes. Geographic features (objects) are approximated by a series of lines or areas. Each object is referenced by a unique identifier. Geo- and attribute- information stored separately

3. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 3 Points Points (nodes) are geo-locations Data attributes at points form a higher- dimensional data vector. Types of data –Spatial data about the object at the point –Attribute data about the point –Topological data relating point to others

4. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 4 Point Vector Examples Well (depth, water quality data) Wind data (velocity, direction) Rainfall (depth, amount/time) Weather stations (data frames) Pipeline pumps (tag name, pump rate, etc.) Elevation gradient (for watersheds) Radiation intensity (antennas, nuclear, etc.)

5. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 5 Sea Wind Velocity and Direction Ocean Surface Wind - NASA

6. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 6 Locating Rain Gauges Arkansas-Red Basin River Forecast Center (ABRFC), http://www.srh.noaa.gov/abrfc/p1vol.html

7. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 7 Land Stations and Wind Direction © 2004 NOAA-CIRP

8. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 8 Part of Station Raw Data Frame (other time) Weather Station Data LAT/LONDATE/TIMESPEEDDIR.HUM.BAROM. 40.011167N/075.42333W20070630/130455z5321751014.7 4000.67N/07526.54W_128/000g003t068r000p001P000h61b10146-/ Data Table

9. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 9 Weather Data Storage Station File: One entry per station Raw Data File Many entries per station Note: Files are linked by their station identifier

10. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 10 Lines Also known as edges Begin and end at nodes (geo-positions) Have length May be straight or may be smooth curves Curved boundaries/paths may be represented by multiple straight lines

11. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 11 Line Vector Examples Roads Large objects Streams Watersheds Contours Political boundaries

12. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 12 Example - Map Vector Layers Roads Railroads Rivers/Streams Cities Political boundaries

13. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 13 TIGER ® Line Files Maintained by U. S. Census Bureau Organized by counties (county codes) Describe line, curve, and area objects Geo-coded database format Web address: http://www.census.gov/geo/www/tiger/index.html

14. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 14 2008 TIGER ® Line Files Web Address: http://www.census.gov/geo/www/tiger/tgrshp2008/tgrshp2008.html

15. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 15 PA TIGER ® Line Files Down load file: TGR42029.ZIP Notes: –TGR code is for TIGER ® files –42 code is for Pennsylvania –029 code is for Chester County

16. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 16 PA TIGER ® Directory

17. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 17 File Contents Refer to document: TGR06SE.pdf Refer to metadata: TGR42029.met Data files are in ASCII text format Browse with text editor Read as ASCII characters Objects are coded

18. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 18 Example: Street Open file TGR42029.RT1 in text editor Search for Hillcrest Road –The one we want is below Upper Gulph –Read code number: 179539612 Search for the code number Read geo-data for street segments

19. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 19 Sample Data Points The data points are: -75410512+40051514 -75410566+40051654 -75410661+40051861 -75410740+40052004 -75410872+40052218 -75411683+40053363 (Interpreted as Longitude+Latitude, each with the format: +/- XX.XXXXXX degrees.)

20. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 20 Locate Data points Use Google ™ Earth Locate the data points shown in Slide 19 Note: Must be in reverse (Lat / Lon) order.

21. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 21 The National Atlas Site Web address: http://nationalatlas.gov/index.html Web address for raw data http://nationalatlas.gov/atlasftp.html http://nationalatlas.gov/atlasftp.html

22. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 22 County Boundaries Web address for products: http://gos2.geodata.gov/wps/portal/gos/kcxml/04_Sj9SPykssy0x PLMnMz0vM0Y_QjzKL9443cnIFSYGYfpb6kehCFhhCJpZeEDE Ty0CYmCNIGsTwApkBU-cDVefoDhML84cIhQXr-3rk56bqe- sH6BfkhoJARLmjoiIATRe4MQ!!/delta/base64xml/L3dJdyEvUUd 3QndNQSEvNElVRS82X0tfNDlW http://gos2.geodata.gov/wps/portal/gos/kcxml/04_Sj9SPykssy0x PLMnMz0vM0Y_QjzKL9443cnIFSYGYfpb6kehCFhhCJpZeEDE Ty0CYmCNIGsTwApkBU-cDVefoDhML84cIhQXr-3rk56bqe- sH6BfkhoJARLmjoiIATRe4MQ!!/delta/base64xml/L3dJdyEvUUd 3QndNQSEvNElVRS82X0tfNDlW Web address for data: http://www.census.gov/geo/www/cob/co2000.html#ascii http://www.census.gov/geo/www/cob/co2000.html#ascii

23. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 23 Download County Boundary File File name: co42_d00_ascii.zip co42_d00_ascii.zip Be sure to download the metadata, also.

24. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 24 The Record Number File Co42_d00a.dat Locate Chester County - Record # “60”: ==> 60 "42" "029" "Chester" "06" "County"

25. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 25 The Boundary Data Co42_d00.dat 60 -0.757768101698604E+02 0.400817137777778E+02 -0.756749750000000E+02 0.402428760000000E+02 -0.756748890000000E+02 0.402429190000000E+02 -0.756726310000000E+02 0.402439950000000E+02 -0.756686310000000E+02 0.402448950000000E+02 -0.756651310000000E+02 0.402448950000000E+02...

26. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 26 View in Google TM Earth Image © 2007 TerraMetrics, © 2007 Europa Technologies County boundary is green trace. A single point is shown. Note straight line vectors.

27. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 27 Areas (2-Dimensional Enclosures) Vectors defined by endpoints Line around all points encloses area Related data can add attributes Types of data –Spatial data about the object at the point –Attribute data about the point

28. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 28 Area Data Vector Examples Buildings Parks Lakes Shopping malls

29. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 29 Example - Exton Mall Open TIGER ® file: TGR42029.RT1 Search for: Exton Sq Pkwy Read Record Number: 179526148 Open TIGER ® file: TGR42029.RT2 Search for: 179526148 Data points follow:

30. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 30 Example - Exton Mall 20107 179526148 1 -75624753+40033188 - 75622782+40033361 -75622665+40033356 - 75622549+40033337 -75622439+40033305 - 75622326+40033254 These points are located on the parkway surrounding the Exton Mall

31. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 31 View in Google TM Earth © 2007, Europa Technologies

32. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 32 Area Computations Plane Areas –Break into triangles –Add triangular areas Spherical surface triangular areas –Add angles [radians] –Subtract π[radians] –Multiply by R 2 [radius units]

33. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 33 Area of Spherical Polygon Polygons (for n angles of θ n, radius R) Triangles (for angles A, B, and C, radius R)

34. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 34 Plane Triangle Area Note: Cartesian coordinates used.

35. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 35 Plane Calculation Result Area = 1/2 (-xb ya + xc ya + xa yb - xc yb - xa yc + xb yc)

36. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 36 Simple Example Vector data points (corners): (2,2), (1,4), (1,8), (1,12), (7,10), (9,6), (7,4), (7,2) Computed area: 61

37. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 37 Area Boundary Points Boundary points are labeled by number as shown. Delaunay triangulation will produce a connection list defining triangles. Areas of triangles will then be computed.

38. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 38 Delaunay - Connection List {{1, {8, 7, 2}}, {2, {1, 7, 3}}, {3, {2, 7, 5, 4}}, {4, {3, 5}}, {5, {4, 3, 7, 6}}, {6, {5, 7, 8}}, {7, {3, 2, 1, 8, 6, 5}}, {8, {6, 7, 1}}} Note: Points are labeled by number, as on the previous diagram.

39. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 39 Delaunay Triangulation Result of Delaunay triangulation, the connection list, from which the area of the enclosed convex hull can be computed.

40. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 40 Method for Local Plane Areas NOTE: Works for convex areas only Get rectangular coordinates Make a Delaunay triangulation Compute and sum areas of triangles See Delaunay2 example in Models file

41. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 41 Outline of Computation dt1 = data2D[[ta]]; dt2 = data2D[[tb]]; dt3 = data2D[[tc]]; (* Form determinant matrix *) dt1 = AppendTo[dt1, 1]; dt2 = AppendTo[dt2, 1]; dt3 = AppendTo[dt3, 1]; dtt = List[Null]; dtt = List[dt1, dt2, dt3]; (* Add area of triangle *) aa = aa + Abs[Det[dtt]/2.0]; kt++ ]

42. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 42 Details For computational details, see the Delaunay Triangulation2 notebook in the Models file. REMINDER: the method rounds the outermost points into a convex area.

43. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 43 Detailed Area Computation Steps Read in the data (Get UTM coordinates) Do Delaunay triangulation Compute node adjacency lists and counts Extract triangles Remove duplicates Form determinants (Use Cartesian coord.) Compute total area of triangles

44. Area of Convex polygon http://www.mathwords.com/a/area_convex_polygon.htm http://mathworld.wolfram.com/PolygonArea.html 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 44

45. 5/25/2016© 2009 Raymond P. Jefferis III Lect 03 - 45 Homework Compute land area inside the Exton Square Parkway (surrounding the Exton Mall). Follow previous example Answer file will be given after due date of assignment.