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

5/25/2016© 2009 Raymond P. Jefferis III Lect 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

5/25/2016© 2009 Raymond P. Jefferis III Lect 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

5/25/2016© 2009 Raymond P. Jefferis III Lect 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.)

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

5/25/2016© 2009 Raymond P. Jefferis III Lect Locating Rain Gauges Arkansas-Red Basin River Forecast Center (ABRFC),

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

5/25/2016© 2009 Raymond P. Jefferis III Lect Part of Station Raw Data Frame (other time) Weather Station Data LAT/LONDATE/TIMESPEEDDIR.HUM.BAROM N/ W /130455z N/ W_128/000g003t068r000p001P000h61b10146-/ Data Table

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

5/25/2016© 2009 Raymond P. Jefferis III Lect 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

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

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

5/25/2016© 2009 Raymond P. Jefferis III Lect 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:

5/25/2016© 2009 Raymond P. Jefferis III Lect TIGER ® Line Files Web Address:

5/25/2016© 2009 Raymond P. Jefferis III Lect 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

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

5/25/2016© 2009 Raymond P. Jefferis III Lect 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

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

5/25/2016© 2009 Raymond P. Jefferis III Lect Sample Data Points The data points are: (Interpreted as Longitude+Latitude, each with the format: +/- XX.XXXXXX degrees.)

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

5/25/2016© 2009 Raymond P. Jefferis III Lect The National Atlas Site Web address: Web address for raw data

5/25/2016© 2009 Raymond P. Jefferis III Lect County Boundaries Web address for products: PLMnMz0vM0Y_QjzKL9443cnIFSYGYfpb6kehCFhhCJpZeEDE Ty0CYmCNIGsTwApkBU-cDVefoDhML84cIhQXr-3rk56bqe- sH6BfkhoJARLmjoiIATRe4MQ!!/delta/base64xml/L3dJdyEvUUd 3QndNQSEvNElVRS82X0tfNDlW PLMnMz0vM0Y_QjzKL9443cnIFSYGYfpb6kehCFhhCJpZeEDE Ty0CYmCNIGsTwApkBU-cDVefoDhML84cIhQXr-3rk56bqe- sH6BfkhoJARLmjoiIATRe4MQ!!/delta/base64xml/L3dJdyEvUUd 3QndNQSEvNElVRS82X0tfNDlW Web address for data:

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

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

5/25/2016© 2009 Raymond P. Jefferis III Lect The Boundary Data Co42_d00.dat E E E E E E E E E E E E+02...

5/25/2016© 2009 Raymond P. Jefferis III Lect 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.

5/25/2016© 2009 Raymond P. Jefferis III Lect 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

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

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

5/25/2016© 2009 Raymond P. Jefferis III Lect Example - Exton Mall These points are located on the parkway surrounding the Exton Mall

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

5/25/2016© 2009 Raymond P. Jefferis III Lect 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]

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

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

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

5/25/2016© 2009 Raymond P. Jefferis III Lect 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

5/25/2016© 2009 Raymond P. Jefferis III Lect 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.

5/25/2016© 2009 Raymond P. Jefferis III Lect 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.

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

5/25/2016© 2009 Raymond P. Jefferis III Lect 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

5/25/2016© 2009 Raymond P. Jefferis III Lect 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++ ]

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

5/25/2016© 2009 Raymond P. Jefferis III Lect 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

Area of Convex polygon 5/25/2016© 2009 Raymond P. Jefferis III Lect

5/25/2016© 2009 Raymond P. Jefferis III Lect 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.