TIGER DATA SET

• Gap between the real world data formats and the theoretical data structures
• Witness the plethora of graphics file formats and trade books on them
• We address an important format called TIGER (Topologically Integrated Geographic Encoding and Referencing System)
• Developed by the U.S. Bureau of the Census ( http://www.census.gov)
• TIGER homepage: http://www.census.gov/geo/www/tiger.

• Geographic encoding of whole USA, with census and map data
• Data set is county-based. Over 3200 counties.
• FIPS: a 6 digit identifier for each county
• E.g. FIPS for New York County (i.e., Manhattan) is 36061. Kings County (i.e., Brooklyn) is 36047.
• The first two digits of the FIPS the state (New York State is 36).

• Each county has up to 17 different record types
• Records of a given type is stored in a single file (So, up to 17 files per county)
• The files for Manhattan are named TGR36061.RT1, TGR36061.RT2, TGR36061.RTA, etc.
• File suffixes are RT X where X is one of:
  

  1, 2 ,¼, 9, A, C, H, I, P, R, S, Z.

• The suffix RT1, RT2, etc, indicates ``Record Type 1'', ``Record Type 2'', etc.
• Each file is an ASCII (or text) file
• Each record is stored in one line of file
• Each line has fixed length , and a fixed number of fields in predetermined positions.

• Longitude/Latitudes coordinate system
• Each Longitude is given as a signed 9 digit sequence, with an implied 6 decimal places.
• E.g., -123456789 really represents -123.456789.
• Each latitude is given as a signed 8 digit sequence, also with an implied 6 decimal places.
• E.g., +12345678 really represents +123.45678.
• N.B. Negative Longitude means West of Greenwich Meridian. Negative Latitude means South of the Equator. Also, ``longitude 123456789'' does not mean 12 degrees, 34', 56.89", etc.
• E.g., the bounding box for New York State is (minLon, maxLon, minLat, maxLat) = ( -79.762418, -71.778137, 40.477408, 45.010840).

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  Accuracy

• The accuracy of the map is that of a 1:100,000 scale map, which is correct up to ±167 feet.
• Relative positions of any specified points (with respect to the plane subdivision of the Tiger data) is correct. N.B. To within each county?
• Versions: the TIGER data set are regularly updated. The latest version is 2000. It is important to remember that map information may not be consistent between versions.

• 3 kinds geometric objects: points, polygonal lines and polygons.
• Polygonal lines have registered name of TIGER/Line (R) , also called ``complete chains''.
• Each Tiger Line has a unique ID (or TLID).
• Each polygon, which we will call Tiger Polygons, also has an ID (or POLYID), unique only within each county.
• N.B. To make unique, concantenate POLYID with the FIPS.
• Each Tiger Line is basically the maximal polygonal chain that share the same ``line features'' (see below)
• Typical line features: ``road'' or ``county boundary''.
• 2 kinds of points in a Tiger line: endpoints and non-endpoints (latter is called detail points)
• In RT1 file, 2 endpoints are stored with each Tiger Line. The detail points are stored in RT2.
• In RT2, the detail points for a Tiger Line are stored in groups of 10 details points per record (the last group may have less than 10).
• N.B. Points do not have independent existence (i.e., no unique ID's). This could potentially lead to inconsistencies. But endpoints will generally be shared by two or more Tiger Lines.

• Tiger Polygons
• Interior point per polygon
• Each Tiger line bounds one or 2 polygons
• Non-Geometric Data: census data, postal address ranges, zip code, land type, metropolitan area.
• Landmark Data: hospital, school, park, airport, etc.

· The following Table summarizes important fields in Tiger files.

• Conversion: from Tiger to, say, half-edge structure. Interesting: incremental (partial) processing techniques
• Distance: often we need to evaluate the distance between two points in earth (Lon/Lat) coordinates. The following information is taken from the paper ``TSPLIB95'' by Gerhard Reinelt from the University of Heidelbergi. Suppose the coordinates x, y of point (x,y) are in the form DDD^°MM¢, but represented as a decimal as DDD.MM. Assume the earth is a perfect sphere of radius R=6378.388 kilometers. We convert x=DDD.MM to radians using the function rad(x)

  	Pi = 3.141592;
  	deg = (int)x;
  	minute = x - deg;
  	rad(x) = PI * (deg + 5.0 * minute / 3.0 ) /180.0;

  Then the distance D(p,p¢) in kilometers between p=(x,y) and p¢=(x¢,y¢) is given by

  	q1 = cos( rad(x) - rad(x') );
  	q2 = cos( rad(y) - rad(y') );
  	q3 = cos( rad(y) + rad(y') );
  	D(p,p') = (int) (R * arccos[ 0.5*( (1.0 + q1)* q2 - (1.0 - q1)*q3 ) ] + 1.0);

• Display: must choose projection to avoid distortion.
• Projection surface P and globe surface G. Wanted, a partial map p: G® P.
• Sterographic projection. P is a plane tangent to G at any p₀ Î G. For p Î G, p(p) Î S is intersection of P with the ray r(p) that emanates from the center of the globe and passing through p.
• Cylindrical projection. P is the cylinder that touches G at the equator. The projection point p(p) is the intersection of r(p) with P.
• Easy to calculate if p Î G is given by longitude-latitude (q,f) Î [-p,p)×(-p/2,p/2). and cylinder P has the rectangular coordinates [-p,p) ×R.

  N.B. Assume points (q,f) on the equator projects to p(q,f)=(q, 0).

• Merging counties: inconsistencies or unexpected topology. i
• E.g., we discovered in merging Manhattan with neighboring New Jersey counties that the Liberty Island belongs to Manhattan County but is surrounded by New Jersey water.
• How do we check for topological consistency and regularity?

Exercises

Exercise 3.1:

 Write a Java program to pull out all Tiger Lines and Polygons that lie within some longitude/latitute range. ¨

Exercise 3.2:

 Derive formulae for the projections discussed above:
(a) stereographic projection with respect to a point p₀,
(b) cylindrical projection. ¨

Exercise 3.3:

 (a) Write a program which, given a computer file directory (storing all the Tiger files for a single county), will extract the minimum bounding box (in terms o longitude/latitude) for the county.
(b) Construct a data base for the entire USA storing a minimum bounding box for each county.
(c) Using this, write a program to construct a list of all the counties that (potentially) intersects a given longitude/latitute range. ¨

Exercise 3.4:

 Write a program for checking the topological consistency of the data in (a) a single Tiger county, and (b) in several Tiger counties. Basically we need to check that the endpoints of Tiger Lines are consistent. ¨

Exercise 3.5:

 Write a program which, given a directory storing the Tiger files for a single county, and a postal address, will compute and determine the longitude/latitude of a point near this address. Extra credit: also extract the zip code. ¨