17. Projection Exercises

Here’s a reminder of some of the functions we have seen. Hint: they should be useful for the exercises!

• sum(expression) aggregate to return a sum for a set of records

• ST_Length(linestring) returns the length of the linestring

• ST_SRID(geometry) returns the SRID of the geometry

• ST_Transform(geometry, srid) converts geometries into different spatial reference systems

• ST_GeomFromText(text) returns geometry

• ST_AsText(geometry) returns WKT text

• ST_AsGML(geometry) returns GML text

Remember the online resources that are available to you:

• https://epsg.io/

Also remember the tables we have available:

• nyc_census_blocks

  • name, popn_total, boroname, geom

• nyc_streets

  • name, type, geom

• nyc_subway_stations

  • name, geom

• nyc_neighborhoods

  • name, boroname, geom

17.1. Exercises

• What is the length of all streets in New York, as measured in UTM 18?

  SELECT Sum(ST_Length(geom))
    FROM nyc_streets;
  

  10418904.7172
  

• What is the WKT definition of SRID 2831?

  SELECT srtext FROM spatial_ref_sys
  WHERE SRID = 2831;
  

  Or, via https://epsg.io/2831

  PROJCS["NAD83(HARN) / New York Long Island",
    GEOGCS["NAD83(HARN)",
      DATUM["NAD83 (High Accuracy Regional Network)",
        SPHEROID["GRS 1980", 6378137.0, 298.257222101,
          AUTHORITY["EPSG","7019"]],
        TOWGS84[-0.991, 1.9072, 0.5129, 0.0257899075194932, -0.009650098960270402, -0.011659943232342112, 0.0],
        AUTHORITY["EPSG","6152"]],
      PRIMEM["Greenwich", 0.0,
        AUTHORITY["EPSG","8901"]],
      UNIT["degree", 0.017453292519943295],
      AXIS["Geodetic longitude", EAST],
      AXIS["Geodetic latitude", NORTH],
      AUTHORITY["EPSG","4152"]],
    PROJECTION["Lambert Conic Conformal (2SP)",
      AUTHORITY["EPSG","9802"]],
    PARAMETER["central_meridian", -74.0],
    PARAMETER["latitude_of_origin", 40.166666666666664],
    PARAMETER["standard_parallel_1", 41.03333333333333],
    PARAMETER["false_easting", 300000.0],
    PARAMETER["false_northing", 0.0],
    PARAMETER["scale_factor", 1.0],
    PARAMETER["standard_parallel_2", 40.666666666666664],
    UNIT["m", 1.0],
    AXIS["Easting", EAST],
    AXIS["Northing", NORTH],
    AUTHORITY["EPSG","2831"]]
  

• What is the length of all streets in New York, as measured in SRID 2831?

  SELECT Sum(ST_Length(ST_Transform(geom,2831)))
    FROM nyc_streets;
  

  10421993.706374
  

  Nota

  The difference between the UTM 18 and the State Plane Long Island measurements is (10421993 - 10418904)/10418904, or 0.02%. Calculated on the spheroid using Geography the total street length is 10421999, which is closer to the State Plane value. This is not surprising, since the State Plane Long Island projection is precisely calibrated for a very small area (New York City) while UTM 18 has to provide reasonable results for a large regional area.

• How many streets cross the 74th meridian?

  SELECT Count(*)
  FROM nyc_streets
  WHERE ST_Intersects(
    ST_Transform(geom, 4326),
    'SRID=4326;LINESTRING(-74 20, -74 60)'
    );
  

  223
  

  The «74th meridian» is a fancy way of saying «a vertical line in geographics where the X value is -74». We can construct such a line and then compare it to the streets, projected into geographics also. Projecting the line into UTM and comparing it there will return a slightly different answer. To get the same answer, you need to «segmentize» it, so it has more points, before transforming.

  SELECT Count(*)
  FROM nyc_streets
  WHERE ST_Intersects(
    geom,
    ST_Transform(ST_Segmentize('SRID=4326;LINESTRING(-74 20, -74 60)'::geometry,0.001), 26918)
    );