Mapping Toolbox

Polygon Area

For vector data in polygon format, geographic areas can be calculated using the command areaint. The function performs a numerical integration using Green's Theorem for the area on a surface enclosed by a polygon. Since this is a discrete integration on discrete data, the results are not exact. Nevertheless, the method provides the best means of calculating the area of arbitrarily shaped regions. Better measures result from better data.

The Mapping Toolbox function areaint (for area by integration), like the other area functions areaquad and areamat, returns areas as a fraction of the entire planet's surface, unless a radius is provided. Here we calculate the area of the continental United States using the usalo workspace. Three areas are returned, because the data contains three polygons: Long Island, Martha's Vineyard, and the rest of the continental U.S.:

• load usalo
  earthradius = almanac('earth','radius');
  area = areaint(uslat,uslon,earthradius)
  area =
    1.0e+06 *
          7.9256
          0.0035
          0.0004
  

Since the default Earth radius is in kilometers, the area is in square kilometers. From the same workspace, the areas of the Great Lakes can be calculated, this time in square miles:

• earthradius = almanac('earth','radius','miles');
  area = areaint(gtlakelat,gtlakelon,earthradius)
  area =
    1.0e+04 *
          8.0124
          1.0382
          0.7635
  

Again, three areas are returned, the largest for the polygon representing Superior, Michigan, and Huron together, the other two for Erie and Ontario.

Geographic Interpolation

Vector Calculations - Intersections