Polygon trimming using a modified azimuthal map projection
AssigneeThe MathWorks, Inc.
InventorRobert P. Comer
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Abstract
In one embodiment, a system, method and computer readable media are disclosed for trimming geographic data that defines polygons to boundaries of a quadrangle. The geographic data is converted to map coordinates in a novel azimuthal map projection. Each map projected point in the azimuthal map projection has an azimuthal angle that is proportional to longitude of the point, and has a radius from the center of the azimuthal map projection that is proportional to both the longitude and latitude of the point. Polygons are trimmed along a lower limit of the quadrangle and along an upper longitude limit of the quadrangle using the azimuthal map projection. The map coordinates in the azimuthal map projection are then converted back to geographic data.
Claims33
A method for trimming geographic data that defines polygons to boundaries of a quadrangle, comprising:
- converting the geographic data into map coordinates in a modified azimuthal map projection, a map coordinate in the modified azimuthal map projection describing a projected point having an azimuthal angle proportional to longitude of the point, and having a radius from the center of the modified azimuthal map projection proportional to both longitude and latitude of the point such that parallels in the modified azimuthal map projection are projected as squares, the modified azimuthal map projection being non-equidistant;
- trimming one or more polygons along a lower longitude limit of the quadrangle in the modified azimuthal map projection;
- trimming one or more polygons along an upper longitude limit of the quadrangle in the modified azimuthal map projection;
- and
- converting the map coordinates in the modified azimuthal map projection back to geographic data.
An apparatus for trimming geographic data that defines polygons to boundaries of a quadrangle, comprising:
- a processor configured to execute instructions for one or more units;
- and
- a polygon to quadrangle trimming unit configured to convert the geographic data into map coordinates in a modified azimuthal map projection, a map coordinate in the modified azimuthal map projection describing a projected point having an azimuthal angle proportional to longitude of the point, and having a radius from the center of the modified azimuthal map projection proportional to both longitude and latitude of the point such that parallels in the modified azimuthal map projection are projected as squares, wherein the modified azimuthal map projection is non-equidistant,
- wherein the polygon to quadrangle trimming unit is further configured to trim polygons along a lower and an upper longitude limit of the quadrangle in the modified azimuthal map projection, and to convert the map coordinates in the modified azimuthal map projection back to geographic data.
The apparatus of 22, wherein the polygon to quadrangle trimming unit is further configured to multiply sine of the longitude of the point by the sum of latitude of the point and a constant, divided by an adjustment factor, and multiply cosine of the longitude of the point by the sum of latitude of the point and the constant, divided by the adjustment factor.
The apparatus of 13, wherein the polygon to quadrangle trimming unit is further configured to employ the expressions,
- r=(lat+pi/2)/scalefactor(lon);
- x=r*sin(−lon);
- y=r*cos(lon);
- where “lat” and “lon” are latitude and longitude vectors storing polygon data, “scalefactor(lon)” is an adjustment factor based upon longitude, “x” and “y” are vectors storing x-axis and y-axis values of map coordinates of polygon vertices in the modified azimuthal map projection, and “pi” is an approximation of the mathematical constant pi.
An apparatus for trimming geographic data to boundaries of a quadrangle, comprising:
- means for converting the geographic data into map coordinates in a modified azimuthal map projection, a map coordinate in the modified azimuthal map projection to describe a projected point having an azimuthal angle proportional to longitude of the point, and having a radius from the center of the modified azimuthal map projection proportional to both longitude and latitude of the point such that parallels in the modified azimuthal map projection are projected as squares, wherein the modified azimuthal map projection is non-equidistant;
- means for trimming one or more polygons along a lower longitude limit of the quadrangle in the modified azimuthal map projection;
- means for trimming the one or more polygons along an upper longitude limit of the quadrangle in the modified azimuthal map projection;
- and
- means for converting the map coordinates in the modified azimuthal map projection back to geographic data.
A non-transitory, tangible computer-readable media comprising program instructions that, when executed, are operable to:
- convert geographic data into map coordinates in a modified azimuthal map projection, a map coordinate in the modified azimuthal map projection to describe a projected point having an azimuthal angle proportional to longitude of the point, and having a radius from the center of the modified azimuthal map projection proportional to both longitude and latitude of the point such that parallels in the modified azimuthal map projection are projected as squares, wherein the modified azimuthal map projection is non-equidistant;
- trim one or more polygons along a lower longitude limit of the quadrangle in the modified azimuthal map projection;
- trim one or more polygons along an upper longitude limit of the quadrangle in the modified azimuthal map projection;
- and
- convert the map coordinates in the modified azimuthal map projection back to geographic data.
Dependencies are inferred from the claim text.