STK splits the total grid into regions of 9^n points, creating a 3^n X 3^n shape, where n is a level that STK iterates during access computations. STK optimizes the size of these computation regions to remain as close to 20 degrees in latitude as possible while also keeping the grid spacing as close as possible to the spacing requested in the Coverage Definition. Additionally, these grids require that n <= 3 and that the latitude spanned by the sum of the regions is equal to the latitude span you enter, either explicitly in the case of a latitude bound grid or implicitly in the case of a custom grid. Here is a simple example. You request a latitude span of 50 degrees with a grid spacing of 4 degrees. The following are possible combinations of latitude spacing that STK might consider:
a) One region of 50-degree span having 81 points (9x9) would provide a grid spacing of 50/10 = 5 degrees. The number 10 in this case comes from there being nine total points in the latitudinal direction (9x9), creating 10 subregions.
b) Two regions of 25-degree span having 9 points each would provide a grid spacing of 50/7 = 7 degrees.
c) Two regions of 25-degree span having 81 points each would provide a grid spacing of 50/19 = 2.6 degrees.
d) Three regions of 16.6-degree span having 9 points each would provide a grid spacing of 50/10 = 5 degrees.
e) Four regions of 12.5-deg span having 9 points each would provide a grid spacing of 50/13 = 3.8 degrees.
In this case, STK would select option (e) because the regions have n <= 3, a span close enough to 20 degrees, and a spacing very close to the requested 4 degrees. Internally, the algorithm is designed to optimize these conditions rather than just choose from a few options, but this example demonstrates the intent.
STK computes the longitude span of the regions after the latitude spacing. STK tries to make the longitude span as close as possible to the latitude span at the equator, while also satisfying the requirement that an integer number of regions must fit into 360 degrees. STK computes a unique regional longitude span for each band of regions; in the example above, there would be four bands. STK computes the regional longitude span for each band by first computing a target span, dividing the desired span at the equator by the cosine of the latitude at the center of the band. It then computes the actual span by dividing 360 by the target span, rounding to the closest integer and then dividing 360 by that integer number of regions. The points are then evenly spaced within each region. Suppose that the example (option e) were using a latitude range of -20 degrees to 30 degrees. The southernmost band of regions would then be centered on a latitude of -13.75 degrees. STK would then have a desired longitude span of 12.5/cos(-13.75) = 12.87 degrees for this band. It would then compute the number of regions (360/12.87 + 1+ 0.5) = 29.47 regions and round to 29 regions to compute the actual longitude span of 360/29 = 12.41 degrees. The longitude spacing of the points would therefore be 360/(3*29) = 4.14 degrees. |
