﻿ Algorithms

# Algorithms

• Arc second spacing conversion factors: this is the factor needed to sort of get GCS DEMs to work correctly in some software.  You can use only one factor, and must pick if you want the X direction, the Y direction, or the average.  Shows the number of meters in a degree and an arc second.  You can get a graph from the database created.

 LAT M_DEG_Y M_DEG_X M_DEG_AVG M_SEC_Y M_SEC_X M_SEC_AVG 85 111685.375 9734.4 60709.887 31.024 2.704 16.864 84 111681.615 11674.624 61678.12 31.023 3.243 17.133 83 111677.184 13611.221 62644.202 31.021 3.781 17.401 82 111672.085 15543.589 63607.837 31.02 4.318 17.669 81 111666.326 17471.131 64568.728 31.018 4.853 17.936 80 111659.913 19393.247 65526.58 31.017 5.387 18.202

Output

• Table for every 1 degree of latitude (same results in both hemispheres)
• Can get graphs in MICRODEM or Excel, and you can filter the results as desired

Gives

• Meters per degree in the x, and y directions, and the average
• Meters per second in the x, and y directions, and the average
• These can be used, not very effectivley but it's they best they can do, in software that cannot do Slope algorithms for arc second DEMs

• Arc second rectangular pixel approximation

 LAT SEC SIDE_M BASE_M TOP_M ERROR_PC RECT 85 1 31.0237 2.704 2.7038 0.00554088 0.0872 85 3 93.0712 8.1119 8.1105 0.01662265 0.0871 85 30 930.7118 81.121 80.9862 0.16623594 0.087 85 60 1861.4239 162.242 161.7026 0.33247403 0.0869 85 450 13960.7019 1216.8151 1186.4706 2.49376366 0.085 85 3600 111687.0008 9734.4 7791.152 19.96268876 0.0698

Output

• Table for every 5 degrees of latitude (same results in both hemispheres), for 5 spacings in arc seconds
• Can get graphs in MICRODEM or Excel, and you can filter the results as desired

Applicable to a quadrangle map, or the pixels in a geographic grid.

Gives

• the size in meters of the side (same east and west), top, and bottom each each quad/pixel
• ERROR_PC Gives the percent difference between the top and bottom.  This will be a max at the pole, and zero at the equator
• RECT gives the ratio of TOP/BOTTOM, on how rectangular the pixels are
• UTM spacing and grid-true angle

 LAT W_SPACE W_ROTATE MID_SPACE MID_ROTATE E_SPACE E_ROTATE 80 30.011 357.05 30.012 0 30.011 2.95 79 30.011 357.06 30.012 0 30.011 2.94 78 30.01 357.07 30.012 0 30.01 2.93 77 30.01 357.08 30.012 0 30.01 2.92 76 30.01 357.09 30.012 0 30.01 2.91 75 30.009 357.1 30.012 0 30.009 2.9 5 29.971 359.74 30.012 0 29.971 0.26 4 29.971 359.79 30.012 0 29.971 0.21 3 29.971 359.84 30.012 0 29.971 0.16 2 29.971 359.9 30.012 0 29.971 0.1 1 29.971 359.95 30.012 0 29.971 0.05 0 29.971 0 30.012 0 29.971 0

For every one degree of latitude for a UTM zone and a 30 m DEM, gives

• Spacing in meters for the western edge, center, and and eastern edge of the zone.  These are true meters, and the projected metgers are a constant 30 m
• The grid north to trun north rotation angle at the same three locations

• GDAL slopes arc second DEMs (requires open DEM): creates 6 maps using the Zevenbergen and Thorne algorithms, with three spacings: the x,y, and average.  None give correct answers; compare with the slope maps from MICRODEM.

Last revision  7/16/2021