Queen's Aspect Ratio

 Aspect roses for a floating point DEM on the left, and an integer version on the right.Note the spikes on the integer version.  The Queen's aspect ratio calculates the severity of the spikes.

Diagonal := round(arctan(AverageYSpace/AverageXSpace) / DegToRad);  This compensates for geographic DEMs, where the 45 degree spikes might be at a different direction because 1 sec is not the same length in the x and y directions.

QueensAspect := (AspectFreq[0] + AspectFreq[Diagonal] + AspectFreq[90] +
AspectFreq[180-Diagonal] + AspectFreq[180] + AspectFreq[180+Diagonal] +
AspectFreq[270] + AspectFreq[360-Diagonal] + AspectFreq[360]) / (TotalAspects) * 45;

• Diagonal allows for arc sec DEMs, where the neighbors might not be at 45 degrees
• This takes the aspects that are directly toward the queen's neighbors, divides by the total number of aspects, and multiples by 45
• The 45 derives from eight queen's neighbors out of the total 360 possible aspects.
• The ratio is dimensionless.
• A value of 1 means that the Queens neighbor aspect arise equally to other aspects.
• Values less than 1 (probably not likely) means that the Queens aspect neighbors are less frequent.
• Values greater than 1 (probably very likely) means that the Queens aspect neighbors are less frequent.

Low relief and short DEM spacing relative to the vertical resolution probably lead to larger values of the Queens aspect ratio.  DEM quality (partially expressed by the contour ghost ratio, probably not relevant to most current DEMs) probably also affects the ratio.

Floating point DEMs have ratios close to 1, and integer DEMs have a much larger ratio.

This was first introduced in MICRODEM 2001, with the work on the SSO diagram.

Last revision 12/11/2021