calc_sde {aspace}R Documentation

Calculating the Standard Deviation Ellipse

Description

This function computes the Standard Deviation Ellipse (SDE) from a set of points. The SDE is a centrographic measure used to characterize the dispersion of point observations along two orthogonal axes. The SDE also captures directional bias in a spatial point pattern, the ellipse will be oriented in the direction of maximum dispersion.

Usage

calc_sde(id=1, filename="SDE_Output.txt", centre.xy=NULL, calccentre=TRUE, weighted=FALSE, weights=NULL, CMD.npts=10000, points=activities, verbose=FALSE)

Arguments

id A unique integer to identify the shape
filename A string indicating the ASCII textfile where shape coordinates will be written
centre.xy A vector of length 2, containing the x- and y-coordinates of the SDE centre (Planar Coordinates Only!)
calccentre Boolean: Set to TRUE if the mean center is to be calculated
weighted Boolean: Set to TRUE if the weighted mean center is to be computed with weighted coordinates
weights Weights applied to point observations, number of weights should equal the number of observations
CMD.npts The approximate number of points to generate for the centre of minimum distance (CMD) calculation
points A 2-column matrix or data frame containing point coordinates
verbose Boolean: Set to TRUE if extensive feedback is desired on the standard output

Details

This function is most powerful when used repetitively within a loop to compute the SDE for subsets of points stored in a large data table.

Value

The returned result is a list:

id Identifier for the SDE shape - it should be unique
calccentre Boolean: TRUE if mean centre is computed
weighted Boolean: TRUE if the weighted mean centre is to be used instead
CENTRE.x X-coordinate of the centre
CENTRE.y Y-coordinate of the centre
Sigma.x Half-length of axis along x-axis
Sigma.y Half-length of axis along y-axis
Major String indicating which axis is the major elliptical axis
Minor String indicating which axis is the minor elliptical axis
Theta Rotation angle in degrees
Eccentricity A measure of eccentricity (i.e., the flatness of the ellipse)
Area.sde Area of the SDE
TanTheta Trigonometric result
SinTheta Trigonometric result
CosTheta Trigonometric result
SinThetaCosTheta Trigonometric result
Sin2Theta Trigonometric result
Cos2Theta Trigonometric result
ThetaCorr Corrected theta angle for rotation of major axis from north
central.x X-coordinate of the identified central feature
central.y Y-coordinate of the identified central feature
median.x X-coordinate of median centre, median value of the X-coordinate vector
median.y Y-coordinate of median centre, median value of the Y-coordinate vector
CMD.x X-coordinate of estimated centre of minimum distance
CMD.y Y-coordinate of estimated centre of minimum distance

Note

Results are stored in the r.SDE object (required for graphical visualization using plot_sde). This function can be used on its own (once) or repetitively in a loop to process grouped point data stored in a larger table. When used repetitively, be sure to increment the id parameter to ensure that each SDE has a unique identifier. The output ASCII coordinate file can be further processed using the makeshapes function to generate an ESRI Shapefile for SDE polygons.

Author(s)

Randy Bui, Ron N. Buliung, Tarmo K. Remmel

References

See chapter 4 of the documentation manual for CrimeStat at http://www.icpsr.umich.edu/CRIMESTAT/ and Ebdon, D. 1987. Statistics in geography. 2nd edition. New York, NY Basil Blackwell Ltd. 232 p.

See Also

plot_sde, calc_sdd, calc_mcp, calc_box makeshapes, mcp, gridpts, ellipse3

Examples

calc_sde(id=1, filename="SDE_Output.txt", centre.xy=NULL, calccentre=TRUE, weighted=FALSE, weights=NULL, CMD.npts=10000, points=activities, verbose=TRUE)

[Package aspace version 2.2 Index]