calc_sde: Calculate 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, centre.xy=NULL, calccentre=TRUE,
weighted=FALSE, weights=NULL, points=NULL, verbose=FALSE)

Value

The returned result is a list:

TYPE: The type of calculation results stored in the object: BOX, SDD, SDE, CF, or CF2PTS
DATE: The date and time that the function was run
LOCATIONS: Locations pertinent for the BOX that can be used with ATTRIBUTES if wishing to build a vector point file for geographic data outside of this pacakge.
FORPLOTTING: Coordinates and identifiers used for plotting by plot_sde()
ATTRIBUTES: Attributes for the output BOX that can be used with LOCATIONS coordinates if wishing to build a vector point file for geographic data outside of this package.
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

Arguments

id: A unique integer to identify the shape
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
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

Author

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

Details

Use the LOCATIONS element in the output list object along with the ATTRIBUTES elements can be used to produce shapefiles or other vector point files for geographic data.

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.

Examples

Run this code

# SDE EXAMPLE
data(activities)
a <- calc_sde(id=1, centre.xy=NULL, points=activities)
str(a)
print(a)

# IF THE RESULT OF THIS FUNCTION IS STORED TO AN OBJECT, THE plot_sde()
# FUNCTION WILL TAKE THAT OBJECT AS INPUT FOR PLOTTING VIA THE datin ARGUMENT

# SDE TO SHAPEFILE EXAMPLE (REMOVE THE COMMENTS TO RUN)
# shp <- convert.to.shapefile(a$LOCATIONS, a$ATTRIBUTES, "id", 5)
# write.shapefile(shp, "SDE_Shape", arcgis=T)

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