aspace (version 2.5)

calc_sde: 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

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

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.

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)