# 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

1 2 |

### 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 |

`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

Use the sdeloc (coordinates) and sdeatt(attributes) to produce shapefiles using the convert.to.shapefile and write.shapefile from the shapefiles library

### 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 |

### Note

Results are stored in the r.SDE object (required for 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 shapefiles package 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_box`

,`gridpts`

### Examples

1 2 3 4 5 6 7 8 9 | ```
## SDE example
calc_sde(id=1, filename="SDE_Output.txt", centre.xy=NULL, calccentre=TRUE,
weighted=FALSE, weights=NULL, points=activities, verbose=FALSE)
## plot_sde by default takes as input the result produced from the calc_sde, read from the current workspace.
## SDE to shapefile example (exclude the comments below to run script)
## shp <- convert.to.shapefile(sdeloc,sdeatt,"id",5)
## write.shapefile(shp, "SDE_Shape", arcgis=T)
``` |