# Calculate the Standard Deviation Box

### Description

The orthogonal dispersion of a set of points can be described using the standard deviation of the x- and y-coordinates of a set of point observations. The orthogonal dispersion can then be visualized with a Standard Deviation Box. This function computes the properties of the Standard Deviation Box (SD Box) from a set of point observations.

### Usage

1 2 |

### Arguments

`id` |
A unique integer to identify a SD Box |

`filename` |
A string indicating the ASCII textfile where the box coordinates will be written |

`centre.xy` |
A vector of length 2, containing the x- and y-coordinates of the geographic centre of the SD Box |

`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 the set of point observations input to the calc_box function |

`verbose` |
Boolean: Set to TRUE if extensive feedback is desired on the standard output |

### Details

Use the boxloc (coordinates) and boxatt(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 SD Box shape - it should be unique |

`calccentre` |
Boolean: TRUE if the mean centre was estimated |

`weighted` |
Boolean: TRUE if the weighted mean centre was estimated |

`CENTRE.x` |
X-coordinate of the centre |

`CENTRE.y` |
Y-coordinate of the centre |

`SD.x` |
Orthogonal standard deviation in the x-axis |

`SD.y` |
Orthogonal standard deviation in the y-axis |

`Box.area` |
Area of the standard deviation box |

`NW.coord` |
North-west coordinates of SD Box |

`NE.coord` |
North-east coordinates of SD Box |

`SW.coord` |
South-west coordinates of SD Box |

`SE.coord` |
South-east coordinates of SD Box |

### Note

Results are stored in the r.BOX object (required for plot_box). 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 SD BOX has a unique identifier. The output ASCII coordinate file can be further processed using the shapefiles package to generate an ESRI Shapefile for SD BOX polygons.

### Author(s)

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

### See Also

`plot_box`

, `calc_sde`

, `calc_sdd`

,
`wtd.var`

### Examples

1 2 3 4 5 6 7 8 9 | ```
## BOX example
calc_box(id=1, filename="BOX_Output.txt", centre.xy=NULL, calccentre=TRUE,
weighted=FALSE, weights=NULL, points=activities, verbose=FALSE)
## plot_box by default takes as input the result produced from the calc_box, read from the current workspace.
## SD Box to shapefile example (exclude the comments below to run script)
## shp <- convert.to.shapefile(boxloc,boxatt,"id",5)
## write.shapefile(shp, "BOX_Shape", arcgis=T)
``` |