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   sphinx-quickstart on Sun Feb 12 17:11:03 2015.
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********************************************
The QGIS Standard Deviational Ellipse Plugin
********************************************

.. toctree::
   :maxdepth: 2


The QGIS Standard Deviational Ellipse plugin implements the
method presented in
`The Standard Deviational Ellipse; An Updated Tool for Spatial Description`_
Robert S. Yuill.
Geografiska Annaler. Series B, Human Geography.
Vol. 53, No. 1 (1971), pp. 28-39.
URL: https://www.jstor.org/stable/490885

Apparently, there are many definitions of a Standard
Deviational Ellipse.
CrimeStat implements a method that produces different results
from the Yuill method, and this method is offered as an
alternative.  This method is also implemented in the R aspace
package.
   
Functionality
=================

- The QGIS Standard Deviational Ellipse plugin can be used to
  investigate point patterns, showing a summary of the
  distribution as a standard deviational ellipse.

- Output is a polygon layer with the standard deviational
  ellipse as the only feature.  The following attributes are
  available for the layer / ellipse: meanx, meany, majorsd (SD along
  the major axis), minorsd (SD along the minor axis that is normal
  to the major axis), majorangle(rad) (major axis angle in radians
  counter-clockwise relative to x/east), directiond(eg) ("compass"
  direction - degrees clockwise relative to north) and eccentricity.

Options
=============

- The user can choose between different methods

  - Yuill (see introduction)

  - CrimeStat (as implemented in the R package aspace)

- Specify if only selected features are to be used (but if
  no features are selected, all features will be used)

- Select an attribute for weighting (for Yuill's method).

- For Yuill's method, it is possible to try a DOF (degrees
  of freedom) correction and a sqrt(2) correction
  (to make the standard deviational ellipse equal to the
  standard distance deviation when the distribution of points
  is random and even in all directions).
  With both of these corrections applied, the result will be
  the same as for the CrimeStat method.

Implementation
================

The calculations of the standard deviational ellipse parameters
is performed in a separate thread.


Versions
===============
The current version is 1.2.

- 1.2: Added "compass" direction for the major axis and eccentricity.
  Fixed DOF calculations.
  User interface and robustness improvements.
  Close the SDE polygon to make it valid.

- 1.1: Added the CrimeStat option.
  Added some more options and modified the user interface.

- 1.0: First official version.


Links
=======

`Standard Deviational Ellipse Plugin`_

`Standard Deviational Ellipse code repository`_

`Standard Deviational Ellipse issues`_

Robert S. Yuill: `The Standard Deviational Ellipse; An Updated Tool for Spatial Description`_

Bin Wang, Wenzhong Shi and Zelang Miao: `Confidence Analysis of Standard Deviational Ellipse and Its Extension into Higher Dimensional Euclidean Space`_

Jianxin Gong: `Clarifying the Standard Deviational Ellipse`_

Ned Levine: `CrimeStat IV, Part II Spatial Description`_


Citation
==========

Would you like to cite / reference this plugin?

Tveite, H. (2016). The QGIS Standard Deviational Ellipse Plugin. http://plugins.qgis.org/plugins/SDEllipse/.

Bibtex:

.. code-block:: latex

  @misc{tveitesde,
    author =   {Håvard Tveite},
    title =    {The {QGIS} {Standard} {Deviational} {Ellipse} Plugin},
    howpublished = {\url{http://plugins.qgis.org/plugins/SDEllipse/}},
    year = {2016--2018}
  }


.. _The Standard Deviational Ellipse; An Updated Tool for Spatial Description: https://www.jstor.org/stable/490885
.. _Standard Deviational Ellipse code repository: https://github.com/havatv/qgisstandarddeviationalellipseplugin.git
.. _Standard Deviational Ellipse Plugin: http://arken.nmbu.no/~havatv/gis/qgisplugins/SDEllipse
.. _Standard Deviational Ellipse issues: https://github.com/havatv/qgisstandarddeviationalellipseplugin/issues
.. |N2| replace:: N\ :sup:`2`
.. _Confidence Analysis of Standard Deviational Ellipse and Its Extension into Higher Dimensional Euclidean Space: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4358977/
.. _Clarifying the Standard Deviational Ellipse: http://onlinelibrary.wiley.com/doi/10.1111/j.1538-4632.2002.tb01082.x/pdf
.. _CrimeStat IV, Part II Spatial Description: http://nij.gov/topics/technology/maps/documents/crimestat-files/CrimeStat%20IV%20Chapter%204.pdf
