plugin_measures_of_compactness
QGIS Measures of compactness expressions plugin
This plugin adds some common ways to measure the degree of compactness of a geometry(ies) (Polsby–Popper, Reock, Skew, etc…). These functions are added as part functions expression that works in the context of the field calculator in QGIS
These functions are particularly useful to detect gerrymandering, evaluate the regularity of a parcel, lot, etc…
For an introduction on geometry and compactness, see the wonderful Math for the people course https://web.stevenson.edu/mbranson/m4tp/version1/gerrymandering-math-topic-compactness.html
And for a visual representation of these functions see https://fisherzachary.github.io/public/r-output.html
Report an issue here : https://github.com/ValentinBuira/plugin_measures_of_compactness/issues
How to use
The expressions functions of plugin are all located in the field calculator window under the “Compactness” sub menu
Reference
This section give an overview of the functions in the plugin. For a more complete explanation how they work please refer to the “in-line” documentation direclty inside QGIS.
compactness_pp : Polsby-Popper compactness
Calculate a Polsby-Popper(PP) compactness score
The Polsby-Popper (polsby & Popper, 1991) is the ratio of the area(A) of the geometry to the area of a circle whose circumference is equal to the perimeter(P) of the geometry.
Can be written as:
4 * pi * (A / P*P ) * Where *A* is the area of the geometry * Where *P* is the perimeter of the geometry
Scores range from 0 to 1, where 0 is the least compact and 1 is the most compact.
exemple usage : compactness_pp( $geometry )
compactness_skew : Skew compactness
Calculate a skew compactness
A skew compactness compares the area of the maximum inscribed circle (A_mic) to the area of the minimum bounding circle (A_mbc).
Scores range from 0 to 1, where 0 is the least compact and 1 is the most compact.
exemple usage : compactness_skew( $geometry )
Note: only available on QGIS >=3.42
compactness_reock: Reock Compactness
Calculate a reock compactness
A reock compactness is the ratio between the area (A) of the geometry to the area of the minimum bounding circle (A_mbc)
Scores range from 0 to 1, where 0 is the least compact and 1 is the most compact.
exemple usage : compactness_reock( $geometry )
compactness_box_reock: Box Reock Compactness
Calculate a box reock compactness
A box reock compactness is the ratio between the area (A) of the geometry to the area of the minimum bounding box (A_bbox)
Scores range from 0 to 1, where 0 is the least compact and 1 is the most compact.
exemple usage : compactness_box_reock( $geometry )
compactness_schwartz: Schwartzberg Compactness
Calculate a schwartzberg compactness
Can be written as:
S = 1 / (P / (2pi * sqrt(A / pi))) * Where A is the area of the geometry * Where P is the perimeter of the geometry
Scores range from 0 to 1, where 0 is the least compact and 1 is the most compact.
exemple usage : compactness_schwartz( $geometry )
compactness_lw: Length-Width Compactness
Calculate a Length-Width Compactness
Length-Width compactness compares the width and the length of a a geometry using its bouding box
Scores range from 0 to 1, where 0 is the least compact and 1 is the most compact.
exemple usage : compactness_lw( $geometry )
Thanks
This plugin was heavily influenced by the redistmetrics R package made by the ALARM projects see also https://cran.r-project.org/web/packages/redistmetrics/vignettes/compactness.html as a complementary documentation
And to whoever wrote guide that make theses compactness measures easy to understand visually https://fisherzachary.github.io/public/r-output.html