Compactness

You can calculate compactness for a set of districts (shapes), as well as various measures of compactness for a single district (shape) including “know it when you see it” (KIWYSI) compactness.

Compactness for a Set of Districts

To compute average Reock, Polsby-Popper, and KIWYSI compactness for a set of districts (shapes) and by district:

def calc_compactness_metrics(shapes: list[Polygon | MultiPolygon]) -> dict:

“shapes” are shapely Polygons or MultiPolygons:

from shapely.geometry import Polygon, MultiPolygon

This returns a dictionary of results:

results: dict = {
    "avgReock": avg_reock,
    "avgPolsby": avg_polsby,
    "avgKIWYSI": avg_kiwysi,
    "byDistrict": by_district,
}

For each district, the results are of the form:

measures: dict = {
    "reock": reock_flat,
    "polsby": polsby_flat,
    "kiwysiRank": kiwysi_rank, # 1-100, smaller is better
}

KYIWYSI compactness is described below.

Compactness for One District

These are functions to calculate compactness for a single district (shape). They are seven are the “features” for Aaron Kaufman’s “know it when you see it” (KIWYSI) compactness ML model, which is described in the next section.

These functions can compute their metric either assuming the Earth is curved (geodesic=True) or assuming it is flat (geodesic=False). [The Earth is, obviously, spherical, but sometimes compactness is calculated on a flat plane.]

Y-symmetry is the area of a district overlapping with its reflection around a vertical line going through the centroid, divided by the area of the district. Values range [1–2].

def calc_sym_y(shp: Polygon | MultiPolygon, geodesic: bool = True) -> float:

X-symmetry is the same as Y-symmetry except the district is reflected over a horizontal line going through the centroid.

def calc_sym_x(shp: Polygon | MultiPolygon, geodesic: bool = True) -> float:

Reock is the primary measure of the dispersion of district shapes, calculated as “the area of the district to the area of the minimum spanning circle that can enclose the district.”

def calc_reock(shp: Polygon | MultiPolygon, geodesic: bool = True) -> float:

“Bounding-box” here is shorthand for “the ratio of the area of the district to the area of the minimum bounding box of the district.”

def calc_bbox(shp: Polygon | MultiPolygon, geodesic: bool = True) -> float:

Polsby-Popper is the primary measure of the indentation of district shapes, calculated as the “the ratio of the area of the district to the area of a circle whose circumference is equal to the perimeter of the district.”

def calc_polsby(shp: Polygon | MultiPolygon, geodesic: bool = True) -> float:

Convex Hull is a secondary measure of the dispersion of district shapes, calculated as “the ratio of the district area to the area of the minimum convex bounding polygon (also known as a convex hull) enclosing the district.”

def calc_hull(shp: Polygon | MultiPolygon, geodesic: bool = True) -> float:

Schwartzberg is a secondary measure of the degree of indentation of district shapes, calculated as “the ratio of the perimeter of the district to the circumference of a circle whose area is equal to the area of the district.”

def calc_schwartzberg(shp: Polygon | MultiPolygon, geodesic: bool = True) -> float:

“Know it when you see it” Compactness

KIYWSI compactness implements Kaufman, King, and Komisarchik’s “know it when you see it” (KIWYSI) compactness model.

To feature-ize a shape and then rank it [1-100], smaller is better:

def kiwysi_rank_shape(
    shp: Polygon | MultiPolygon, *, geodesic: bool = True, revised: bool = True
) -> float:

The above gives raw results which may fall outside the range [1–100]. To constrain them to that range:

def trim_kiwysi_rank(raw_rank: float) -> float: