This tool provides a measure of overall polygon shape complexity, or irregularity, for vector polygons. Several shape indices have been created to compare a polygon's shape to simple Euclidean shapes (e.g. circles, squares, etc.). One of the problems with this approach is that it inherently convolves the characteristics of polygon complexity and elongation. The Shape Complexity Index (SCI) was developed as a parameter for assessing the complexity of a polygon that is independent of its elongation.

SCI relates a polygon's shape to that of an encompassing convex hull. It is defined as:

> SCI = 1 - A / Ah

Where `A` is the polygon's area and `Ah` is the area of the convex hull containing the polygon. Convex polygons, i.e. those that do not contain concavities or holes, have a value of 0. As the shape of the polygon becomes more complex, the SCI approaches 1. Note that polygon shape complexity also increases with the greater number of holes (i.e. islands), since holes have the effect of reducing the lake area.

The SCI values calculated for each vector polygon feature will be placed in the accompanying database file (.dbf) as a complexity field (COMPLEXITY).

## See Also

shape_complexity_index_raster

## Function Signature

`def shape_complexity_index_vector(self, input: Vector) -> Vector: ...`

## Project Links

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