SHAPELY_CONVEX_HULL
Computes the convex hull of an input geometry provided as WKT. The convex hull is the smallest convex geometry that encloses all points of the original geometry.
In optimization terms, it is the minimal convex set H such that:
G \subseteq H
The function returns the hull WKT as the primary value along with area and perimeter metadata.
Excel Usage
=SHAPELY_CONVEX_HULL(geometry)geometry(str, required): Input geometry (WKT).
Returns (dict): Excel Entity representing the convex hull.
Example 1: Convex hull of points
Inputs:
| geometry |
|---|
| MULTIPOINT (0 0, 10 0, 10 10, 0 10, 5 5) |
Excel formula:
=SHAPELY_CONVEX_HULL("MULTIPOINT (0 0, 10 0, 10 10, 0 10, 5 5)")Expected output:
{"type":"String","basicValue":"POLYGON ((0 0, 0 10, 10 10, 10 0, 0 0))","properties":{"Area":{"type":"Double","basicValue":100},"Perimeter":{"type":"Double","basicValue":40},"WKT":{"type":"String","basicValue":"POLYGON ((0 0, 0 10, 10 10, 10 0, 0 0))"}}}
Example 2: Convex hull of a line
Inputs:
| geometry |
|---|
| LINESTRING (0 0, 3 0, 6 0) |
Excel formula:
=SHAPELY_CONVEX_HULL("LINESTRING (0 0, 3 0, 6 0)")Expected output:
{"type":"String","basicValue":"LINESTRING (0 0, 6 0)","properties":{"Area":{"type":"Double","basicValue":0},"Perimeter":{"type":"Double","basicValue":6},"WKT":{"type":"String","basicValue":"LINESTRING (0 0, 6 0)"}}}
Example 3: Convex hull of concave polygon
Inputs:
| geometry |
|---|
| POLYGON ((0 0, 4 0, 4 4, 2 2, 0 4, 0 0)) |
Excel formula:
=SHAPELY_CONVEX_HULL("POLYGON ((0 0, 4 0, 4 4, 2 2, 0 4, 0 0))")Expected output:
{"type":"String","basicValue":"POLYGON ((0 0, 0 4, 4 4, 4 0, 0 0))","properties":{"Area":{"type":"Double","basicValue":16},"Perimeter":{"type":"Double","basicValue":16},"WKT":{"type":"String","basicValue":"POLYGON ((0 0, 0 4, 4 4, 4 0, 0 0))"}}}
Example 4: Convex hull of a point
Inputs:
| geometry |
|---|
| POINT (2 3) |
Excel formula:
=SHAPELY_CONVEX_HULL("POINT (2 3)")Expected output:
{"type":"String","basicValue":"POINT (2 3)","properties":{"Area":{"type":"Double","basicValue":0},"Perimeter":{"type":"Double","basicValue":0},"WKT":{"type":"String","basicValue":"POINT (2 3)"}}}
Python Code
from shapely import wkt
def shapely_convex_hull(geometry):
"""
Returns the smallest convex polygon that contains all the points in the object.
See: https://shapely.readthedocs.io/en/stable/reference/shapely.convex_hull.html
This example function is provided as-is without any representation of accuracy.
Args:
geometry (str): Input geometry (WKT).
Returns:
dict: Excel Entity representing the convex hull.
"""
try:
if not geometry:
return "Error: Geometry required"
geom = wkt.loads(geometry)
hull = geom.convex_hull
wkt_str = hull.wkt
return {
"type": "String",
"basicValue": wkt_str,
"properties": {
"Area": {"type": "Double", "basicValue": float(hull.area)},
"Perimeter": {"type": "Double", "basicValue": float(hull.length)},
"WKT": {"type": "String", "basicValue": wkt_str}
}
}
except Exception as e:
return f"Error: {str(e)}"