SciPy · Class

spatial.ConvexHull

ConvexHull computes the convex hull enclosing points in N-dimensional space. It returns an object with hull indices, facets, geometric measures, and optional incremental-update methods.

Since: 0.12.0

How it works

Constructing ConvexHull with an array of point coordinates runs Qhull to determine the enclosing convex polytope. The resulting object exposes the input-point indices defining the boundary, geometric measures, simplex facets, and optional incremental-update operations.

Syntax

scipy.spatial.ConvexHull(points, incremental=False, qhull_options=None)

Parameters

Name	Type	Description
`points`	`ndarray`	Coordinates of points to construct a convex hull from; an array of floats with shape (npoints, ndim).
`incremental`	`bool, optional`	Whether to allow adding new points incrementally; this uses additional resources.
`qhull_options`	`str, optional`	Extra options passed to Qhull. The default is Qx when ndim > 4 and empty otherwise; Qt is always enabled.

Returns

A ConvexHull object containing the computed hull and its geometric properties.

Key points

The class computes an enclosing convex hull for point sets in arbitrary dimensional spaces.
Each row of points supplies one coordinate vector, with the second dimension determining the ambient space.
Use qhull_options to forward specialized algorithm settings to the underlying Qhull library.
SciPy delegates the hull calculation to Qhull rather than implementing the geometric algorithm itself.
With incremental construction enabled, add_points incorporates another batch into the existing hull.
close finalizes an incremental hull after point updates are complete.
The documentation identifies SciPy 0.12.0 as the introduction version for ConvexHull.

Common mistakes

The triangulation option Qt cannot be disabled through qhull_options because SciPy enables it for every hull.
Setting incremental=True supports later point insertion but consumes extra resources compared with one-shot construction.
The coplanar attribute is unavailable unless the Qhull coplanar-point option Qc is included.

Example: Compute a 2-D convex hull

import numpy as np
from scipy.spatial import ConvexHull

points = np.array([
    [0, 0], [2, 0], [2, 2], [0, 2], [1, 1]
])
hull = ConvexHull(points)
print(hull.vertices)
print(hull.area)
print(hull.volume)

Builds a two-dimensional hull and prints its boundary-point indices, perimeter, and enclosed area.

When to use it

Boundary and size analysis

Summarize a point cloud by its outer boundary and calculate its geometric size.

Incremental point ingestion

Maintain a hull while batches of observations arrive, avoiding an immediate full reconstruction.

Geometric feature extraction

Extract boundary facets and point indices for downstream computational-geometry operations.

Interview questions

QWhat does scipy.spatial.ConvexHull represent?

ConvexHull computes the convex hull of points in N dimensions using Qhull. The input is an array shaped (npoints, ndim), and the returned object stores the hull geometry and related measurements.

Follow-up: How would you preserve boundary points that lie on a facet but are not vertices? Include Qc in qhull_options and inspect the coplanar attribute.

QExplain the constructor parameters.

The points parameter is a floating-point array whose rows are coordinates. incremental enables adding points later, while qhull_options passes additional controls to Qhull; the default is Qx above four dimensions and empty otherwise.

Follow-up: What fixed Qhull behavior should be remembered when customizing options? Qt remains enabled regardless of qhull_options.

QWhich result attributes are useful for geometric analysis?

In two dimensions, area is the perimeter and volume is the enclosed area; in higher dimensions, they correspond to the hull's surface measure and content, respectively. The vertices attribute gives the input indices of hull vertices.

Follow-up: How can new data be incorporated without reconstructing immediately? Construct with incremental=True, call add_points, and call close when incremental processing is finished.

scipy.spatial.Delaunay
scipy.spatial.Voronoi
scipy.spatial.QhullError
ConvexHull.add_points
ConvexHull.close

Source: scipy.spatial.ConvexHull — SciPy v1.13.0 Manual. Checked 2026-10-15.