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CircumscribedBall[{p1,p2,…}]

gives a ball with minimal radius that encloses the points p1, p2, ….

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Scope  
Points  
Properties & Relations  
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CircumscribedBall

CircumscribedBall[{p1,p2,…}]

gives a ball with minimal radius that encloses the points p1, p2, ….

Details

Examples

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Basic Examples  (2)

A 2D circumscribed ball from points:

Wolfram Language code: pts = RandomReal[{-1, 1}, {50, 2}];
Wolfram Language code: ℛ = CircumscribedBall[pts]

The region is the smallest ball that encloses the points:

Wolfram Language code: Region[ℛ, Epilog -> {Black, Point[pts]}]

A 3D circumscribed ball from points:

Wolfram Language code: pts = RandomReal[{-1, 1}, {50, 3}];
Wolfram Language code: ℛ = CircumscribedBall[pts]

The region is the smallest ball that encloses the points:

Wolfram Language code: Show[{Region[Style[Point[pts], Black]], Region[Style[ℛ, Opacity[.5]]]}]

Scope  (1)

Points  (1)

Create a 1D circumscribed ball from a set of points:

Wolfram Language code: pts = RandomReal[{-1, 1}, {50, 1}];
Wolfram Language code: ℛ = CircumscribedBall[pts]

A 2D circumscribed ball:

Wolfram Language code: pts = RandomReal[{-1, 1}, {50, 2}];
Wolfram Language code: ℛ = CircumscribedBall[pts]

A 3D circumscribed ball:

Wolfram Language code: pts = RandomReal[{-1, 1}, {50, 3}];
Wolfram Language code: ℛ = CircumscribedBall[pts]

Properties & Relations  (3)

CircumscribedBall is the smallest Ball that encloses the points:

Wolfram Language code: pts = {{0, 0}, {1, 0}, {2 / 3, 1 / 2}, {0, 1}};
Wolfram Language code: Graphics[{ GrayLevel[.5, .5], CircumscribedBall[pts], Red, Point[pts]}]

Use InscribedBall to get a largest Ball that lies inside the convex hull of points:

Wolfram Language code: pts = {{0, 0}, {1, 0}, {2 / 3, 1 / 2}, {0, 1}};
Wolfram Language code: Graphics[{GrayLevel[.5, .5], ConvexHullRegion[pts], Red, Point[pts], Blue, InscribedBall[pts]}]

Use Circumsphere to get the Sphere that circumscribes the points:

Wolfram Language code: pts = {{0, 0}, {1, 0}, {0, 1}};
Wolfram Language code: Graphics[{GrayLevel[.5, .5], Circumsphere[pts], Red, Point[pts]}]
Wolfram Research (2023), CircumscribedBall, Wolfram Language function, https://reference.wolfram.com/language/ref/CircumscribedBall.html.

Text

Wolfram Research (2023), CircumscribedBall, Wolfram Language function, https://reference.wolfram.com/language/ref/CircumscribedBall.html.

CMS

Wolfram Language. 2023. "CircumscribedBall." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CircumscribedBall.html.

APA

Wolfram Language. (2023). CircumscribedBall. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CircumscribedBall.html

BibTeX

@misc{reference.wolfram_2026_circumscribedball, author="Wolfram Research", title="{CircumscribedBall}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/CircumscribedBall.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_circumscribedball, organization={Wolfram Research}, title={CircumscribedBall}, year={2023}, url={https://reference.wolfram.com/language/ref/CircumscribedBall.html}, note=[Accessed: 12-June-2026]}