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CapsuleShape
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CapsuleShape

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CapsuleShape[{{x1,y1,z1},{x2,y2,z2}},r]

represents the filled capsule between points {xi,yi,zi} and radius r.

Details and Options

Examples

open allclose all

Basic Examples  (2)Summary of the most common use cases

The standard capsule centered at the origin:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-hqtlth
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0k7y41qrt5z92-c7o
Out[2]=2

Volume and centroid:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-7wedhk
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0k7y41qrt5z92-kxw6nj
Out[2]=2

Scope  (19)Survey of the scope of standard use cases

Graphics  (9)

Specification  (4)

The standard capsule:

In[2]:=2
✖
https://wolfram.com/xid/0k7y41qrt5z92-e64f58
Out[2]=2
In[1]:=1
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https://wolfram.com/xid/0k7y41qrt5z92-btz1q2
Out[1]=1

Capsules with different endpoints:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-g96s5y
Out[1]=1

Capsules with different radii:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-l0hn2
Out[1]=1

Short form for a capsule at the origin:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-37iz6
Out[1]=1

Styling  (4)

Colored capsules:

In[1]:=1
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https://wolfram.com/xid/0k7y41qrt5z92-cdxdbh
Out[1]=1

Different properties can be specified for the front and back of faces using FaceForm:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-vb6wx
Out[1]=1

Capsules with different specular exponents:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-d1tyd0
Out[1]=1

White capsule that glows red:

In[2]:=2
✖
https://wolfram.com/xid/0k7y41qrt5z92-ca9zt
Out[2]=2

Opacity specifies the face opacity:

In[1]:=1
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https://wolfram.com/xid/0k7y41qrt5z92-v6995
Out[1]=1

Coordinates  (1)

Points can be Dynamic:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-6gl1zz
Out[1]=1

Regions  (10)

Embedding dimension is the dimension of the space in which the capsule lives:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-y220
Out[1]=1

Geometric dimension is the dimension of the shape itself:

In[2]:=2
✖
https://wolfram.com/xid/0k7y41qrt5z92-bx9tom
Out[2]=2

Membership testing:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-c7lq97
In[2]:=2
✖
https://wolfram.com/xid/0k7y41qrt5z92-f70gib
Out[2]=2

Get conditions for point membership:

In[3]:=3
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https://wolfram.com/xid/0k7y41qrt5z92-inebf9
Out[3]=3

Volume:

In[1]:=1
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https://wolfram.com/xid/0k7y41qrt5z92-se0twe
In[2]:=2
✖
https://wolfram.com/xid/0k7y41qrt5z92-e06l44
Out[2]=2

Centroid:

In[3]:=3
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https://wolfram.com/xid/0k7y41qrt5z92-gwq4b4
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0k7y41qrt5z92-oknxhk
Out[4]=4

Distance from a point:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-jcsb4b
In[2]:=2
✖
https://wolfram.com/xid/0k7y41qrt5z92-8aexdg
Out[2]=2

Signed distance from a point:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-kjgbyj
In[2]:=2
✖
https://wolfram.com/xid/0k7y41qrt5z92-zognbt
Out[2]=2

Nearest point in the region:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-d7g53y
In[2]:=2
✖
https://wolfram.com/xid/0k7y41qrt5z92-mtue
Out[2]=2

Nearest points to an enclosing sphere:

In[3]:=3
✖
https://wolfram.com/xid/0k7y41qrt5z92-e29k5d
In[4]:=4
✖
https://wolfram.com/xid/0k7y41qrt5z92-5ksoo8
In[5]:=5
✖
https://wolfram.com/xid/0k7y41qrt5z92-uv1cfm
Out[5]=5

A capsule is bounded:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-dym4fu
In[2]:=2
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https://wolfram.com/xid/0k7y41qrt5z92-i3tfrr
Out[2]=2

Find its range:

In[3]:=3
✖
https://wolfram.com/xid/0k7y41qrt5z92-l3exhn
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0k7y41qrt5z92-bx1r15
Out[4]=4

Integrate over a capsule region:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-fivgav
In[2]:=2
✖
https://wolfram.com/xid/0k7y41qrt5z92-banwkr
Out[2]=2

Optimize over a capsule region:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-nf9ton
In[2]:=2
✖
https://wolfram.com/xid/0k7y41qrt5z92-hyz4dq
Out[2]=2

Solve equations in a capsule region:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-bnrw6
In[2]:=2
✖
https://wolfram.com/xid/0k7y41qrt5z92-lhnpf3
Out[2]=2

Applications  (6)Sample problems that can be solved with this function

Visualize the Platonic solids using CapsuleShape for the edges:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-2qjdfs
Out[1]=1

Use CapsuleShape to render edges in a GraphPlot3D:

In[1]:=1
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https://wolfram.com/xid/0k7y41qrt5z92-u52ea
Out[1]=1

Use CapsuleShape to render edges in 3D for Graph objects:

In[1]:=1
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https://wolfram.com/xid/0k7y41qrt5z92-bd33w
Out[1]=1

Embed the graph in 3D and use CapsuleShape:

In[2]:=2
✖
https://wolfram.com/xid/0k7y41qrt5z92-8og3p
Out[2]=2

Use CapsuleShape to render edges in 3D BoundaryMeshRegion and MeshRegion objects:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-ha3ypo
Out[1]=1

Using a series of capsules (and a ball), you can create a stick figure:

In[1]:=1
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https://wolfram.com/xid/0k7y41qrt5z92-kjzjdr
In[2]:=2
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https://wolfram.com/xid/0k7y41qrt5z92-kuwjtr
In[3]:=3
✖
https://wolfram.com/xid/0k7y41qrt5z92-jscy64
Out[3]=3

Furthermore, you can use RotationTransform to make the stick figure's limbs pivot:

In[4]:=4
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https://wolfram.com/xid/0k7y41qrt5z92-yffc4
In[5]:=5
✖
https://wolfram.com/xid/0k7y41qrt5z92-dkc9x1
Out[5]=5

CO2 cartridges have many applications, ranging from sports to soda-making to life jackets. A 12g CO2 cartridge is about 18.6 mm in diameter and 82.5 mm long, with a neck about 12 mm long and 7.3 mm in diameter:

In[1]:=1
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https://wolfram.com/xid/0k7y41qrt5z92-fnusxy

It can be approximated as a capsule and a cylinder:

In[2]:=2
✖
https://wolfram.com/xid/0k7y41qrt5z92-brp46l
In[3]:=3
✖
https://wolfram.com/xid/0k7y41qrt5z92-mgksm
Out[3]=3

Knowing that the ideal gas law states , where is the universal gas constant, find the volume of the gas within the cartridge at standard temperature and pressure (273.15 K and 1 bar):

In[4]:=4
✖
https://wolfram.com/xid/0k7y41qrt5z92-p8o0ho
Out[4]=4

Find the ratio of the normal to compressed volume:

In[5]:=5
✖
https://wolfram.com/xid/0k7y41qrt5z92-cybbw9
Out[5]=5

Properties & Relations  (6)Properties of the function, and connections to other functions

The 2D version of CapsuleShape is StadiumShape:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-w9d5pi
Out[1]=1

Ball is the limit of CapsuleShape as p1 approaches p2:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-nbfmqu
Out[1]=1

A CapsuleShape formed from the RegionUnion of balls and a cylinder:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-kqbrp8
In[2]:=2
✖
https://wolfram.com/xid/0k7y41qrt5z92-fnab5w
Out[2]=2

The volume is the sum of ball and cylinder volumes:

In[3]:=3
✖
https://wolfram.com/xid/0k7y41qrt5z92-g2pbs1
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0k7y41qrt5z92-3skz2
Out[4]=4

CapsuleShape is all points at most from a Line:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-buaxwa
In[2]:=2
✖
https://wolfram.com/xid/0k7y41qrt5z92-j7ugz8
Out[2]=2

ImplicitRegion can represent any CapsuleShape:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-dxgz06
In[2]:=2
✖
https://wolfram.com/xid/0k7y41qrt5z92-x052kg
In[3]:=3
✖
https://wolfram.com/xid/0k7y41qrt5z92-w46t89
Out[3]=3

A rounded Tube looks like a CapsuleShape:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-je7ia
Out[1]=1

Neat Examples  (3)Surprising or curious use cases

Random unit capsules:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-fbt4h6
Out[1]=1

Sweep a capsule around an axis:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-t3qbb8
Out[1]=1

Nested transparent capsules:

In[1]:=1
✖
https://wolfram.com/xid/0k7y41qrt5z92-ffbvsr
Out[1]=1
Wolfram Research (2015), CapsuleShape, Wolfram Language function, https://reference.wolfram.com/language/ref/CapsuleShape.html.
✖
Wolfram Research (2015), CapsuleShape, Wolfram Language function, https://reference.wolfram.com/language/ref/CapsuleShape.html.

Text

Wolfram Research (2015), CapsuleShape, Wolfram Language function, https://reference.wolfram.com/language/ref/CapsuleShape.html.

✖
Wolfram Research (2015), CapsuleShape, Wolfram Language function, https://reference.wolfram.com/language/ref/CapsuleShape.html.

CMS

Wolfram Language. 2015. "CapsuleShape." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CapsuleShape.html.

✖
Wolfram Language. 2015. "CapsuleShape." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CapsuleShape.html.

APA

Wolfram Language. (2015). CapsuleShape. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CapsuleShape.html

✖
Wolfram Language. (2015). CapsuleShape. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CapsuleShape.html

BibTeX

@misc{reference.wolfram_2025_capsuleshape, author="Wolfram Research", title="{CapsuleShape}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/CapsuleShape.html}", note=[Accessed: 29-April-2025 ]}

✖
@misc{reference.wolfram_2025_capsuleshape, author="Wolfram Research", title="{CapsuleShape}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/CapsuleShape.html}", note=[Accessed: 29-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_capsuleshape, organization={Wolfram Research}, title={CapsuleShape}, year={2015}, url={https://reference.wolfram.com/language/ref/CapsuleShape.html}, note=[Accessed: 29-April-2025 ]}

✖
@online{reference.wolfram_2025_capsuleshape, organization={Wolfram Research}, title={CapsuleShape}, year={2015}, url={https://reference.wolfram.com/language/ref/CapsuleShape.html}, note=[Accessed: 29-April-2025 ]}