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DiskSegment
✖
DiskSegment

✖
DiskSegment[{x,y},r,{θ1,θ2}]

represents the disk segment from angle θ1 to θ2 in a disk centered at {x,y} of radius r.

✖
DiskSegment[{x,y},{rx,ry},{θ1,θ2}]

represents the ellipse segment from angle θ1 to θ2 in an axis-aligned ellipse with semiaxes lengths rx and ry.

Details and Options

  • DiskSegment can be used as a geometric region and a graphics primitive.
  • DiskSegment represents the filled segment part of Disk with the same arguments.
  • Angles are measured in radians counterclockwise from the positive x direction.
  • DiskSegment can be used in Graphics.
  • In graphics, the point {x,y} can be Dynamic expressions.
  • Graphics rendering is affected by directives such as FaceForm, EdgeForm, and color.

Examples

open allclose all

Basic Examples  (5)Summary of the most common use cases

Half of a unit disk:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-hyt4k
Out[1]=1

A disk segment:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-bfjqp8
Out[1]=1

A segment of an elliptical disk:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-ji3kpm
Out[1]=1

Differently styled disk segments:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-kweje
Out[1]=1

Get the Area of a disk segment (half disk):

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-98q61
Out[1]=1

The area of an ellipse segment:

In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-ib74kk
Out[2]=2

Scope  (17)Survey of the scope of standard use cases

Graphics  (7)

Specification  (4)

Specify radii:

In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-ha2yy
Out[2]=2

Specify centers:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-grolsm
Out[1]=1

Specify the angle:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-cgrbk7
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-d643pc
Out[2]=2

An elliptical disk segment:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-fdnn39
Out[1]=1

Styling  (2)

Color directives specify the face colors of disk segments:

In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-nnskqd
Out[2]=2

FaceForm and EdgeForm can be used to specify the styles of the interiors and boundaries:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-ju7459
Out[1]=1

Boundaries of a disk segment:

In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-dkckj
Out[2]=2

Coordinates  (1)

Points can be Dynamic:

In[4]:=4
✖
https://wolfram.com/xid/0mlbmx4owowi-6gl1zz
Out[4]=4

Regions  (10)

Embedding dimension:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-y220
Out[1]=1

Geometric dimension:

In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-bx9tom
Out[2]=2

Point membership test:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-ck0pr1
Out[1]=1

Get conditions for point membership:

In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-l724rh
Out[2]=2

Area:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-1kpb38
In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-b92dul
Out[2]=2

Centroid:

In[3]:=3
✖
https://wolfram.com/xid/0mlbmx4owowi-dxlbau
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0mlbmx4owowi-5fiohw
Out[4]=4

Distance from a point:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-efuwvi
In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-bjikjq
Out[2]=2

Signed distance from a point:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-cybvpc
In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-bm4ed
Out[2]=2

Nearest point in the region:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-btejnv
In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-et4yza
Out[2]=2

Nearest points:

In[3]:=3
✖
https://wolfram.com/xid/0mlbmx4owowi-eoyt0e
In[4]:=4
✖
https://wolfram.com/xid/0mlbmx4owowi-fq1ssz
Out[4]=4

An ellipse segment is bounded:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-gqhe1k
In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-b5d6xy
Out[2]=2

Get its range:

In[3]:=3
✖
https://wolfram.com/xid/0mlbmx4owowi-vq86d4
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0mlbmx4owowi-jl5g5a
Out[4]=4

Integrate over an ellipse segment:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-fivgav
In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-banwkr
Out[2]=2

Optimize over an ellipse segment:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-rk57l2
In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-hyz4dq
Out[2]=2

Solve equations in an ellipse segment:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-bnrw6
In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-c7lkth
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0mlbmx4owowi-jacwaq
Out[3]=3

Applications  (5)Sample problems that can be solved with this function

Plot a function over a disk segment:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-ubcdr9
Out[1]=1

Create a 3D disk segment extrusion with RegionProduct:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-xqbmll
In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-efqqx9
Out[2]=2

To show the region difference between a disk and a regular polygon, a set of disk segments may be used. First you get a set of arcs:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-kgkpgd
Out[1]=1

However, some of arcs are not increasing angle ranges, so in those cases is added to the second angle to make it increasing:

In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-f5my01
Out[2]=2

Finally, visualize:

In[3]:=3
✖
https://wolfram.com/xid/0mlbmx4owowi-c9rejn
Out[3]=3

A lens can be modeled as two adjacent disk segments. Create a rightward-facing lens segment of height and radius of , centered on the origin:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-frm94l
In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-h3i2y1
Out[2]=2

For the leftward-facing part of the lens, you need to switch the position and switch the direction of the arc:

In[3]:=3
✖
https://wolfram.com/xid/0mlbmx4owowi-b1w9z
In[4]:=4
✖
https://wolfram.com/xid/0mlbmx4owowi-cf69o1
Out[4]=4

Now make a function that will construct a pair of disk segments for given height and radii, and visualize it for a range of radius values:

In[5]:=5
✖
https://wolfram.com/xid/0mlbmx4owowi-bga70i
In[6]:=6
✖
https://wolfram.com/xid/0mlbmx4owowi-zr47v
Out[6]=6

You can find an approximate measure of a region by finding the fraction of random points within a region of known volume that fall within the region whose measure you seek. Use a disk segment as an example:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-dszu2i

This region can be contained within the region and , which has an area of 16. Generate a list of random points within this general region:

In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-xugmz

Find the percent of these random points that fall within the disk segment:

In[3]:=3
✖
https://wolfram.com/xid/0mlbmx4owowi-cfu87x
Out[3]=3

The area of the region (the disk segment) should be close to that ratio times the area over which the random points are distributed. Compare this approximation to the actual value:

In[4]:=4
✖
https://wolfram.com/xid/0mlbmx4owowi-ckvka1
Out[4]=4
In[5]:=5
✖
https://wolfram.com/xid/0mlbmx4owowi-zyquu
Out[5]=5

Properties & Relations  (4)Properties of the function, and connections to other functions

DiskSegment can be represented by a FilledCurve:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-fg0xy9
In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-m8qtk2
In[3]:=3
✖
https://wolfram.com/xid/0mlbmx4owowi-f32m64
Out[3]=3

A disk segment may result from the RegionIntersection of a Disk and another region:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-fex658
In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-w76vsx
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0mlbmx4owowi-vx78oy
Out[3]=3

ImplicitRegion can represent any DiskSegment:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-dxgz06
In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-i1r2cs
In[3]:=3
✖
https://wolfram.com/xid/0mlbmx4owowi-b56hh2
Out[3]=3

ParametricRegion can represent a DiskSegment:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-6nmxzs
In[2]:=2
✖
https://wolfram.com/xid/0mlbmx4owowi-zgzu65
In[3]:=3
✖
https://wolfram.com/xid/0mlbmx4owowi-80tx6x
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0mlbmx4owowi-ntipsv
Out[4]=4

Neat Examples  (3)Surprising or curious use cases

Random disk segment collections:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-05l4p
Out[1]=1

A family of disk segments:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-6xqpd
Out[1]=1

Digital petals:

In[1]:=1
✖
https://wolfram.com/xid/0mlbmx4owowi-dqe8jj
Out[1]=1
Wolfram Research (2015), DiskSegment, Wolfram Language function, https://reference.wolfram.com/language/ref/DiskSegment.html.
✖
Wolfram Research (2015), DiskSegment, Wolfram Language function, https://reference.wolfram.com/language/ref/DiskSegment.html.

Text

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

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

CMS

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

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

APA

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

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

BibTeX

@misc{reference.wolfram_2025_disksegment, author="Wolfram Research", title="{DiskSegment}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/DiskSegment.html}", note=[Accessed: 29-April-2025 ]}

✖
@misc{reference.wolfram_2025_disksegment, author="Wolfram Research", title="{DiskSegment}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/DiskSegment.html}", note=[Accessed: 29-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_disksegment, organization={Wolfram Research}, title={DiskSegment}, year={2015}, url={https://reference.wolfram.com/language/ref/DiskSegment.html}, note=[Accessed: 29-April-2025 ]}

✖
@online{reference.wolfram_2025_disksegment, organization={Wolfram Research}, title={DiskSegment}, year={2015}, url={https://reference.wolfram.com/language/ref/DiskSegment.html}, note=[Accessed: 29-April-2025 ]}