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CircularArcThrough
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CircularArcThrough

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CircularArcThrough[{p1,p2,…}]

represents a circular arc passing through the points pi.

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CircularArcThrough[{p1,p2,…},q]

represents a circular arc with center q.

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CircularArcThrough[{p1,p2,…},q,r]

represents a circular arc with radius r.

Details

Examples

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

A circular arc passing through three points:

In[1]:=1
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https://wolfram.com/xid/0fq4uw97ur71m-ex52rz
In[2]:=2
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https://wolfram.com/xid/0fq4uw97ur71m-8omd3e
Out[2]=2

Display the arc:

In[3]:=3
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https://wolfram.com/xid/0fq4uw97ur71m-3jd653
Out[3]=3

ArcLength of an arc passing through a set of points:

In[1]:=1
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https://wolfram.com/xid/0fq4uw97ur71m-5zszx5
Out[1]=1

Scope  (3)Survey of the scope of standard use cases

CircularArcThrough works on coordinates:

In[4]:=4
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https://wolfram.com/xid/0fq4uw97ur71m-0od1tm
Out[4]=4

Multiple points:

In[8]:=8
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https://wolfram.com/xid/0fq4uw97ur71m-oekcq6
Out[8]=8

Specify constraints for the center of the circular arc:

In[1]:=1
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https://wolfram.com/xid/0fq4uw97ur71m-b01me0
Out[1]=1

Constraints on the radius:

In[2]:=2
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https://wolfram.com/xid/0fq4uw97ur71m-hm86po
Out[2]=2

CircularArcThrough works with points in 2D:

In[1]:=1
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https://wolfram.com/xid/0fq4uw97ur71m-7ysgzb
Out[1]=1

Applications  (3)Sample problems that can be solved with this function

Basic Applications  (3)

Visualize the arc passing through three points:

In[1]:=1
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https://wolfram.com/xid/0fq4uw97ur71m-nfu42m
In[2]:=2
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https://wolfram.com/xid/0fq4uw97ur71m-hvl9sc
Out[2]=2

Find the implicit representation of the arc passing through three points:

In[1]:=1
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https://wolfram.com/xid/0fq4uw97ur71m-0x47om
Out[1]=1

The parametric representation:

In[2]:=2
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https://wolfram.com/xid/0fq4uw97ur71m-dovl1h
Out[2]=2

Find the circumcircle of a triangle:

In[1]:=1
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https://wolfram.com/xid/0fq4uw97ur71m-zf15dh
In[2]:=2
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https://wolfram.com/xid/0fq4uw97ur71m-6xil7p
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0fq4uw97ur71m-6ciqa2
Out[3]=3

Properties & Relations  (5)Properties of the function, and connections to other functions

CircularArcThrough returns a Circle:

In[1]:=1
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https://wolfram.com/xid/0fq4uw97ur71m-9h0c60
In[7]:=7
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https://wolfram.com/xid/0fq4uw97ur71m-oj10iv
Out[7]=7

Use RegionMember to test point membership:

In[1]:=1
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https://wolfram.com/xid/0fq4uw97ur71m-7u3io1
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0fq4uw97ur71m-zrbsng
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0fq4uw97ur71m-th9aki
Out[3]=3

CircularArcThrough gives a circular arc passing through points:

In[1]:=1
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https://wolfram.com/xid/0fq4uw97ur71m-h4lk9x
In[2]:=2
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https://wolfram.com/xid/0fq4uw97ur71m-uzjauh
Out[2]=2

Obtain the full circle:

In[3]:=3
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https://wolfram.com/xid/0fq4uw97ur71m-81c4i3
Out[3]=3

Use RegionFit to find a circle that fits a set of points:

In[1]:=1
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https://wolfram.com/xid/0fq4uw97ur71m-nbp42n
In[2]:=2
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https://wolfram.com/xid/0fq4uw97ur71m-7ezrw3
Out[2]=2

The arc passing the first 3 points:

In[3]:=3
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https://wolfram.com/xid/0fq4uw97ur71m-xj5rvr
Out[3]=3

Use CirclePoints to generate equally spaced points on the unit circle:

In[1]:=1
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https://wolfram.com/xid/0fq4uw97ur71m-y4b22g
Out[1]=1

An arc passing through points on the unit circle:

In[2]:=2
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https://wolfram.com/xid/0fq4uw97ur71m-hcbyp0
Out[2]=2
Wolfram Research (2022), CircularArcThrough, Wolfram Language function, https://reference.wolfram.com/language/ref/CircularArcThrough.html.
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Wolfram Research (2022), CircularArcThrough, Wolfram Language function, https://reference.wolfram.com/language/ref/CircularArcThrough.html.

Text

Wolfram Research (2022), CircularArcThrough, Wolfram Language function, https://reference.wolfram.com/language/ref/CircularArcThrough.html.

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Wolfram Research (2022), CircularArcThrough, Wolfram Language function, https://reference.wolfram.com/language/ref/CircularArcThrough.html.

CMS

Wolfram Language. 2022. "CircularArcThrough." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CircularArcThrough.html.

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Wolfram Language. 2022. "CircularArcThrough." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CircularArcThrough.html.

APA

Wolfram Language. (2022). CircularArcThrough. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CircularArcThrough.html

✖
Wolfram Language. (2022). CircularArcThrough. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CircularArcThrough.html

BibTeX

@misc{reference.wolfram_2025_circulararcthrough, author="Wolfram Research", title="{CircularArcThrough}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/CircularArcThrough.html}", note=[Accessed: 28-March-2025 ]}

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@misc{reference.wolfram_2025_circulararcthrough, author="Wolfram Research", title="{CircularArcThrough}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/CircularArcThrough.html}", note=[Accessed: 28-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_circulararcthrough, organization={Wolfram Research}, title={CircularArcThrough}, year={2022}, url={https://reference.wolfram.com/language/ref/CircularArcThrough.html}, note=[Accessed: 28-March-2025 ]}

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@online{reference.wolfram_2025_circulararcthrough, organization={Wolfram Research}, title={CircularArcThrough}, year={2022}, url={https://reference.wolfram.com/language/ref/CircularArcThrough.html}, note=[Accessed: 28-March-2025 ]}