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RegionConvert
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RegionConvert

Updated in 14.1

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RegionConvert[reg,form]

converts the region representation reg to the specified form.

Details

  • RegionConvert will produce an expression equivalent to expr.
  • RegionConvert is typically used for comparing regions with different representations or to get a representation suitable for different functions, e.g. optimization expects implicit forms of region constraints, whereas integration over a region expects the parametric form of a region.
  • The following forms can be used for converting between region representations:
  • "Implicit"implicit representation
    "Mesh"mesh representation
    "Parametric"parametric representation
    "Spline"spline representation

Examples

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

Convert the unit disk to the implicit form:

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In[1]:=1
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https://wolfram.com/xid/0i1ptbg6s-2xydgs
Direct link to example
Out[1]=1

Parametric form:

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In[2]:=2
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https://wolfram.com/xid/0i1ptbg6s-5v3pw6
Direct link to example
Out[2]=2

Convert a cube to the implicit form:

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In[1]:=1
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https://wolfram.com/xid/0i1ptbg6s-p58ut
Direct link to example
Out[1]=1

Parametric form:

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In[2]:=2
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https://wolfram.com/xid/0i1ptbg6s-kdicv5
Direct link to example
Out[2]=2

Scope  (11)Survey of the scope of standard use cases

Special Regions  (5)

Convert Rectangle to the implicit form:

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In[1]:=1
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https://wolfram.com/xid/0i1ptbg6s-kij4q
Direct link to example
Out[1]=1

Parametric form:

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In[2]:=2
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https://wolfram.com/xid/0i1ptbg6s-ewues0
Direct link to example
Out[2]=2

Visualize it:

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In[3]:=3
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https://wolfram.com/xid/0i1ptbg6s-igwg55
Direct link to example
Out[3]=3

Convert DiskSegment to the implicit form:

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In[1]:=1
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https://wolfram.com/xid/0i1ptbg6s-miim3k
Direct link to example
Out[1]=1

Parametric form:

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In[2]:=2
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https://wolfram.com/xid/0i1ptbg6s-mhxeza
Direct link to example
Out[2]=2

Visualize it:

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In[3]:=3
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https://wolfram.com/xid/0i1ptbg6s-bcs6a5
Direct link to example
Out[3]=3

Convert CapsuleShape to the implicit form:

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In[1]:=1
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https://wolfram.com/xid/0i1ptbg6s-f0h323
Direct link to example
Out[1]=1

Parametric form:

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In[2]:=2
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https://wolfram.com/xid/0i1ptbg6s-i6jk1m
Direct link to example
Out[2]=2

Visualize it:

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In[3]:=3
✖
https://wolfram.com/xid/0i1ptbg6s-hwrtev
Direct link to example
Out[3]=3

Convert Hyperplane to the implicit form:

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In[1]:=1
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https://wolfram.com/xid/0i1ptbg6s-7iwuz
Direct link to example
Out[1]=1

Parametric form:

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In[2]:=2
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https://wolfram.com/xid/0i1ptbg6s-ch09za
Direct link to example
Out[2]=2

Visualize it:

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In[3]:=3
✖
https://wolfram.com/xid/0i1ptbg6s-eoxk6w
Direct link to example
Out[3]=3

Represent Sphere as a B-spline surface:

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In[1]:=1
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https://wolfram.com/xid/0i1ptbg6s-vu8hoo
Direct link to example
Out[1]=1

Visualize it, along with the control points:

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In[2]:=2
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https://wolfram.com/xid/0i1ptbg6s-mpfq7r
Direct link to example
Out[2]=2

Formula Regions  (2)

Convert an ImplicitRegion object to the implicit form:

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In[1]:=1
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https://wolfram.com/xid/0i1ptbg6s-gav02k
Direct link to example
Copy to clipboard.
In[2]:=2
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https://wolfram.com/xid/0i1ptbg6s-p5g6yh
Direct link to example
Out[2]=2

Convert a ParametricRegion object to the implicit form:

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In[1]:=1
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https://wolfram.com/xid/0i1ptbg6s-jn2pq8
Direct link to example
Copy to clipboard.
In[2]:=2
✖
https://wolfram.com/xid/0i1ptbg6s-bery3a
Direct link to example
Out[2]=2

Mesh Regions  (2)

Convert a MeshRegion object to the implicit form:

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In[13]:=13
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https://wolfram.com/xid/0i1ptbg6s-c8u11i
Direct link to example
Out[13]=13
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In[14]:=14
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https://wolfram.com/xid/0i1ptbg6s-efc9lj
Direct link to example
Out[14]=14

A mesh region with disconnected components:

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In[4]:=4
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https://wolfram.com/xid/0i1ptbg6s-hu8tog
Direct link to example
Out[4]=4
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In[5]:=5
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https://wolfram.com/xid/0i1ptbg6s-c567di
Direct link to example
Out[5]=5

Convert a BoundaryMeshRegion object to the implicit form:

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In[1]:=1
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https://wolfram.com/xid/0i1ptbg6s-mzbks2
Direct link to example
Out[1]=1
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In[2]:=2
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https://wolfram.com/xid/0i1ptbg6s-c8jhhl
Direct link to example
Out[2]=2

A boundary mesh region with disconnected components:

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In[3]:=3
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https://wolfram.com/xid/0i1ptbg6s-bmua2u
Direct link to example
Out[3]=3
Copy to clipboard.
In[4]:=4
✖
https://wolfram.com/xid/0i1ptbg6s-4bane
Direct link to example
Out[4]=4

Derived Regions  (2)

Convert a BooleanRegion object to the implicit form:

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In[4]:=4
✖
https://wolfram.com/xid/0i1ptbg6s-j262h
Direct link to example
Copy to clipboard.
In[5]:=5
✖
https://wolfram.com/xid/0i1ptbg6s-izi1np
Direct link to example
Out[5]=5

Visualize it:

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In[6]:=6
✖
https://wolfram.com/xid/0i1ptbg6s-koe3l9
Direct link to example
Out[6]=6

Convert a TransformedRegion object to the implicit form:

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In[1]:=1
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https://wolfram.com/xid/0i1ptbg6s-rd3iq1
Direct link to example
Copy to clipboard.
In[2]:=2
✖
https://wolfram.com/xid/0i1ptbg6s-hj2g71
Direct link to example
Out[2]=2

Visualize it:

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In[3]:=3
✖
https://wolfram.com/xid/0i1ptbg6s-c2ee5
Direct link to example
Out[3]=3

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

Compute the area of an annulus using its implicit form:

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In[2]:=2
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https://wolfram.com/xid/0i1ptbg6s-k1tqm
Direct link to example
Out[2]=2
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In[3]:=3
✖
https://wolfram.com/xid/0i1ptbg6s-bufvwl
Direct link to example
Out[3]=3

Compare:

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In[4]:=4
✖
https://wolfram.com/xid/0i1ptbg6s-jetzr4
Direct link to example
Out[4]=4

Compute the volume of a ball using its implicit form:

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In[1]:=1
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https://wolfram.com/xid/0i1ptbg6s-cwwbuj
Direct link to example
Out[1]=1
Copy to clipboard.
In[2]:=2
✖
https://wolfram.com/xid/0i1ptbg6s-geo5pm
Direct link to example
Out[2]=2

Compare:

Copy to clipboard.
In[3]:=3
✖
https://wolfram.com/xid/0i1ptbg6s-lhj8tp
Direct link to example
Out[3]=3

Find the projection of an implicit region on the plane in :

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In[1]:=1
✖
https://wolfram.com/xid/0i1ptbg6s-kgrvxn
Direct link to example
Copy to clipboard.
In[2]:=2
✖
https://wolfram.com/xid/0i1ptbg6s-ike791
Direct link to example

Visualize the projection:

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In[3]:=3
✖
https://wolfram.com/xid/0i1ptbg6s-jg191j
Direct link to example
Out[3]=3

Properties & Relations  (3)Properties of the function, and connections to other functions

Use CanonicalizePolygon to convert a region representation to a polygon form:

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In[1]:=1
✖
https://wolfram.com/xid/0i1ptbg6s-wmj05z
Direct link to example
Out[1]=1

Use CanonicalizePolyhedron to convert a region representation to a polyhedron form:

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In[1]:=1
✖
https://wolfram.com/xid/0i1ptbg6s-wrh8b9
Direct link to example
Out[1]=1

Use DiscretizeRegion to convert a region into a mesh:

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In[1]:=1
✖
https://wolfram.com/xid/0i1ptbg6s-7vplql
Direct link to example
Out[1]=1
Wolfram Research (2021), RegionConvert, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionConvert.html (updated 2024).
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Wolfram Research (2021), RegionConvert, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionConvert.html (updated 2024).

Text

Wolfram Research (2021), RegionConvert, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionConvert.html (updated 2024).

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Wolfram Research (2021), RegionConvert, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionConvert.html (updated 2024).

CMS

Wolfram Language. 2021. "RegionConvert." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/RegionConvert.html.

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Wolfram Language. 2021. "RegionConvert." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/RegionConvert.html.

APA

Wolfram Language. (2021). RegionConvert. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RegionConvert.html

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Wolfram Language. (2021). RegionConvert. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RegionConvert.html

BibTeX

@misc{reference.wolfram_2025_regionconvert, author="Wolfram Research", title="{RegionConvert}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/RegionConvert.html}", note=[Accessed: 26-March-2025 ]}

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@misc{reference.wolfram_2025_regionconvert, author="Wolfram Research", title="{RegionConvert}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/RegionConvert.html}", note=[Accessed: 26-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_regionconvert, organization={Wolfram Research}, title={RegionConvert}, year={2024}, url={https://reference.wolfram.com/language/ref/RegionConvert.html}, note=[Accessed: 26-March-2025 ]}

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@online{reference.wolfram_2025_regionconvert, organization={Wolfram Research}, title={RegionConvert}, year={2024}, url={https://reference.wolfram.com/language/ref/RegionConvert.html}, note=[Accessed: 26-March-2025 ]}