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ConvexRegionQ
✖
ConvexRegionQ

✖

gives True if reg is a convex region and False otherwise.

Details

  • A region is convex if no line segment between two points in the region ever goes outside the region.
  • A region is convex if for points p1,p2∈reg, λ p1+(1-λ)p2∈reg for all 0≤λ≤1.

Examples

open allclose all

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

Test whether a rectangle is convex:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-gnbcgh
Out[1]=1

A circle is not a convex region:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-gr0cff
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-hrgrv0
Out[2]=2

Scope  (20)Survey of the scope of standard use cases

Special Regions  (4)

Regions in including Point:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-7tst6f
Out[1]=1

Interval:

In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-dj73or
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0dcz7l4qmnyb-eoamtr
Out[4]=4

A HalfLine is unbounded:

In[5]:=5
✖
https://wolfram.com/xid/0dcz7l4qmnyb-p4ffeh
Out[5]=5

Regions in including Point:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-e3sii5
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-lba1w1
Out[2]=2

Line:

In[3]:=3
✖
https://wolfram.com/xid/0dcz7l4qmnyb-7ow13g
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0dcz7l4qmnyb-cvkhkk
Out[4]=4

Polygon:

In[5]:=5
✖
https://wolfram.com/xid/0dcz7l4qmnyb-n7vm36
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/0dcz7l4qmnyb-gcmddu
Out[6]=6

Circle:

In[7]:=7
✖
https://wolfram.com/xid/0dcz7l4qmnyb-v5tx6
Out[7]=7
In[8]:=8
✖
https://wolfram.com/xid/0dcz7l4qmnyb-8gritl
Out[8]=8

Disk:

In[9]:=9
✖
https://wolfram.com/xid/0dcz7l4qmnyb-siy4wx
Out[9]=9
In[10]:=10
✖
https://wolfram.com/xid/0dcz7l4qmnyb-i64gy
Out[10]=10

Regions in including Point:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-j2v4ga
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-eeut6h
Out[2]=2

Line:

In[3]:=3
✖
https://wolfram.com/xid/0dcz7l4qmnyb-r9ycq9
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0dcz7l4qmnyb-kntd0w
Out[4]=4

Polygon:

In[5]:=5
✖
https://wolfram.com/xid/0dcz7l4qmnyb-dna1yf
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/0dcz7l4qmnyb-5hlc7h
Out[6]=6

Cylinder:

In[7]:=7
✖
https://wolfram.com/xid/0dcz7l4qmnyb-q8f7mk
Out[7]=7
In[8]:=8
✖
https://wolfram.com/xid/0dcz7l4qmnyb-dd6avs
Out[8]=8

Regions in including Simplex in :

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-dvw3bn
Out[1]=1

Cuboid in :

In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-cst625
Out[2]=2

Ball in :

In[3]:=3
✖
https://wolfram.com/xid/0dcz7l4qmnyb-ml0h0x
Out[3]=3

Mesh Regions  (4)

MeshRegion in 1D:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-iqe1up
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-ehbrzk
Out[2]=2

2D:

In[3]:=3
✖
https://wolfram.com/xid/0dcz7l4qmnyb-c3y92k
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0dcz7l4qmnyb-gvtt33
Out[4]=4

3D:

In[5]:=5
✖
https://wolfram.com/xid/0dcz7l4qmnyb-cjwqu5
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/0dcz7l4qmnyb-unylaj
Out[6]=6

MeshRegion that represents a curve in 2D:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-qkprr
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-h9ete0
Out[2]=2

A MeshRegion can have components of different dimensions:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-cuq63
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-0no20h
Out[2]=2

BoundaryMeshRegion in 1D:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-drx9rf
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-c5odcz
Out[2]=2

2D:

In[3]:=3
✖
https://wolfram.com/xid/0dcz7l4qmnyb-f7vysv
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0dcz7l4qmnyb-ki2nz3
Out[4]=4

3D:

In[5]:=5
✖
https://wolfram.com/xid/0dcz7l4qmnyb-nptsvs
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/0dcz7l4qmnyb-ct48wo
Out[6]=6

Formula Regions  (3)

A parabolic region as an ImplicitRegion:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-xbpzk
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-wrqh28
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0dcz7l4qmnyb-qjnxx
Out[3]=3

A parabola represented as a ParametricRegion:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-fogd2z
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-8v8wqg
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0dcz7l4qmnyb-jgtmd
Out[3]=3

ImplicitRegion can have several components of different dimensions:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-d4mmo3
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-5yjq36
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0dcz7l4qmnyb-5bdj3a
Out[3]=3

Derived Regions  (6)

RegionIntersection of two regions:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-h26j4l
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-7i1z1p
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0dcz7l4qmnyb-qvjt67
Out[3]=3

RegionUnion of mixed-dimensional regions:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-2bfm2l
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-wio6nk
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0dcz7l4qmnyb-zbaaik
Out[3]=3

General BooleanRegion combination:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-0buysy
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-8a4r4a
Out[2]=2

TransformedRegion:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-rzrhgq
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-ke6drp
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0dcz7l4qmnyb-b8clh7
Out[3]=3

InverseTransformedRegion:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-ysabtk
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-f59beu
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0dcz7l4qmnyb-o0s5l3
Out[3]=3

RegionBoundary:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-9nd1ps
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-0buix0
Out[2]=2

Geographic Regions  (3)

Test a polygon with GeoPosition:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-1lk1dy
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-8vjhh8
Out[2]=2

Polygons with GeoPositionXYZ:

In[3]:=3
✖
https://wolfram.com/xid/0dcz7l4qmnyb-4dy58p
In[4]:=4
✖
https://wolfram.com/xid/0dcz7l4qmnyb-pzmsx0
Out[4]=4

Polygons with GeoPositionENU:

In[5]:=5
✖
https://wolfram.com/xid/0dcz7l4qmnyb-sz3fv8
In[6]:=6
✖
https://wolfram.com/xid/0dcz7l4qmnyb-pjpdg1
Out[6]=6

The area of a polygon with GeoGridPosition:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-ipsiqu
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-yjciq7
Out[2]=2

ConvexRegionQ works on polygons with geographic entities:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-zu3lep
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-njt70z
Out[2]=2

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

Platonic solids are convex:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-5za8yg
Out[1]=1

Test whether a basic region is convex:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-5qdx2d
Out[1]=1

The convex hull of a compound of five tetrahedra is a dodecahedron:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-wm7tr7
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-bzqthc
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0dcz7l4qmnyb-ndgyn2
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0dcz7l4qmnyb-wfug83
Out[4]=4

Test whether a polygon is concave:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-9imvre
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-vigl3p
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0dcz7l4qmnyb-2tz0wv
Out[3]=3

Generate random polygons for testing algorithms and verification of time complexity:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-dko19g
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-i6opfi
In[3]:=3
✖
https://wolfram.com/xid/0dcz7l4qmnyb-34otit
Out[3]=3

Time complexity for algorithms for convex polygons:

In[4]:=4
✖
https://wolfram.com/xid/0dcz7l4qmnyb-hqm8h7
In[5]:=5
✖
https://wolfram.com/xid/0dcz7l4qmnyb-oztoqj
Out[5]=5

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

If two regions are convex, the intersection is convex:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-9d8dsw
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-ftmyqn
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0dcz7l4qmnyb-bkxhrt
Out[3]=3

The InverseTransformedRegion of a convex region is convex:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-n54l2r
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-ia1t51
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0dcz7l4qmnyb-nmznzh
Out[3]=3

Using ConvexHullRegion to create a convex region:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-b8g6ay
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-vqsuum
Out[2]=2

Possible Issues  (1)Common pitfalls and unexpected behavior

ConvexRegionQ returns False for nonconstant regions:

In[1]:=1
✖
https://wolfram.com/xid/0dcz7l4qmnyb-dft85s
In[2]:=2
✖
https://wolfram.com/xid/0dcz7l4qmnyb-d4damb
Out[2]=2
Wolfram Research (2020), ConvexRegionQ, Wolfram Language function, https://reference.wolfram.com/language/ref/ConvexRegionQ.html.
✖
Wolfram Research (2020), ConvexRegionQ, Wolfram Language function, https://reference.wolfram.com/language/ref/ConvexRegionQ.html.

Text

Wolfram Research (2020), ConvexRegionQ, Wolfram Language function, https://reference.wolfram.com/language/ref/ConvexRegionQ.html.

✖
Wolfram Research (2020), ConvexRegionQ, Wolfram Language function, https://reference.wolfram.com/language/ref/ConvexRegionQ.html.

CMS

Wolfram Language. 2020. "ConvexRegionQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ConvexRegionQ.html.

✖
Wolfram Language. 2020. "ConvexRegionQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ConvexRegionQ.html.

APA

Wolfram Language. (2020). ConvexRegionQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ConvexRegionQ.html

✖
Wolfram Language. (2020). ConvexRegionQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ConvexRegionQ.html

BibTeX

@misc{reference.wolfram_2025_convexregionq, author="Wolfram Research", title="{ConvexRegionQ}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/ConvexRegionQ.html}", note=[Accessed: 27-April-2025 ]}

✖
@misc{reference.wolfram_2025_convexregionq, author="Wolfram Research", title="{ConvexRegionQ}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/ConvexRegionQ.html}", note=[Accessed: 27-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_convexregionq, organization={Wolfram Research}, title={ConvexRegionQ}, year={2020}, url={https://reference.wolfram.com/language/ref/ConvexRegionQ.html}, note=[Accessed: 27-April-2025 ]}

✖
@online{reference.wolfram_2025_convexregionq, organization={Wolfram Research}, title={ConvexRegionQ}, year={2020}, url={https://reference.wolfram.com/language/ref/ConvexRegionQ.html}, note=[Accessed: 27-April-2025 ]}