RegionQ
RegionQ
Examples
open all close allBasic Examples (3)
RegionQ[Circle[]]RegionQ[Cuboid[{a, b, c}, {d, e, f}]]RegionQ[ImplicitRegion[x ^ 2 + y ^ 2 ≤ 1, {x, y}]]RegionQ[ParametricRegion[{Cos[t], Sin[t]}, {{t, 0, 2π}}]]ℛ = DelaunayMesh[RandomReal[1, {25, 2}]]RegionQ[ℛ]ℛ = ConvexHullMesh[RandomReal[1, {25, 2}]]RegionQ[ℛ]Scope (19)
Special Regions (4)
Regions in 
including Point:
RegionQ[Point[{1}]]ℛ = Interval[{1, 2}];
NumberLinePlot[ℛ]RegionQ[ℛ]Regions in 
including Point:
ℛ = Point[Tuples[Range[5], 2]];
Region[ℛ]RegionQ[ℛ]Line:
ℛ = Line[{{1, 2}, {4, 3}}];
Region[ℛ]RegionQ[ℛ]ℛ = Circle[{1, 2}, 3];
Region[ℛ]RegionQ[ℛ]Disk:
ℛ = Disk[{1, 2}, {4, 3}];
Region[ℛ]RegionQ[ℛ]Regions in 
including Point:
ℛ = Point[Tuples[Range[5], 3]];
Region[ℛ]RegionQ[ℛ]Line:
ℛ = Line[{{1, 2, 3}, {6, 5, 4}}];
Region[ℛ]RegionQ[ℛ]ℛ = Polygon[{{0, 0}, {2, -1}, {1, 0}, {2, 1}}];
Region[ℛ]RegionQ[ℛ]ℛ = Cylinder[{{0, 0, 0}, {1, 1, 1}}, 2];
Region[ℛ]RegionQ[ℛ]Regions in 
including Simplex in 
:
RegionQ[Simplex[{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}]]Cuboid in 
:
RegionQ[Cuboid[{1, 2, 3, 4, 5}, {6, 7, 8, 9, 10}]]Ball in 
:
RegionQ[Ball[{1, 2, 3, 4, 5, 6, 7}, 8]]Formula Regions (3)
A disk represented as an ImplicitRegion:
RegionQ[ImplicitRegion[x^2 + y^2 ≤ 1, {x, y}]]RegionQ[ImplicitRegion[x^2 + y^2 ≤ 1, {x, y, {z, 0, 2}}]]A disk represented as a ParametricRegion:
RegionQ[ParametricRegion[{r Cos[θ], r Sin[θ]}, {{r, 0, 1}, {θ, 0, 2π}}]]Using a rational parametrization of the disk:
RegionQ[ParametricRegion[{r(1 - t^2/1 + t^2), r(2t/1 + t^2)}, {t, {r, 0, 1}}]]RegionQ[ParametricRegion[{r Cos[θ], r Sin[θ], z}, {{r, 0, 1}, {θ, 0, 2π}, {z, 0, 2}}]]ImplicitRegion can have several components of different dimension:
ℛ = ImplicitRegion[x^2 + y^2 ≤ 1∨x == y, {x, y}];DiscretizeRegion[ℛ, {{-2, 2}, {-2, 2}}]RegionQ[ℛ]Mesh Regions (4)
MeshRegion in 1D:
DelaunayMesh[RandomReal[1, {10, 1}]]RegionQ[%]DelaunayMesh[RandomReal[1, {50, 2}]]RegionQ[%]DelaunayMesh[RandomReal[1, {100, 3}]]RegionQ[%]BoundaryMeshRegion in 1D:
ConvexHullMesh[RandomReal[1, {10, 1}]]RegionQ[%]ConvexHullMesh[RandomReal[1, {50, 2}]]RegionQ[%]ConvexHullMesh[RandomReal[1, {50, 3}]]RegionQ[%]MeshRegion that represents a curve in 2D:
ℛ = MeshRegion[{{0, 0}, {1, 0}, {2, -1}, {2, 1}}, {Line[{{1, 2, 3, 4, 2}}]}]RegionQ[ℛ]A MeshRegion can have components of different dimension:
ℛ = MeshRegion[{{0, 0}, {1, 0}, {2, -1}, {2, 1}}, {Line[{{1, 2}}], Polygon[{{2, 3, 4}}]}]RegionQ[ℛ]Derived Regions (4)
RegionIntersection of two regions:
ℛ = RegionIntersection[Disk[{0, 0}, 1], Disk[{0, 1}, 1]];Region[ℛ]RegionQ[ℛ]RegionUnion of mixed-dimensional regions:
ℛ = RegionUnion[Circle[{1, 0}, 1], Disk[{0, 0}, 1]];Region[ℛ]RegionQ[ℛ]ℛ = TransformedRegion[Disk[{0, 0}, 1], ScalingTransform[{3, 2}]];Region[ℛ]RegionQ[ℛ]Subscript[ℛ, 1] = Disk[];
Subscript[ℛ, 2] = RegionBoundary[Subscript[ℛ, 1]]Graphics[{{Yellow, Subscript[ℛ, 1]}, {Red, Subscript[ℛ, 2]}}]{RegionQ[Subscript[ℛ, 1]], RegionQ[Subscript[ℛ, 2]]}Geographical Regions (2)
Polygons with GeoPosition:
ℛ = Polygon[GeoPosition[{{{40.083441, -88.235716}, {40.083607, -88.257488}, {40.082603, -88.257149},
{40.076136999999996, -88.25740499999999}, {40.076178, -88.270888}, {40.076516, -88.271558},
{40.083686, -88.271512}, {40.083659999999995, -88.267046}, ... 33323}, {40.098112, -88.228687},
{40.095216, -88.228627}, {40.095179, -88.238547}, {40.094480999999995, -88.238546},
{40.094508999999995, -88.23267}, {40.094106, -88.232556}, {40.090666999999996, -88.232477},
{40.090741, -88.235745}}}]];RegionQ[ℛ]Polygons with GeoPositionXYZ:
ℛ = Polygon[GeoPositionXYZ[{{{150451.6968462432, -4.884430486484052*^6, 4.085078564164219*^6},
{148595.27532671497, -4.884475441490381*^6, 4.085092666620835*^6},
{148626.35829777512, -4.884546311005128*^6, 4.0850073717259285*^6},
{148618.5908634042 ... 7*^6, 4.0860187668081024*^6},
{150697.56410771207, -4.8836599487428395*^6, 4.085984535480795*^6},
{150711.88303095422, -4.883905546449982*^6, 4.0856924143435075*^6},
{150433.15479548014, -4.883908845676418*^6, 4.0856987003255524*^6}}}]];RegionQ[ℛ]Polygons with GeoPositionENU:
ℛ = Polygon[GeoPositionENU[{{{3378.2547059731055, -3369.2234780923936, -0.7440009205072329},
{1521.3211635380246, -3351.391253626573, -0.022340134218666208},
{1550.2571145363192, -3462.8657556618973, -0.08899812728964207},
{1528.5672303494055, -418 ... 63383291193, -0.37494203351275246},
{3654.121991908476, -2566.7472331234085, -0.5214977847472255},
{3375.420726854886, -2558.6597093173914, -0.3648706331350695}}},
GeoPosition[{40.11379115639895, -88.2753251202516, -1.0415787873318691}]]];RegionQ[ℛ]Polygons with GeoGridPosition:
ℛ = Polygon[GeoGridPosition[{{{-0.9950503945490105, 1.2366760550756015},
{-0.9952074890903578, 1.2369207053693891}, {-0.9952196732768064, 1.2369073327446167},
{-0.9953160063787643, 1.236848436956935}, {-0.9954141759436825, 1.2369993898475449},
{-0. ... 197645333103}, {-0.9949098578570917, 1.2368130881428654},
{-0.9948663952535768, 1.2367477711687371}, {-0.9948714472169538, 1.2367426500757825},
{-0.9949211061652593, 1.2367089232486177}, {-0.9949439717990124, 1.236746107097628}}}, "Bonne"]];RegionQ[ℛ]CSG Regions (1)
CSGRegion in 2D:
ℛ = CSGRegion["Difference", {Disk[], Disk[{1 / 2, 1 / 2}]}]RegionQ[ℛ]ℛ = CSGRegion["Difference", {Cube[2], Cylinder[{{1, 1, 1}, {1, -1, 1}}]}]RegionQ[ℛ]Subdivision Regions (1)
SubdivisionRegion in 2D:
ℛ = SubdivisionRegion[Rectangle[]]RegionQ[ℛ]ℛ = SubdivisionRegion[Tetrahedron[]]RegionQ[ℛ]Applications (1)
Properties & Relations (2)
MeshRegionQ and BoundaryMeshRegionQ can be used to check more specialized region types:
Subscript[ℛ, 1] = DelaunayMesh[RandomReal[1, {10, 2}]];
Subscript[ℛ, 2] = ConvexHullMesh[RandomReal[1, {10, 2}]];MeshRegionQ /@ {Subscript[ℛ, 1], Subscript[ℛ, 2]}BoundaryMeshRegionQ /@ {Subscript[ℛ, 1], Subscript[ℛ, 2]}ConstantRegionQ and BoundedRegionQ can be used to check region properties:
ConstantRegionQ /@ {Disk[{0, 0}, 2], Disk[{0, 0}, r]}BoundedRegionQ /@ {Disk[], InfiniteLine[{0, 0}, {1, 1}]}Possible Issues (3)
Graphics and Graphics3D are not RegionQ:
RegionQ[Graphics[Circle[]]]RegionQ[Graphics3D[Sphere[]]]Use DiscretizeGraphics to convert to a valid region:
Subscript[ℛ, 1] = {DiscretizeGraphics[Graphics[Circle[]]], DiscretizeGraphics[Graphics3D[Sphere[]]]}RegionQ /@ Subscript[ℛ, 1]Or use BoundaryDiscretizeGraphics for full-dimensional graphics only:
Subscript[ℛ, 2] = {BoundaryDiscretizeGraphics[Graphics[Disk[]]], BoundaryDiscretizeGraphics[Graphics3D[Ball[]]]}RegionQ /@ Subscript[ℛ, 2]g = Graph[{12, 23, 31}]RegionQ[g]Convert the graph to a MeshRegion:
MeshRegion[GraphEmbedding[g], Line[{##}]&@@@EdgeList[g]]RegionQ[%]Degenerate polyhedra are not valid geometric regions:
Polyhedron[{{0, 0, 0}, {1, 1, 0}, {0, 1, 0}, {0, 0, 1}}, {{2, 3, 4}, {3, 2, 1}}]RegionQ[%]Degenerate polygons are not valid geometric regions:
Polygon[{{0, 0, 0}, {1, 1, 0}, {0, 1, 0}, {0, 0, 1}}]RegionQ[%]
Wolfram Research (2014), RegionQ, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionQ.html.
Text
Wolfram Research (2014), RegionQ, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionQ.html.
CMS
Wolfram Language. 2014. "RegionQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RegionQ.html.
APA
Wolfram Language. (2014). RegionQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RegionQ.html