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RegionMemberFunction[reg,…]

代表一个函数， 函数值给出是否一个点在区域 reg.

更多信息
Details and Options Details and Options
范例  
基本范例  
范围  
特定区域  
公式区域  
网格区域  
导出区域  
CSG 区域  
细分区域  
应用  
属性和关系  
可能存在的问题  
参见
相关指南
历史
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RegionMemberFunction

RegionMemberFunction[reg,…]

代表一个函数， 函数值给出是否一个点在区域 reg.

更多信息

范例

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基本范例  (1)

区域的 RegionMember 生成一个 RegionMemberFunction：

Wolfram Language code: mf = RegionMember[Disk[]]

对成员检测重复应用函数：

Wolfram Language code: Map[mf, RandomReal[{-1, 1}, {10, 2}]]

范围  (20)

特定区域  (5)

使用 RegionMember 生成一个 RegionMemberFunction：

Wolfram Language code: ℛ = Polygon[{{0, 0}, {2, -1}, {1, 0}, {2, 1}}]; Region[ℛ]
Wolfram Language code: mf = RegionMember[ℛ]

将其应用到一个点的列表进行隶属检验：

Wolfram Language code: mf[{{1 / 2, 0}, {3, 4}}]
Wolfram Language code: pts = RandomVariate[UniformDistribution[RegionBounds[ℛ]], 10 ^ 3]; col = mf[pts] /. {False -> Gray, True -> Red};
Wolfram Language code: Graphics[{ℛ, AbsolutePointSize[1.6], {col, Point /@ pts}}]

在 Interval 之内作点的检验：

Wolfram Language code: ℛ = Interval[{0, 1}]; gr = NumberLinePlot[ℛ]
Wolfram Language code: mf = RegionMember[ℛ]

将其应用到一个点的列表进行隶属检验：

Wolfram Language code: pts = RandomVariate[UniformDistribution[{{-0.5, 1.5}}], 100]; col = mf[pts] /. {False -> Gray, True -> Red};
Wolfram Language code: gp = Graphics[{AbsolutePointSize[1.6], Table[{col[[i]], Point[{pts[[i, 1]], 3}]}, {i, 100}]}];
Wolfram Language code: Show[gr, gp, PlotRange -> All]

在一个 Disk 内作点的检验：

Wolfram Language code: ℛ = Disk[{0, 0}, 2]; Region[ℛ]
Wolfram Language code: mf = RegionMember[ℛ]

将其应用到一个点的列表进行隶属检验：

Wolfram Language code: pts = RandomVariate[UniformDistribution[RegionBounds[ℛ]], 10 ^ 3]; col = mf[pts] /. {False -> Gray, True -> Red};
Wolfram Language code: Graphics[{ℛ, AbsolutePointSize[1.6], {col, Point /@ pts}}]

在 Cylinder 之内作点的检验：

Wolfram Language code: ℛ = Cylinder[{{0, 0, 0}, {2, 2, 2}}, 2]; gr = Graphics3D[{Opacity[0.3], ℛ}, Boxed -> False, Lighting -> "Neutral"]
Wolfram Language code: mf = RegionMember[ℛ]

将其应用到一个点的列表进行隶属检验：

Wolfram Language code: pts = RandomVariate[UniformDistribution[RegionBounds[ℛ]], 10 ^ 3]; col = mf[pts] /. {False -> Gray, True -> Red};
Wolfram Language code: Show[gr, Graphics3D[{AbsolutePointSize[2], {col, Point /@ pts}}]]

在 的区域：

Wolfram Language code: ℛ = Ball[{0, 0, 0, 0, 0, 0, 0}, 1]; pl = RandomReal[{0, 0.7}, {7, 7}];
Wolfram Language code: mf = RegionMember[ℛ];
Wolfram Language code: mf /@ pl

公式区域  (3)

作为 ImplicitRegion 的两个圆盘的并集：

Wolfram Language code: ℛ = ImplicitRegion[x^2 + y^2 ≤ 4∨(x - 3)^2 + y^2 ≤ 3, {x, y}]; DiscretizeRegion[ℛ, {{-6, 6}, {-2, 2}}]
Wolfram Language code: mf = RegionMember[ℛ]

将其应用到一个点的列表进行隶属检验：

Wolfram Language code: mf[{{1, 1}, {2, 2}}]
Wolfram Language code: pts = RandomVariate[UniformDistribution[RegionBounds[ℛ]], 10 ^ 4]; col = mf[pts] /. {False -> Gray, True -> Red};
Wolfram Language code: Graphics[{AbsolutePointSize[1], {col, Point /@ pts}}]

作为 ImplicitRegion 的两个圆柱的并集：

Wolfram Language code: ℛ = ImplicitRegion[x^2 + y^2 ≤ 2∨(x - 2)^2 + y^2 ≤ 1, {x, y, {z, 0, 2}}]; DiscretizeRegion[ℛ, {2{-2, 2}, {-2, 2}, {0, 2}}]
Wolfram Language code: mf = RegionMember[ℛ]

将其应用到一个点的列表进行隶属检验：

Wolfram Language code: pts = RandomVariate[UniformDistribution[RegionBounds[ℛ]], 10 ^ 4]; col = mf[pts] /. {False -> Gray, True -> Red};
Wolfram Language code: Graphics3D[{AbsolutePointSize[1.6], {col, Point /@ pts}}]

表示成 ParametricRegion 的圆盘：

Wolfram Language code: ℛ = ParametricRegion[{r Cos[θ], r Sin[θ]}, {{r, 0, 1}, {θ, 0, 2π}}];
Wolfram Language code: mf = RegionMember[ℛ]

将其应用到一个点的列表进行隶属检验：

Wolfram Language code: pts = RandomVariate[UniformDistribution[RegionBounds[ℛ]], 10 ^ 4]; col = mf[pts] /. {False -> Gray, True -> Red};
Wolfram Language code: Graphics[{AbsolutePointSize[1], {col, Point /@ pts}}]

网格区域  (6)

在一维的 MeshRegion：

Wolfram Language code: ℛ = DelaunayMesh[RandomReal[1, {10, 1}]]
Wolfram Language code: mf = RegionMember[ℛ]

将其应用到一个点的列表进行隶属检验：

Wolfram Language code: mf[{{1 / 2}, {3}}]

二维：

Wolfram Language code: ℛ = DelaunayMesh[RandomReal[2, {50, 2}]]
Wolfram Language code: mf = RegionMember[ℛ]

将其应用到一个点的列表进行隶属检验：

Wolfram Language code: pts = RandomVariate[UniformDistribution[RegionBounds[ℛ]], 10 ^ 4]; col = mf[pts] /. {False -> Gray, True -> Red};
Wolfram Language code: Graphics[{AbsolutePointSize[1], {col, Point /@ pts}}]

三维：

Wolfram Language code: ℛ = DelaunayMesh[RandomReal[1, {100, 3}]]
Wolfram Language code: mf = RegionMember[ℛ]

将其应用到一个点的列表进行隶属检验：

Wolfram Language code: pts = RandomVariate[UniformDistribution[RegionBounds[ℛ]], 10 ^ 4]; col = mf[pts] /. {False -> Gray, True -> Red};
Wolfram Language code: Graphics3D[{AbsolutePointSize[1], {col, Point /@ pts}}]

在一维的 BoundaryMeshRegion：

Wolfram Language code: ℛ = ConvexHullMesh[RandomReal[1, {10, 1}]]
Wolfram Language code: mf = RegionMember[ℛ]

将其应用到一个点的列表进行隶属检验：

Wolfram Language code: mf[{{1 / 2}, {3}}]

二维：

Wolfram Language code: ℛ = ConvexHullMesh[RandomReal[1, {50, 2}]]
Wolfram Language code: mf = RegionMember[ℛ]

将其应用到一个点的列表进行隶属检验：

Wolfram Language code: pts = RandomVariate[UniformDistribution[RegionBounds[ℛ]], 10 ^ 4]; col = mf[pts] /. {False -> Gray, True -> Red};
Wolfram Language code: Graphics[{AbsolutePointSize[1], {col, Point /@ pts}}]

三维：

Wolfram Language code: ℛ = ConvexHullMesh[RandomReal[1, {100, 3}]]
Wolfram Language code: mf = RegionMember[ℛ]

MeshCoordinates 始终是区域的成员：

Wolfram Language code: AllTrue[MeshCoordinates[ℛ], mf]

导出区域  (2)

两个区域的 RegionIntersection：

Wolfram Language code: ℛ = RegionIntersection[Disk[{0, 0}, 1], Disk[{0, 1}, 1]];
Wolfram Language code: Region[ℛ]
Wolfram Language code: mf = RegionMember[ℛ]

将其应用到一个点的列表进行隶属检验：

Wolfram Language code: mf[{{0, 1}, {3, 4}}]
Wolfram Language code: pts = RandomVariate[UniformDistribution[RegionBounds[ℛ]], 10 ^ 4]; col = mf[pts] /. {False -> Gray, True -> Red};
Wolfram Language code: Graphics[{AbsolutePointSize[1], {col, Point /@ pts}}]

TransformedRegion：

Wolfram Language code: ℛ = TransformedRegion[Disk[{0, 0}, 1], ScalingTransform[{3, 2}]];
Wolfram Language code: DiscretizeRegion[ℛ, {{-3, 3}, {-2, 2}}]
Wolfram Language code: mf = RegionMember[ℛ]

将其应用到一个点的列表进行隶属检验：

Wolfram Language code: pts = RandomVariate[UniformDistribution[RegionBounds[ℛ]], 10 ^ 4]; col = mf[pts] /. {False -> Gray, True -> Red};
Wolfram Language code: Graphics[{AbsolutePointSize[1], {col, Point /@ pts}}]

CSG 区域  (2)

二维空间中的 CSGRegion：

Wolfram Language code: ℛ = CSGRegion["Difference", {Disk[], Disk[{1 / 2, 1 / 2}]}];
Wolfram Language code: mf = RegionMember[ℛ]

将其应用到一个点的列表进行隶属检验：

Wolfram Language code: pts = RandomVariate[UniformDistribution[RegionBounds[ℛ]], 10 ^ 4]; col = mf[pts] /. {False -> Gray, True -> Red};
Wolfram Language code: Graphics[{AbsolutePointSize[1], {col, Point /@ pts}}]

三维空间中的 CSGRegion：

Wolfram Language code: ℛ = CSGRegion["Difference", {Cube[3], Cuboid[{-1, -3, -1}, {3, 3, 3}]}];
Wolfram Language code: mf = RegionMember[ℛ]

将其应用到一个点的列表进行隶属检验：

Wolfram Language code: pts = RandomVariate[UniformDistribution[RegionBounds[ℛ]], 10 ^ 4]; col = mf[pts] /. {False -> Gray, True -> Red};
Wolfram Language code: Graphics3D[{AbsolutePointSize[1], {col, Point /@ pts}}]

细分区域  (2)

二维空间中的 SubdivisionRegion：

Wolfram Language code: ℛ = SubdivisionRegion[Rectangle[]];
Wolfram Language code: mf = RegionMember[ℛ]

将其应用到一个点的列表进行隶属检验：

Wolfram Language code: pts = RandomVariate[UniformDistribution[RegionBounds[ℛ]], 10 ^ 4]; col = mf[pts] /. {False -> Gray, True -> Red};
Wolfram Language code: Graphics[{AbsolutePointSize[1], {col, Point /@ pts}}]

三维空间中的 SubdivisionRegion：

Wolfram Language code: ℛ = SubdivisionRegion[Tetrahedron[]];
Wolfram Language code: mf = RegionMember[ℛ]

将其应用到一个点的列表进行隶属检验：

Wolfram Language code: pts = RandomVariate[UniformDistribution[RegionBounds[ℛ]], 10 ^ 4]; col = mf[pts] /. {False -> Gray, True -> Red};
Wolfram Language code: Graphics3D[{AbsolutePointSize[1], {col, Point /@ pts}}]

应用  (3)

通过过滤一组均匀的点，在一个区域上生成一些点：

Wolfram Language code: ℛ = BoundaryDiscretizeGraphics[CountryData["US", {"Polygon", "Equirectangular"}]];

获得区域的界限：

Wolfram Language code: bounds = RegionBounds[ℛ];

在区域的边界框上均匀采样：

Wolfram Language code: pts = RandomVariate[UniformDistribution[bounds], 10 ^ 4];

选择成员点：

Wolfram Language code: mpts = Select[pts, RegionMember[ℛ]];

可视化成员点：

Wolfram Language code: Graphics[{AbsolutePointSize[1], Point[mpts]}]

根据点所隶属的区域来涂点的颜色：

Wolfram Language code: Subscript[ℛ, 1] = BoundaryDiscretizeGraphics[CountryData["US", {"Polygon", "Equirectangular"}]]; Subscript[ℛ, 2] = BoundaryDiscretizeGraphics[CountryData["Canada", {"Polygon", "Equirectangular"}]];

给每一个产生隶属函数：

Wolfram Language code: mf1 = RegionMember[Subscript[ℛ, 1]]; mf2 = RegionMember[Subscript[ℛ, 2]];

在两个区域的边界框生成点：

Wolfram Language code: pts = RandomVariate[UniformDistribution[RegionBounds[RegionUnion[Subscript[ℛ, 1], Subscript[ℛ, 2]]]], 10 ^ 4];

可视化：

Wolfram Language code: Graphics[{AbsolutePointSize[1], {Red, Point@Select[pts, mf1]}, {Blue, Point@Select[pts, mf2]}, {Black, Point@Select[pts, !mf1[#] && !mf2[#]&]}}]

用区域里的随机点进行蒙特卡罗积分：

Wolfram Language code: ℛ = ImplicitRegion[2 ≤ x^2 + y^2 ≤ 4, {x, y}]; mf = RegionMember[ℛ]; pts = Select[RandomVariate[UniformDistribution[RegionBounds[ℛ]], 10 ^ 5], mf];

在每一个采样点对函数求值并取它们的平均值：

Wolfram Language code: f[x_, y_] := x^3 + y^4; intVal = Mean[f@@@pts] * RegionMeasure[ℛ]

与精确值比较：

Wolfram Language code: Integrate[f[x, y], {x, y}∈ℛ]
Wolfram Language code: %//N

属性和关系  (1)

RegionMemberFunction 是由 RegionMember 生成的：

Wolfram Language code: mf = RegionMember[Disk[{0, 0}, 1]]
Wolfram Language code: mf@RandomReal[1, {7, 2}]

可能存在的问题  (1)

RegionMemberFunction 只能为 ConstantRegionQ 区域生成：

Wolfram Language code: ℛ = Disk[{x, y}, r]
Wolfram Language code: ConstantRegionQ[ℛ]
Wolfram Language code: RegionMember[ℛ]

为一个特定实例生成成员函数：

Wolfram Language code: mf = RegionMember[ℛ /. {x -> 0, y -> 2, r -> 1}]
Wolfram Language code: mf[{{0, 1}, {10, 10}}]
Wolfram Research (2014)，RegionMemberFunction，Wolfram 语言函数，https://reference.wolfram.com/language/ref/RegionMemberFunction.html.

文本

Wolfram Research (2014)，RegionMemberFunction，Wolfram 语言函数，https://reference.wolfram.com/language/ref/RegionMemberFunction.html.

CMS

Wolfram 语言. 2014. "RegionMemberFunction." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/RegionMemberFunction.html.

APA

Wolfram 语言. (2014). RegionMemberFunction. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/RegionMemberFunction.html 年

BibTeX

@misc{reference.wolfram_2026_regionmemberfunction, author="Wolfram Research", title="{RegionMemberFunction}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/RegionMemberFunction.html}", note=[Accessed: 02-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_regionmemberfunction, organization={Wolfram Research}, title={RegionMemberFunction}, year={2014}, url={https://reference.wolfram.com/language/ref/RegionMemberFunction.html}, note=[Accessed: 02-November-2026]}