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RegionMemberFunction[reg,…]

ある点が領域 reg に含まれるかどうかを示すような値を持つ関数を表す．

詳細
Details and Options Details and Options
例題  
例  
スコープ  
特別領域  
数式定義領域  
メッシュ領域  
派生領域  
CSG領域  
細分割領域  
アプリケーション  
特性と関係  
考えられる問題  
関連項目
関連するガイド
履歴
引用書式

RegionMemberFunction

RegionMemberFunction[reg,…]

ある点が領域 reg に含まれるかどうかを示すような値を持つ関数を表す．

詳細

例題

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例  (1)

ある領域のRegionMemberはRegionMemberFunctionを生成する：

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

帰属判定のために，関数を繰り返し適用する：

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

スコープ  (20)

特別領域  (5)

RegionMemberを使ってRegionMemberFunctionを生成する：

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

これを点のリストに適用して帰属判定を行う：

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}}]

Interval内の点について判定する：

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

これを点のリストに適用して帰属判定を行う：

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]

Disk内の点について検定する：

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

これを点のリストに適用して帰属判定を行う：

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}}]

Cylinder内の点について検定する：

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]

これを点のリストに適用して帰属判定を行う：

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}}]]

内の領域：

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

数式定義領域  (3)

ImplicitRegionとしての2つの円板の和集合：

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]

これを点のリストに適用して帰属判定を行う：

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}}]

ImplicitRegionとしての2つの円柱の和集合：

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]

これを点のリストに適用して帰属判定を行う：

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}}]

ParametricRegionとして表された円板：

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

これを点のリストに適用して帰属判定を行う：

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}}]

メッシュ領域  (6)

1DにおけるMeshRegion：

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

これを点のリストに適用して帰属判定を行う：

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

2D：

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

これを点のリストに適用して帰属判定を行う：

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}}]

3D：

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

これを点のリストに適用して帰属判定を行う：

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}}]

1DにおけるBoundaryMeshRegion：

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

これを点のリストに適用して帰属判定を行う：

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

2D：

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

これを点のリストに適用して帰属判定を行う：

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}}]

3D：

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

MeshCoordinatesは常に領域に帰属する：

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

派生領域  (2)

2つの領域の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]

これを点のリストに適用して帰属判定を行う：

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]

これを点のリストに適用して帰属判定を行う：

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領域  (2)

2DのCSGRegion：

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

これを点のリストに適用して領域帰属をテストする：

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}}]

3DのCSGRegion：

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

これを点のリストに適用して領域帰属をテストする：

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}}]

細分割領域  (2)

2DのSubdivisionRegion：

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

これを点のリストに適用して領域帰属をテストする：

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}}]

3DのSubdivisionRegion：

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

これを点のリストに適用して領域帰属をテストする：

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}}]

アプリケーション  (3)

一様な点集合をフィルタすることで，領域上に点を生成する：

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

領域の境界を得る：

Wolfram Language code: bounds = RegionBounds[ℛ];

領域の境界ボックス上で一様にサンプルを取る：

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

帰属点を選択する：

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

帰属点を可視化する：

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

所属する領域に基づいて点に彩色する：

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

それぞれについて帰属判定関数を作る：

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

両方の領域の境界ボックス上に点を生成する：

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

可視化する：

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

領域内のランダムな点を使ってモンテカルロ積分を実行する：

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];

各サンプル点で関数を評価し，その平均を取る：

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

厳密値と比較する：

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

特性と関係  (1)

RegionMemberFunctionはRegionMemberによって生成される：

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

考えられる問題  (1)

RegionMemberFunctionは，ConstantRegionQ領域に対してのみ生成される：

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

特定の場合用に帰属関数を生成する：

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言語関数， https://reference.wolfram.com/language/ref/RegionMemberFunction.html.

テキスト

Wolfram Research (2014), RegionMemberFunction, Wolfram言語関数， https://reference.wolfram.com/language/ref/RegionMemberFunction.html.

CMS

Wolfram Language. 2014. "RegionMemberFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RegionMemberFunction.html.

APA

Wolfram Language. (2014). RegionMemberFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RegionMemberFunction.html

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: 29-October-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: 29-October-2026]}