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BooleanRegion[bfunc,{reg1,reg2,…}]

領域 reg1, reg2, …の論理結合 bfunc を表す．

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例題  
例  
スコープ  
特別な領域  
数式定義領域  
メッシュ領域  
派生領域  
アプリケーション  
特性と関係  
考えられる問題  
おもしろい例題  
関連項目
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BooleanRegion

BooleanRegion[bfunc,{reg1,reg2,…}]

領域 reg1, reg2, …の論理結合 bfunc を表す．

詳細とオプション

例題

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例  (2)

2つの円板の論理Xor：

Wolfram Language code: BooleanRegion[Xor, {Disk[{-1 / 3, 0}, 1], Disk[{1 / 3, 0}, 1]}];

可視化する：

Wolfram Language code: Region[%]

MeshRegionオブジェクトに適用されたブール関数：

Wolfram Language code: BooleanRegion[¬#2∧#1&, {[image], [image]}]

スコープ  (11)

特別な領域  (5)

Line領域の論理Or：

Wolfram Language code: ℛ = BooleanRegion[Or, {Line[{{1}, {2}}], Line[{{3}, {4}}], Line[{{5}, {6}}]}];

可視化する：

Wolfram Language code: Region[ℛ]

Polygon領域に適用されたBooleanCountingFunction：

Wolfram Language code: pts = {{-5, 0}, {1, -2}, {-1, 0}, {1, 2}}; {p1, p2, p3, p4} = Polygon /@ {pts, -pts, Reverse /@ pts, -Reverse /@ pts};
Wolfram Language code: ℛ = BooleanRegion[BooleanCountingFunction[{1, 2}, 4], {p1, p2, p3, p4}];

このAreaを計算する：

Wolfram Language code: Area[ℛ]

2つのDisk領域の論理Xor：

Wolfram Language code: ℛ = BooleanRegion[Xor, {Disk[{0, 0}, 1], Disk[{1, 0}, 1]}];

可視化する：

Wolfram Language code: Region[ℛ]

2つのCuboid領域の論理Or：

Wolfram Language code: ℛ = BooleanRegion[Or, {Cuboid[], Cuboid[{0.5, 0.5, 0.5}]}];

可視化する：

Wolfram Language code: Region[ℛ]

RegionDimensionが異なる領域の論理And：

Wolfram Language code: ℛ = BooleanRegion[And, {Disk[{0, 0}, 1], Circle[{0, 1}, 1]}];

可視化する：

Wolfram Language code: Region[ℛ]

数式定義領域  (2)

ImplicitRegionオブジェクトの論理XorはImplicitRegionである：

Wolfram Language code: Subscript[ℛ, 1] = ImplicitRegion[x ≤ 1, {x}]; Subscript[ℛ, 2] = ImplicitRegion[x ≥ -1, {x}];
Wolfram Language code: BooleanRegion[Xor, {Subscript[ℛ, 1], Subscript[ℛ, 2]}]

2D：

Wolfram Language code: Subscript[ℛ, 1] = ImplicitRegion[x^2 + y^2 ≤ 1, {x, y}]; Subscript[ℛ, 2] = ImplicitRegion[x^2 + (y - 1)^2 ≤ 1, {x, y}];
Wolfram Language code: BooleanRegion[Xor, {Subscript[ℛ, 1], Subscript[ℛ, 2]}]

3D：

Wolfram Language code: Subscript[ℛ, 1] = ImplicitRegion[x^2 + y^2 + z^2 ≤ 1, {x, y, z}]; Subscript[ℛ, 2] = ImplicitRegion[(x - 1)^2 + y^2 + z^2 ≤ 1, {x, y, z}];
Wolfram Language code: BooleanRegion[Xor, {Subscript[ℛ, 1], Subscript[ℛ, 2]}]

nD：

Wolfram Language code: Subscript[ℛ, 1] = ImplicitRegion[x^2 + y^2 + z^2 + u^2 + v^2 ≤ 1, {x, y, z, u, v}]; Subscript[ℛ, 2] = ImplicitRegion[(x - 1)^2 + y^2 + z^2 + u^2 + v^2 ≤ 1, {x, y, z, u, v}];
Wolfram Language code: BooleanRegion[Xor, {Subscript[ℛ, 1], Subscript[ℛ, 2]}]

ParametricRegionオブジェクトに適用されたブール関数：

Wolfram Language code: Subscript[ℛ, 1] = ParametricRegion[{u, v, w}, {{u, 0, 2}, {v, 0, 2}, {w, 0, 2}}]; Subscript[ℛ, 2] = ParametricRegion[{u - 1, v + 1, w - 1}, {{u, 0, 2}, {v, 0, 2}, {w, 0, 2}}];
Wolfram Language code: ℛ = BooleanRegion[¬#1∧#2&, {Subscript[ℛ, 1], Subscript[ℛ, 2]}];

可視化する：

Wolfram Language code: Region[ℛ]

メッシュ領域  (2)

BoundaryMeshRegionオブジェクトのブール関数はBoundaryMeshRegionである：

Wolfram Language code: BooleanRegion[¬#2∧#1&, {[image], [image]}]
Wolfram Language code: BoundedRegionQ[%]

2D：

Wolfram Language code: BooleanRegion[¬#2∧#1&, {[image], [image]}]
Wolfram Language code: BoundedRegionQ[%]

3D：

Wolfram Language code: BooleanRegion[¬#2∧#1&, {[image], [image]}]
Wolfram Language code: BoundedRegionQ[%]

全次元のMeshRegionオブジェクトのブール関数はMeshRegionである：

Wolfram Language code: BooleanRegion[¬#2∧#1&, {[image], [image]}]
Wolfram Language code: MeshRegionQ[%]

2D：

Wolfram Language code: BooleanRegion[¬#2∧#1&, {[image], [image]}]
Wolfram Language code: MeshRegionQ[%]

3D：

Wolfram Language code: BooleanRegion[¬#2∧#1&, {[image], [image]}]
Wolfram Language code: MeshRegionQ[%]

派生領域  (2)

BooleanRegionオブジェクトのブール関数：

Wolfram Language code: Subscript[ℛ, 1] = BooleanRegion[Or, {Triangle[{{0, 0}, {2, 3}, {-2, 3}}], Triangle[{{0, 2}, {2, -1}, {-2, -1}}]}]; Subscript[ℛ, 2] = BooleanRegion[And, {Triangle[{{0, 0}, {2, 3}, {-2, 3}}], Triangle[{{0, 2}, {2, -1}, {-2, 2}}]}];
Wolfram Language code: ℛ = BooleanRegion[¬#2∧#1&, {Subscript[ℛ, 1], Subscript[ℛ, 2]}];

可視化する：

Wolfram Language code: Region[ℛ]

論理OrまたはTransformedRegionオブジェクト：

Wolfram Language code: Subscript[ℛ, 1] = TransformedRegion[Cuboid[], RotationTransform[Pi / 8, {1, 0, 0}]]; Subscript[ℛ, 2] = TransformedRegion[Cuboid[], RotationTransform[Pi / 8, {0, 1, 0}]];
Wolfram Language code: ℛ = BooleanRegion[Or, {Subscript[ℛ, 1], Subscript[ℛ, 2]}];

可視化する：

Wolfram Language code: Region[ℛ]

アプリケーション  (1)

領域に対するブール演算：

Wolfram Language code: {a, b} = {[image], [image]};
Wolfram Language code: Multicolumn[Table[BooleanRegion[op, {a, b}, PlotLabel -> op, BaseStyle -> Opacity[0.7]], {op, {Or, And, ¬#2∧#1&, #1⊻#2&}}], 2]

特性と関係  (2)

RegionUnionは，領域の論理結合結合Orである：

Wolfram Language code: {Subscript[ℛ, 1], Subscript[ℛ, 2]} = {[image], [image]};
Wolfram Language code: RegionUnion[Subscript[ℛ, 1], Subscript[ℛ, 2]] == BooleanRegion[Or, {Subscript[ℛ, 1], Subscript[ℛ, 2]}]

RegionIntersection：

Wolfram Language code: RegionIntersection[Subscript[ℛ, 1], Subscript[ℛ, 2]] == BooleanRegion[And, {Subscript[ℛ, 1], Subscript[ℛ, 2]}]

RegionDifference：

Wolfram Language code: RegionDifference[Subscript[ℛ, 1], Subscript[ℛ, 2]] == BooleanRegion[¬#2∧#1&, {Subscript[ℛ, 1], Subscript[ℛ, 2]}]

RegionSymmetricDifference：

Wolfram Language code: RegionSymmetricDifference[Subscript[ℛ, 1], Subscript[ℛ, 2]] == BooleanRegion[Xor, {Subscript[ℛ, 1], Subscript[ℛ, 2]}]

ブール演算子AndのRegionMeasureは単純な式に従う：

Wolfram Language code: Subscript[ℛ, 1] = Disk[{0, 0}, 1]; Subscript[ℛ, 2] = Disk[{1, 0}, 1]; Subscript[ℛ, 3] = BooleanRegion[And, {Subscript[ℛ, 1], Subscript[ℛ, 2]}];

RegionUnionの測度を測度の話から引く：

Wolfram Language code: RegionMeasure[Subscript[ℛ, 3]] == RegionMeasure[Subscript[ℛ, 1]] + RegionMeasure[Subscript[ℛ, 2]] - RegionMeasure[RegionUnion[Subscript[ℛ, 1], Subscript[ℛ, 2]]]

考えられる問題  (3)

BooleanRegionは，RegionEmbeddingDimensionが等しい領域についてのみ定義される：

Wolfram Language code: Subscript[ℛ, 1] = Disk[]; Subscript[ℛ, 2] = Ball[{0, 0, 1}, 1];
Wolfram Language code: BooleanRegion[Or, {Subscript[ℛ, 1], Subscript[ℛ, 2]}]

埋込み次元より低い次元の成分は省略されることがある：

Wolfram Language code: Subscript[ℛ, 1] = MeshRegion[{{0, 0, 0}, {2, 0, 0}, {2, 2, 0}, {1, 1, 2}}, Tetrahedron[{1, 2, 3, 4}]]; Subscript[ℛ, 2] = MeshRegion[{{0, 0, 0}, {2, 2, 0}, {0, 2, 0}, {1, 1, 2}}, Tetrahedron[{1, 2, 3, 4}], PlotTheme -> "Web"];
Wolfram Language code: Show[{Subscript[ℛ, 1], Subscript[ℛ, 2]}]
Wolfram Language code: BooleanRegion[And, {Subscript[ℛ, 1], Subscript[ℛ, 2]}]

メッセージが出るようにする：

Wolfram Language code: On[BooleanRegion::drc]
Wolfram Language code: BooleanRegion[And, {Subscript[ℛ, 1], Subscript[ℛ, 2]}]

BooleanRegionは，より低い次元の重なり合う成分を含むことがある：

Wolfram Language code: Subscript[ℛ, 1] = Sphere[]; Subscript[ℛ, 2] = Ball[{1 / 2, 0, 0}];
Wolfram Language code: Graphics3D[{Yellow, Subscript[ℛ, 1], Green, Opacity@.5, Subscript[ℛ, 2]}]
Wolfram Language code: Subscript[ℛ, 3] = BooleanRegion[Or, {DiscretizeGraphics[Subscript[ℛ, 1]], BoundaryDiscretizeGraphics[Subscript[ℛ, 2]]}]

連結メッシュ成分：

Wolfram Language code: ConnectedMeshComponents[Subscript[ℛ, 3]]

おもしろい例題  (1)

2つの螺線多角形のブール演算Xor：

Wolfram Language code: BooleanRegion[Xor, {[image], [image]}]
Wolfram Research (2014), BooleanRegion, Wolfram言語関数， https://reference.wolfram.com/language/ref/BooleanRegion.html （2017年に更新）.

テキスト

Wolfram Research (2014), BooleanRegion, Wolfram言語関数， https://reference.wolfram.com/language/ref/BooleanRegion.html （2017年に更新）.

CMS

Wolfram Language. 2014. "BooleanRegion." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/BooleanRegion.html.

APA

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

BibTeX

@misc{reference.wolfram_2026_booleanregion, author="Wolfram Research", title="{BooleanRegion}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/BooleanRegion.html}", note=[Accessed: 17-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_booleanregion, organization={Wolfram Research}, title={BooleanRegion}, year={2017}, url={https://reference.wolfram.com/language/ref/BooleanRegion.html}, note=[Accessed: 17-August-2026]}