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RegionEqual[reg1,reg2]

領域 reg1と reg2が等しいときにTrueを返す．

RegionEqual[reg1,reg2,reg3,…]

領域 reg1，reg2，reg3，…がすべて等しいときにTrueを返す．

詳細とオプション
Details and Options Details and Options
例題  
例  
スコープ  
基本的な用法  
基本的な領域  
数式定義領域  
メッシュ領域  
派生領域  
オプション  
Assumptions  
GenerateConditions  
アプリケーション  
特性と関係  
関連項目
関連するガイド
履歴
引用書式

RegionEqual

RegionEqual[reg1,reg2]

領域 reg1と reg2が等しいときにTrueを返す．

RegionEqual[reg1,reg2,reg3,…]

領域 reg1，reg2，reg3，…がすべて等しいときにTrueを返す．

詳細とオプション

  • reg1内のすべての点がreg2内の点であるとき領域 reg1と reg2は等しく，逆もまた真である．
  • すべての regiがパラメトリックフリーの領域である，つまりConstantRegionQ[regi]がTrueのとき，その領域は点集合であり，一般にTrueまたはFalseが返される．
  • regiの中にパラメータに依存する点が含まれるとき，つまりConstantRegionQ[regi]がFalseのとき，regiは領域の族を表し，RegionEqualは領域が等しくなるためのパラメータの条件を計算しようとする．
  • 次は使用可能なオプションである．
  • Assumptions $Assumptionsパラメータについての仮定
    GenerateConditions Falseパラメータについての条件を生成するかどうか

例題

すべて開く すべて閉じる

例  (2)

2つの領域が等しいかどうかを判定する：

Wolfram Language code: Subscript[ℛ, 1] = Rectangle[]; Subscript[ℛ, 2] = Polygon[{{0, 0}, {1, 0}, {1, 1}, {0, 1}}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

2つの領域が等しくなる条件を生成する：

Wolfram Language code: Subscript[ℛ, 1] = Circle[]; Subscript[ℛ, 2] = ImplicitRegion[x^2 + y^2 == r, {x, y}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

スコープ  (16)

基本的な用法  (4)

等価性を判定する：

Wolfram Language code: Subscript[ℛ, 1] = Rectangle[{0, 0}, {2, 1}]; Subscript[ℛ, 2] = ImplicitRegion[0 ≤ x ≤ 2 && 0 ≤ y ≤ 1, {x, y}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

2つの領域が等しくないことを示す：

Wolfram Language code: Subscript[ℛ, 1] = Line[{{0, 0}, {1, 1}}]; Subscript[ℛ, 2] = Line[{{0, 0}, {-1, 1}}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

領域が等しくなる条件を求める：

Wolfram Language code: Subscript[ℛ, 1] = Disk[]; Subscript[ℛ, 2] = Disk[{x, y}, r, {0, θ}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

3つの領域を同時に比較する：

Wolfram Language code: Subscript[ℛ, 1] = Interval[{0, 1}]; Subscript[ℛ, 2] = MeshRegion[{{0}, {1}}, Line[{1, 2}]]; Subscript[ℛ, 3] = ImplicitRegion[0 ≤ x ≤ 1, x];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2], Subscript[ℛ, 3]]

基本的な領域  (4)

LineとIntervalを含む内の領域：

Wolfram Language code: RegionEqual[Line[{{0}, {1}}], Interval[{0, 1}]]

Point：

Wolfram Language code: RegionEqual[Point[{2}], Interval[{2, 2}]]

Ball：

Wolfram Language code: RegionEqual[Ball[1], Interval[{-1, 1}]]

InfiniteLine：

Wolfram Language code: RegionEqual[InfiniteLine[{0}, {1}], FullRegion[1]]

Pointを含む内の領域：

Wolfram Language code: Subscript[ℛ, 1] = Point[Tuples[Range[3], 2]]; Subscript[ℛ, 2] = Point[Join@@Table[{i, j}, {j, 3}, {i, 3}]];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

Line：

Wolfram Language code: Subscript[ℛ, 1] = Line[{{0, 0}, {3, 3}, {5, -1}, {7, -1}}]; Subscript[ℛ, 2] = Line[{{7, -1}, {6, -1}, {5, -1}, {3, 3}, {1, 1}, {0, 0}}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

Polygon：

Wolfram Language code: Subscript[ℛ, 1] = Polygon[{{0, 0}, {1, 0}, {1, 1}, {0, 1}}]; Subscript[ℛ, 2] = Rectangle[];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]
Wolfram Language code: Subscript[ℛ, 1] = Polygon[CirclePoints[5]]; Subscript[ℛ, 2] = RegularPolygon[5];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

Disk，Ball，Ellipsoid：

Wolfram Language code: Subscript[ℛ, 1] = Disk[]; Subscript[ℛ, 2] = Ball[2]; Subscript[ℛ, 3] = Ellipsoid[{0, 0}, {1, 1}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2], Subscript[ℛ, 3]]

RectangleとRegularPolygon：

Wolfram Language code: RegionEqual[Rectangle[{x1, y1}, {x2, y2}], RegularPolygon[r, n]]

Pointを含む内の領域：

Wolfram Language code: Subscript[ℛ, 1] = Point[Tuples[Range[5], 3]]; Subscript[ℛ, 2] = Point[Flatten[Table[{i, j, k}, {j, 5}, {k, 5}, {i, 5}], 2]];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

Line：

Wolfram Language code: Subscript[ℛ, 1] = Line[{{0, 0, 0}, {3, 3, 3}, {5, -1, 0}, {7, -1, 1}}]; Subscript[ℛ, 2] = Line[{{7, -1, 1}, {5, -1, 0}, {3, 3, 3}, {1, 1, 1}, {0, 0, 0}}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

Polygon：

Wolfram Language code: Subscript[ℛ, 1] = Polygon[{{1, 0, 0}, {0, 0, 1}, {0, 1, 1}, {1, 1, 0}}]; Subscript[ℛ, 2] = Triangle[{{{1, 0, 0}, {0, 0, 1}, {0, 1, 1}}, {{1, 0, 0}, {0, 1, 1}, {1, 1, 0}}}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

CuboidとHexahedron：

Wolfram Language code: Subscript[ℛ, 1] = Cuboid[]; Subscript[ℛ, 2] = Hexahedron[{{0, 0, 0}, {1, 0, 0}, {2, 1, 0}, {1, 1, 0}, {0, 0, 1}, {1, 0, 1}, {2, 1, 1}, {1, 1, 1}}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

BallとEllipsoid：

Wolfram Language code: Subscript[ℛ, 1] = Ball[3]; Subscript[ℛ, 2] = Ellipsoid[{0, 0, 0}, {3, 2, 1}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

TetrahedronとSimplex：

Wolfram Language code: Subscript[ℛ, 1] = Tetrahedron[{{1, 0, 0}, {1, 0, 1}, {1, 1, 1}, {0, 0, 1}}]; Subscript[ℛ, 2] = Simplex[{{1, 0, 1}, {1, 0, 0}, {0, 0, 1}, {1, 1, 1}}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

内のCuboidとParallelepipedを含む内の領域：

Wolfram Language code: Subscript[ℛ, 1] = Cuboid[{0, 0, 0, 0}, {1, 1, 1, 1}]; Subscript[ℛ, 2] = Parallelepiped[{0, 0, 0, 0}, IdentityMatrix[4]];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

内のEllipsoidとBall：

Wolfram Language code: Subscript[ℛ, 1] = Ellipsoid[Table[0, 10], Table[1, 10]]; Subscript[ℛ, 2] = Ball[10];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

数式定義領域  (4)

陰的領域：

Wolfram Language code: Subscript[ℛ, 1] = ImplicitRegion[x^2 + y^2 == 1, {x, y}]; Subscript[ℛ, 2] = ImplicitRegion[y == Sqrt[1 - x^2] || y == -Sqrt[1 - x^2], {x, y}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

パラメトリック領域：

Wolfram Language code: Subscript[ℛ, 1] = ParametricRegion[{Cos[t], Sin[t]}, t]; Subscript[ℛ, 2] = ParametricRegion[{Cos[2t + π / 5], Sin[2t + π / 5]}, t];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

2つの数式定義領域を比較する：

Wolfram Language code: Subscript[ℛ, 1] = ImplicitRegion[-1 ≤ x ≤ 1 && y^2 ≤ x^4 - 2x^2 + 1, {x, y}]; Subscript[ℛ, 2] = ParametricRegion[{t, s (1 - t^2)}, {{s, -1, 1}, {t, -1, 1}}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

一定ではない数式定義領域：

Wolfram Language code: RegionEqual[Annulus[], ImplicitRegion[r1 ≤ x^2 + y^2 ≤ r2, {x, y}]]

メッシュ領域  (3)

内のMeshRegionを比較する：

Wolfram Language code: Subscript[ℛ, 1] = MeshRegion[{{0}, {1}}, Line[{1, 2}]]; Subscript[ℛ, 2] = MeshRegion[{{0}, {1 / 2}, {1}}, Line[{3, 2, 1}]];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

内の：

Wolfram Language code: Subscript[ℛ, 1] = MeshRegion[{{0, 0}, {1, 0}, {1, 1}, {0, 1}}, Polygon[{1, 2, 3, 4}]]; Subscript[ℛ, 2] = TriangulateMesh[Subscript[ℛ, 1]];
Wolfram Language code: {Subscript[ℛ, 1], Subscript[ℛ, 2]}
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

内の：

Wolfram Language code: Subscript[ℛ, 1] = DiscretizeGraphics[Cuboid[{0, 0, 0}, {1, 1, 1}]]; Subscript[ℛ, 2] = DiscretizeGraphics[Ball[]];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

内のBoundaryMeshRegionを比較する：

Wolfram Language code: Subscript[ℛ, 1] = BoundaryMeshRegion[{{0}, {1}}, Point[{1, 2}]]; Subscript[ℛ, 2] = BoundaryMeshRegion[{{0}, {1}}, Point[{2, 1}]];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

内の：

Wolfram Language code: Subscript[ℛ, 1] = BoundaryMeshRegion[{{0, 0}, {2, 0}, {2, 2}, {0, 2}}, Line[{1, 2, 3, 4, 1}]]; Subscript[ℛ, 2] = BoundaryMeshRegion[{{0, 0}, {1, 0}, {2, 0}, {2, 2}, {0, 2}}, Line[{1, 2, 3, 4, 5, 1}]];
Wolfram Language code: {Subscript[ℛ, 1], Subscript[ℛ, 2]}
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

内の：

Wolfram Language code: Subscript[ℛ, 1] = BoundaryDiscretizeGraphics[Cuboid[{0, 0, 0}, {1, 1, 1}]]; Subscript[ℛ, 2] = BoundaryDiscretizeGraphics[Ball[]];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

内のMeshRegionとBoundaryMeshRegionを比較する：

Wolfram Language code: Subscript[ℛ, 1] = DelaunayMesh[RandomReal[{-1, 1}, {25, 2}]]; Subscript[ℛ, 2] = BoundaryMesh[Subscript[ℛ, 1]];
Wolfram Language code: {Subscript[ℛ, 1], Subscript[ℛ, 2]}
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

内の：

Wolfram Language code: Subscript[ℛ, 1] = DelaunayMesh[RandomReal[{-1, 1}, {25, 3}]]; Subscript[ℛ, 2] = BoundaryMesh[Subscript[ℛ, 1]];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

派生領域  (1)

BooleanRegionを比較する：

Wolfram Language code: Subscript[ℛ, 1] = BooleanRegion[Xnor, {Disk[], Disk[{1, 0}]}]; Subscript[ℛ, 2] = BooleanRegion[(!#1 || #2) && (#1 || !#2)&, {Disk[], Disk[{1, 0}]}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

オプション  (2)

Assumptions  (1)

単位円を説明するすべての半径を求める：

Wolfram Language code: Subscript[ℛ, 1] = Circle[]; Subscript[ℛ, 2] = ImplicitRegion[x^2 + y^2 == r^2, {x, y}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

正の半径のみを求める：

Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2], Assumptions -> r > 0]

GenerateConditions  (1)

単位円板が陰的に説明されたアニュラスと等しくなるときを求める：

Wolfram Language code: Subscript[ℛ, 1] = Disk[]; Subscript[ℛ, 2] = ImplicitRegion[Subscript[r, 1] ≤ x^2 + y^2 ≤ Subscript[r, 2], {x, y}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

結果が有効になる条件を示す：

Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2], GenerateConditions -> True]

退化した場合を明示的に許容する：

Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2], Assumptions -> Subscript[r, 1]∈Reals]

アプリケーション  (6)

2つのラミナ（ユークリッド平面内の二次元閉領域）が等しくなるときを求める：

Wolfram Language code: Subscript[ℛ, 1] = Entity["Lamina", "FilledDiamond"][EntityProperty["Lamina", "Region"]][a, b]
Wolfram Language code: Subscript[ℛ, 2] = Entity["Lamina", "FilledKite"][EntityProperty["Lamina", "Region"]][2, 2, 1]
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

アニュラスの穴を円板で覆うことで単位円版を作る：

Wolfram Language code: RegionEqual[RegionUnion[Annulus[], Disk[{0, 0}, r]], Disk[]]

この例を示す：

Wolfram Language code: Subscript[r, 0] = RandomReal[{1 / 2, 1}]
Wolfram Language code: Graphics[{Opacity[0.4], {Red, Annulus[]}, {Green, Disk[{0, 0}, Subscript[r, 0]]}}]

アニュラスの穴を正方形で覆うことで単位円版を作る，可能なすべての辺の長さを求める：

Wolfram Language code: RegionEqual[RegionUnion[Annulus[], Rectangle[{-r, -r}, {r, r}]], Disk[]]

この例を示す：

Wolfram Language code: Subscript[r, 0] = RandomReal[{1 / 2, 1 / Sqrt[2]}]
Wolfram Language code: Graphics[{Opacity[0.4], {Red, Annulus[]}, {Green, Rectangle[{-Subscript[r, 0], -Subscript[r, 0]}, {Subscript[r, 0], Subscript[r, 0]}]}}]

Parallelogramを使って単位正方形を表すすべての方法を求める：

Wolfram Language code: Subscript[ℛ, 1] = Rectangle[]; Subscript[ℛ, 2] = Parallelogram[{x, y}, {{a1, a2}, {b1, b2}}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]
Wolfram Language code: Subscript[ℛ, 2] /. Solve[%]

結果を確かめる：

Wolfram Language code: RegionEqual@@Prepend[%, Subscript[ℛ, 1]]

Ellipsoidを介して陰的に定義された楕円を表す：

Wolfram Language code: ℛ = ImplicitRegion[x ^ 2 - x y + 3y ^ 2 ≤ 1, {x, y}];
Wolfram Language code: RegionEqual[ℛ, Ellipsoid[{0, 0}, {{a, b}, {c, d}}]]

各パラメータの値を求める：

Wolfram Language code: Ellipsoid[{0, 0}, {{a, b}, {c, d}}] /. FindInstance[%, {a, b, c, d}]

両方の表現を可視化する：

Wolfram Language code: {RegionPlot[ℛ], Graphics[%, Frame -> True, AspectRatio -> 1]}

ド・モルガン(De Morgan)の定理 を示す：

Wolfram Language code: Subscript[ℛ, 1] = Disk[{0, 0}, 1]; Subscript[ℛ, 2] = Disk[{1, 0}, 1];
Wolfram Language code: complement[reg_] := BooleanRegion[Not, {reg}]
Wolfram Language code: dr1 = RegionIntersection[Subscript[ℛ, 1], Subscript[ℛ, 2]]; dr2 = complement[RegionUnion[complement[Subscript[ℛ, 1]], complement[Subscript[ℛ, 2]]]];
Wolfram Language code: RegionEqual[dr1, dr2]
Wolfram Language code: BoundaryDiscretizeRegion /@ {dr1, dr2}

特性と関係  (4)

等価である領域の点はすべて共通である：

Wolfram Language code: Subscript[ℛ, 1] = Disk[]; Subscript[ℛ, 2] = ImplicitRegion[x^2 + y^2 ≤ 1, {x, y}];
Wolfram Language code: Resolve[ForAll[{x, y}, {x, y}∈Subscript[ℛ, 1]⧦{x, y}∈Subscript[ℛ, 2]], Reals]
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]

RegionEqualはRegionWithinで表すことができる：

Wolfram Language code: Subscript[ℛ, 1] = Rectangle[]; Subscript[ℛ, 2] = Parallelogram[{0, 0}, {{1, 0}, {0, 1}}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]
Wolfram Language code: RegionWithin[Subscript[ℛ, 1], Subscript[ℛ, 2]] && RegionWithin[Subscript[ℛ, 2], Subscript[ℛ, 1]]

非空の領域について，RegionDisjointは，RegionEqualがTrueを返すときにFalseを返す：

Wolfram Language code: Subscript[ℛ, 1] = Rectangle[]; Subscript[ℛ, 2] = Parallelogram[{0, 0}, {{1, 0}, {0, 1}}];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]
Wolfram Language code: RegionDisjoint[Subscript[ℛ, 1], Subscript[ℛ, 2]]

FindInstanceを使って一方の領域にはあるがもう一方の領域にはない点を求める：

Wolfram Language code: Subscript[ℛ, 1] = Rectangle[]; Subscript[ℛ, 2] = Parallelogram[];
Wolfram Language code: RegionEqual[Subscript[ℛ, 1], Subscript[ℛ, 2]]
Wolfram Language code: pts = {x, y} /. FindInstance[{x, y}∈Subscript[ℛ, 1]⊻{x, y}∈Subscript[ℛ, 2], {x, y}, 100];
Wolfram Language code: Graphics[{Point[pts], Opacity[0.5], {Red, Subscript[ℛ, 1]}, {Green, Subscript[ℛ, 2]}}]

RandomPointを使って一方の領域にはあるがもう一方の領域にはない点の一様サンプリングを求める：

Wolfram Language code: pts = RandomPoint[BooleanRegion[Xor, {Subscript[ℛ, 1], Subscript[ℛ, 2]}], 100];
Wolfram Language code: Graphics[{Point[pts], Opacity[0.5], {Red, Subscript[ℛ, 1]}, {Green, Subscript[ℛ, 2]}}]

Reduceを使って2つの領域が異なる場所を求める：

Wolfram Language code: Reduce[{x, y}∈Subscript[ℛ, 1]⊻{x, y}∈Subscript[ℛ, 2], {x, y}]
Wolfram Language code: RegionPlot[%, {x, -1, 3}, {y, -3 / 2, 5 / 2}, PlotPoints -> 60]
Wolfram Research (2017), RegionEqual, Wolfram言語関数， https://reference.wolfram.com/language/ref/RegionEqual.html.

テキスト

Wolfram Research (2017), RegionEqual, Wolfram言語関数， https://reference.wolfram.com/language/ref/RegionEqual.html.

CMS

Wolfram Language. 2017. "RegionEqual." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RegionEqual.html.

APA

Wolfram Language. (2017). RegionEqual. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RegionEqual.html

BibTeX

@misc{reference.wolfram_2026_regionequal, author="Wolfram Research", title="{RegionEqual}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/RegionEqual.html}", note=[Accessed: 20-July-2026]}

BibLaTeX

@online{reference.wolfram_2026_regionequal, organization={Wolfram Research}, title={RegionEqual}, year={2017}, url={https://reference.wolfram.com/language/ref/RegionEqual.html}, note=[Accessed: 20-July-2026]}