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InverseTransformedRegion[reg,f,n]

逆変換された領域を表す．ただし，reg は領域であり f は関数である．

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特別な領域  
数式定義領域  
メッシュ領域  
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派生領域  
地理領域  
CSG領域  
細分割領域  
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InverseTransformedRegion

InverseTransformedRegion[reg,f,n]

逆変換された領域を表す．ただし，reg は領域であり f は関数である．

詳細とオプション

例題

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例  (2)

回転された矩形の逆変換：

Wolfram Language code: ℛ = InverseTransformedRegion[Rectangle[], RotationTransform[π / 4]]
Wolfram Language code: Region[ℛ]
Wolfram Language code: Area[ℛ]

からの円板の逆像：

Wolfram Language code: ℛ = InverseTransformedRegion[Disk[], {Indexed[#, 1] Indexed[#, 2], Indexed[#, 1] + Indexed[#, 2]}&, 2];
Wolfram Language code: Region[ℛ]

スコープ  (24)

特別な領域  (9)

逆変換された領域の中には明示的に計算できるものがある：

Wolfram Language code: ℛ = InverseTransformedRegion[Disk[], ShearingTransform[Pi / 4, {1, 0}, {0, 1}]]

変換を可視化する：

Wolfram Language code: Region[ℛ]

線形分数変換による単位直方体の逆画像：

Wolfram Language code: Subscript[ℛ, 1] = Cuboid[]; 𝒯 = TransformationFunction[{{7, 5, -2, 3}, {3, -8, 9, 4}, {-8, 3, 1, -6}, {1, 0, 0, 5}}]; ℛ = InverseTransformedRegion[Subscript[ℛ, 1], 𝒯]

変換を可視化する：

Wolfram Language code: Region[ℛ]

平行移動された単位Diskの逆変換：

Wolfram Language code: ℛ = InverseTransformedRegion[Disk[], TranslationTransform[{2, 3}]]

これを可視化する：

Wolfram Language code: Region[ℛ]

せん断された単位Rectangleの逆変換：

Wolfram Language code: ℛ = TransformedRegion[Rectangle[], ShearingTransform[30Degree, {1, 0}, {0, 1}]]

これを可視化する：

Wolfram Language code: Region[ℛ]

回転されたTriangleの逆変換：

Wolfram Language code: ℛ = TransformedRegion[Triangle[], RotationTransform[π / 3]]

これを可視化する：

Wolfram Language code: Region[ℛ]

スケールされたCircleの逆変換：

Wolfram Language code: ℛ = InverseTransformedRegion[Circle[], ScalingTransform[2., {1, 1}]];
Wolfram Language code: Region[ℛ]

単位立方体の回転変換を介した逆画像：

Wolfram Language code: ℛ = InverseTransformedRegion[Cuboid[{0, 0, 0}, {1, 1, 1}], RotationTransform[Pi / 3, {1, 1, 1}], 3]

これを可視化する：

Wolfram Language code: Region[ℛ]

線形変換による長方形の逆変換：

Wolfram Language code: ℛ = InverseTransformedRegion[Rectangle[], Function[p, {p[[1]] + p[[2]], p[[1]] - p[[2]]}]]

これを可視化する：

Wolfram Language code: Region[ℛ]

2Dに埋込まれたTriangleからの点を，非線形変換で3Dにマップする：

Wolfram Language code: Subscript[ℛ, 1] = Triangle[{{0, 0}, {0, 1}, {1, 0}}];
Wolfram Language code: ℛ = InverseTransformedRegion[Subscript[ℛ, 1], {Indexed[#, 1] ^ 2 + Indexed[#, 2] ^ 2, Indexed[#, 3]}&, 3];

これを可視化する：

Wolfram Language code: Region[ℛ]

数式定義領域  (4)

せん断されたParametricRegionの逆変換：

Wolfram Language code: pr = ParametricRegion[{Sin[θ], Sin[2θ]}, {{θ, 0, 2π}}];
Wolfram Language code: ℛ = InverseTransformedRegion[pr, ShearingTransform[30Degree, {1, 0}, {0, 1}]]

これを可視化する：

Wolfram Language code: Region[ℛ]

回転されたParametricRegionの逆変換：

Wolfram Language code: pr = ParametricRegion[{{s, (1 + t) s ^ 2 - t}, -1 ≤ s ≤ 1 && 0 ≤ t ≤ 1}, {s, t}];
Wolfram Language code: ℛ = InverseTransformedRegion[pr, RotationTransform[Pi / 4, {1, 1}]]

これを可視化する：

Wolfram Language code: Region[ℛ]

せん断されたImplicitRegionの逆変換：

Wolfram Language code: ir = ImplicitRegion[x ^ 2 - y ^ 2 ≤ 1, {x, y}];
Wolfram Language code: ℛ = InverseTransformedRegion[ir, ShearingTransform[30Degree, {1, 0}, {0, 1}]]

これを可視化する：

Wolfram Language code: Region[ℛ]

スケールされたImplicitRegionの逆変換：

Wolfram Language code: ir = ImplicitRegion[x^2 + y^2 + z^2 < 1 || (x + 1)^2 + y^2 + z^2 < 1, {x, y, z}];
Wolfram Language code: ℛ = InverseTransformedRegion[ir, ScalingTransform[{1, 1 / 2, 1 / 2}]]

これを可視化する：

Wolfram Language code: Region[ℛ]

メッシュ領域  (2)

BoundaryMeshRegionオブジェクトを逆変換したものはBoundaryMeshRegionである：

Wolfram Language code: InverseTransformedRegion[[image], TranslationTransform[{1}]]
Wolfram Language code: BoundedRegionQ[%]

2D：

Wolfram Language code: InverseTransformedRegion[[image], ShearingTransform[30Degree, {1, 0}, {0, 1}]]
Wolfram Language code: BoundedRegionQ[%]

3D：

Wolfram Language code: InverseTransformedRegion[[image], RotationTransform[π / 3, {1, 0, 1}]]
Wolfram Language code: BoundedRegionQ[%]

MeshRegionオブジェクトを逆変換したものはMeshRegionである：

Wolfram Language code: InverseTransformedRegion[[image], TranslationTransform[{1}]]
Wolfram Language code: MeshRegionQ[%]

2D：

Wolfram Language code: InverseTransformedRegion[[image], ShearingTransform[30Degree, {1, 0}, {0, 1}]]
Wolfram Language code: MeshRegionQ[%]

3D：

Wolfram Language code: InverseTransformedRegion[[image], RotationTransform[π / 3, {1, 0, 1}]]
Wolfram Language code: MeshRegionQ[%]

派生領域  (5)

反射されたTransformedRegionの逆変換：

Wolfram Language code: tr = TransformedRegion[Cuboid[], ShearingTransform[30Degree, {1, 0, 0}, {0, 1, 1}]];
Wolfram Language code: ℛ = InverseTransformedRegion[tr, ReflectionTransform[{0, 1, 1}]]

これを可視化する：

Wolfram Language code: Region[ℛ]

回転されたRegionDifferenceの逆変換：

Wolfram Language code: rd = RegionDifference[Rectangle[{0, 0}], Disk[{1, 0}, 1 / 2]];
Wolfram Language code: ℛ = InverseTransformedRegion[rd, RotationTransform[π / 4]];

これを可視化する：

Wolfram Language code: Region[ℛ]

スケールされたRegionBoundaryの逆変換：

Wolfram Language code: rb = RegionBoundary[Polygon[{{0, 0}, {3, -1}, {2, 0}, {3, 1}}]];
Wolfram Language code: ℛ = InverseTransformedRegion[rb, ScalingTransform[2, {1, 1}]];

これを可視化する：

Wolfram Language code: Region[ℛ]

反射されたRegionProductの逆変換：

Wolfram Language code: rp = RegionProduct[Disk[{0, 0}, 1], Line[{{0}, {1}}]];
Wolfram Language code: ℛ = InverseTransformedRegion[rp, ReflectionTransform[{1, 0, 1}]];

これを可視化する：

Wolfram Language code: Region[ℛ]

非線形変換によるRegionUnionの逆変換：

Wolfram Language code: ru = RegionUnion[Disk[{0, 0}, 2], Disk[{3, 0}, 2]];
Wolfram Language code: r1 = InverseTransformedRegion[ru, Function[p, {p[[1]] p[[2]], p[[1]] + p[[2]]}]];

これを可視化する：

Wolfram Language code: Region[r1]

地理領域  (2)

InverseTransformedRegionは地理実体の多角形に使うことができる：

Wolfram Language code: ℛ = Polygon[["france"]];
Wolfram Language code: InverseTransformedRegion[ℛ, RotationTransform[Pi / 3, {1, 1, 0}]]
Wolfram Language code: Region[ℛ]

GeoPositionによる多角形：

Wolfram Language code: 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}}}]];
Wolfram Language code: Region[ℛ]
Wolfram Language code: InverseTransformedRegion[ℛ, RotationTransform[Pi / 3, {1, 1, 0}]]

GeoGridPositionによる多角形：

Wolfram Language code: 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"]];
Wolfram Language code: Region[ℛ]
Wolfram Language code: 𝒯 = InverseTransformedRegion[ℛ, RotationTransform[Pi / 3]]
Wolfram Language code: Region[𝒯]

CSG領域  (1)

線形CSGRegionの逆変換：

Wolfram Language code: InverseTransformedRegion[CSGRegion["Difference", {Rectangle[{-1, -1}, {1, 1}], Rectangle[{-1 / 2, -1 / 2}]}], ScalingTransform[{1, 3}]]

非線形の場合：

Wolfram Language code: InverseTransformedRegion[CSGRegion["Difference", {Disk[], Disk[{0, 0}, 1 / 2]}], ScalingTransform[{1, 3}]]

細分割領域  (1)

2DにおけるSubdivisionRegionの逆変換：

Wolfram Language code: InverseTransformedRegion[SubdivisionRegion[Rectangle[]], ScalingTransform[{1, 3}]]

3Dの場合：

Wolfram Language code: InverseTransformedRegion[SubdivisionRegion[Cube[]], ScalingTransform[{1, 1, 3}]]
Wolfram Research (2014), InverseTransformedRegion, Wolfram言語関数， https://reference.wolfram.com/language/ref/InverseTransformedRegion.html.

テキスト

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_inversetransformedregion, author="Wolfram Research", title="{InverseTransformedRegion}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/InverseTransformedRegion.html}", note=[Accessed: 06-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_inversetransformedregion, organization={Wolfram Research}, title={InverseTransformedRegion}, year={2014}, url={https://reference.wolfram.com/language/ref/InverseTransformedRegion.html}, note=[Accessed: 06-November-2026]}