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ShellRegion[reg]

给出三维区域 reg 的实心壳体.

ShellRegion[reg,t]

给出 reg 具有最小厚度 t 的实心壳体.

更多信息
Details and Options Details and Options
范例  
基本范例  
范围  
基本用途  
特殊区域  
公式区域  
网格区域  
应用  
属性和关系  
可能存在的问题  
参见
相关指南
历史
按以下格式引用：

ShellRegion

ShellRegion[reg]

给出三维区域 reg 的实心壳体.

ShellRegion[reg,t]

给出 reg 具有最小厚度 t 的实心壳体.

更多信息

  • 在打印三维物体时，ShellRegion 通常用于挖空实体以节省材料.
  • ShellRegion 保留物体的外表面.

范例

打开所有单元 关闭所有单元

基本范例  (2)

给出球的外壳：

Wolfram Language code: 𝒮 = ShellRegion[Ball[]]
Wolfram Language code: Graphics3D[{Opacity[0.4], 𝒮}, Boxed -> False]

给出网格区域的外壳：

Wolfram Language code: ℛ = ConvexHullMesh[RandomReal[1, {100, 3}]];
Wolfram Language code: 𝒮 = ShellRegion[ℛ];
Wolfram Language code: BoundaryMeshRegion[𝒮, BaseStyle -> Opacity[0.4]]

指定厚度：

Wolfram Language code: 𝒮 = ShellRegion[ℛ, 0.25];
Wolfram Language code: BoundaryMeshRegion[𝒮, BaseStyle -> Opacity[0.4]]

范围  (16)

基本用途  (3)

ShellRegion 可用于实体区域

Wolfram Language code: ShellRegion[Ball[]]

闭合曲面：

Wolfram Language code: ShellRegion[Sphere[]]

指定壳体的厚度：

Wolfram Language code: ShellRegion[Ball[], 3 / 4]

特殊区域  (8)

给出 Ball 的外壳：

Wolfram Language code: 𝒮 = ShellRegion[Ball[]]
Wolfram Language code: Graphics3D[{Opacity[0.4], 𝒮}, Boxed -> False]

Cuboid:

Wolfram Language code: 𝒮 = ShellRegion[Cuboid[]];
Wolfram Language code: Graphics3D[{Opacity[0.4], 𝒮}, Boxed -> False]

Hexahedron:

Wolfram Language code: 𝒮 = ShellRegion[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: Graphics3D[{Opacity[0.4], 𝒮}, Boxed -> False]

Parallelepiped:

Wolfram Language code: 𝒮 = ShellRegion[Parallelepiped[]];
Wolfram Language code: Graphics3D[{Opacity[0.4], 𝒮}, Boxed -> False]

Prism:

Wolfram Language code: 𝒮 = ShellRegion[Prism[]];
Wolfram Language code: Graphics3D[{Opacity[0.4], 𝒮}, Boxed -> False]

Pyramid:

Wolfram Language code: 𝒮 = ShellRegion[Pyramid[]];
Wolfram Language code: Graphics3D[{Opacity[0.4], 𝒮}, Boxed -> False]

Simplex:

Wolfram Language code: 𝒮 = ShellRegion[Simplex[{{0, 0, 0}, {1, 1, 1}, {2, 1, 0}, {1, 0, 0}}]];
Wolfram Language code: Graphics3D[{Opacity[0.4], 𝒮}, Boxed -> False]

Tetrahedron:

Wolfram Language code: 𝒮 = ShellRegion[Tetrahedron[]];
Wolfram Language code: Graphics3D[{Opacity[0.4], 𝒮}, Boxed -> False]

公式区域  (2)

给出 ImplicitRegion 的外壳：

Wolfram Language code: ℛ = ImplicitRegion[x^2 + y^2 + z^2 ≤ 1, {x, y, z}];
Wolfram Language code: 𝒮 = ShellRegion[ℛ, 1 / 4]

可视化外壳：

Wolfram Language code: RegionPlot3D[𝒮, Boxed -> False, PlotStyle -> Opacity[0.4], PlotPoints -> 40]

不等式的布尔组合：

Wolfram Language code: ℛ = ImplicitRegion[x^2 + y^2 + z^2 ≤ 1 || (0 ≤ x ≤ 1 && 0 ≤ y ≤ 1 && 0 ≤ z ≤ 1) || (x^2 + y^2 ≤ 1 / 9 && -2 ≤ z ≤ 2), {x, y, z}];
Wolfram Language code: 𝒮 = ShellRegion[ℛ];

可视化外壳：

Wolfram Language code: RegionPlot3D[𝒮, Boxed -> False, PlotStyle -> Opacity[0.4], PlotPoints -> 40]

网格区域  (3)

给出 BoundaryMeshRegion 的外壳：

Wolfram Language code: ℛ = BoundaryMeshRegion[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, Polygon[{{3, 2, 1}, {2, 3, 4}, {3, 1, 4}, {1, 2, 4}}]];
Wolfram Language code: 𝒮 = ShellRegion[ℛ];

可视化外壳：

Wolfram Language code: BoundaryMeshRegion[𝒮, BaseStyle -> Opacity[0.4]]

MeshRegion:

Wolfram Language code: ℛ = MeshRegion[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, Tetrahedron[{1, 2, 3, 4}]];
Wolfram Language code: 𝒮 = ShellRegion[ℛ];

可视化外壳：

Wolfram Language code: BoundaryMeshRegion[𝒮, BaseStyle -> Opacity[0.4]]

闭合曲面 MeshRegion：

Wolfram Language code: ℛ = MeshRegion[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, Polygon[{{3, 2, 1}, {2, 3, 4}, {3, 1, 4}, {1, 2, 4}}]];
Wolfram Language code: 𝒮 = ShellRegion[ℛ];

可视化外壳：

Wolfram Language code: BoundaryMeshRegion[𝒮, BaseStyle -> Opacity[0.4]]

应用  (5)

挖空一个三维模型：

Wolfram Language code: model = ExampleData[{"Geometry3D", "Triceratops"}, "BoundaryMeshRegion"];
Wolfram Language code: 𝒮 = ShellRegion[model];
Wolfram Language code: BoundaryMeshRegion[𝒮, BaseStyle -> Opacity[0.4]]

一个圆环：

Wolfram Language code: model = ExampleData[{"Geometry3D", "Torus"}, "BoundaryMeshRegion"];
Wolfram Language code: 𝒮 = ShellRegion[model];
Wolfram Language code: BoundaryMeshRegion[𝒮, BaseStyle -> Opacity[0.4]]

一个分子：

Wolfram Language code: model = ChemicalData["Water", "BoundaryMeshRegion"];
Wolfram Language code: 𝒮 = ShellRegion[model];
Wolfram Language code: BoundaryMeshRegion[𝒮, BaseStyle -> Opacity[0.4]]

求体积大约为原来的四分之一的壳体：

Wolfram Language code: ℛ = PolyhedronData["Dodecahedron", "BoundaryMeshRegion"];

在区域中采样，产生到边界的距离的分布：

Wolfram Language code: dists = -SignedRegionDistance[ℛ, RandomPoint[ℛ, 2000]];
Wolfram Language code: 𝒟 = SmoothKernelDistribution[dists];

给出四分之一的采样点都更靠近边界的距离：

Wolfram Language code: t = Quantile[𝒟, 0.25]

所得壳体：

Wolfram Language code: 𝒮 = BoundaryMeshRegion[ShellRegion[ℛ, t], BaseStyle -> Opacity[0.4]]

比较体积：

Wolfram Language code: Volume[𝒮] / Volume[ℛ]

打印三维物体时用 ShellRegion 来节省材料：

Wolfram Language code: ℛ = ConvexHullMesh[RandomReal[1, {100, 3}]];
Wolfram Language code: 𝒮 = ShellRegion[ℛ];

壳体所需材料更少：

Wolfram Language code: Volume[𝒮] / Volume[ℛ]

属性和关系  (3)

ShellRegion 保留物体的外表面：

Wolfram Language code: ℛ = ExampleData[{"Geometry3D", "Triceratops"}, "BoundaryMeshRegion"];
Wolfram Language code: 𝒮 = ShellRegion[ℛ];

提取外表面：

Wolfram Language code: outer = SortBy[ConnectedMeshComponents[RegionBoundary[𝒮]], Area][[-1]]

比较属性：

Wolfram Language code: RegionBounds[ℛ] == RegionBounds[outer]
Wolfram Language code: Area[RegionBoundary[ℛ]] == Area[outer]

通常情况下，壳体的厚度大致是均匀的：

Wolfram Language code: ℛ = ExampleData[{"Geometry3D", "Triceratops"}, "BoundaryMeshRegion"];
Wolfram Language code: 𝒮 = ShellRegion[ℛ, 0.25];

提取内表面和外表面：

Wolfram Language code: {inner, outer} = SortBy[ConnectedMeshComponents[RegionBoundary[𝒮]], Area]

用 RegionDistance 计算到外表面的距离：

Wolfram Language code: RegionDistance[outer, MeshCoordinates[inner]]//Short

Ball 的外壳是 SphericalShell：

Wolfram Language code: Graphics3D[{Opacity[0.4], SphericalShell[]}, Boxed -> False]

用 ShellRegion 计算其他区域的壳：

Wolfram Language code: Graphics3D[{Opacity[0.4], ShellRegion[Ball[]]}, Boxed -> False]
Wolfram Language code: Graphics3D[{Opacity[0.4], ShellRegion[Cuboid[]]}, Boxed -> False]

可能存在的问题  (2)

壳体的厚度可能不是均匀的：

Wolfram Language code: 𝒮 = ShellRegion[ImplicitRegion[x^2 + y^2 - z^3(1 - z) ≤ 0, {x, y, z}], 1 / 10];
Wolfram Language code: RegionPlot3D[𝒮, Boxed -> False, PlotStyle -> Opacity[0.4], PlotPoints -> 100]

区域的不同表示可能给出不同的结果：

Wolfram Language code: ShellRegion[Ball[]]

以 ImplicitRegion 形式给出的 Ball：

Wolfram Language code: ShellRegion[ImplicitRegion[x^2 + y^2 + z^2 ≤ 1, {x, y, z}]]
Wolfram Research (2016)，ShellRegion，Wolfram 语言函数，https://reference.wolfram.com/language/ref/ShellRegion.html.

文本

Wolfram Research (2016)，ShellRegion，Wolfram 语言函数，https://reference.wolfram.com/language/ref/ShellRegion.html.

CMS

Wolfram 语言. 2016. "ShellRegion." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/ShellRegion.html.

APA

Wolfram 语言. (2016). ShellRegion. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/ShellRegion.html 年

BibTeX

@misc{reference.wolfram_2026_shellregion, author="Wolfram Research", title="{ShellRegion}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/ShellRegion.html}", note=[Accessed: 04-October-2026]}

BibLaTeX

@online{reference.wolfram_2026_shellregion, organization={Wolfram Research}, title={ShellRegion}, year={2016}, url={https://reference.wolfram.com/language/ref/ShellRegion.html}, note=[Accessed: 04-October-2026]}