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ConvexHullMesh[{p1,p2,…}]

给出 BoundaryMeshRegion，表示来自点 p1、p2、… 的凸包.

ConvexHullMesh[mreg]

给出网格区域 mreg 的凸包.

更多信息和选项
Details and Options Details and Options
范例  
基本范例  
范围  
选项  
MeshCellHighlight  
MeshCellLabel  
MeshCellMarker  
MeshCellShapeFunction  
MeshCellStyle  
PlotTheme  
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：

ConvexHullMesh

ConvexHullMesh[{p1,p2,…}]

给出 BoundaryMeshRegion，表示来自点 p1、p2、… 的凸包.

ConvexHullMesh[mreg]

给出网格区域 mreg 的凸包.

更多信息和选项

范例

打开所有单元 关闭所有单元

基本范例  (3)

一维凸包网格：

Wolfram Language code: pts = RandomReal[{-1, 1}, {5, 1}];
Wolfram Language code: ConvexHullMesh[pts]

区域是包括点的最小凸域：

Wolfram Language code: Show[%, Show[%, Graphics[Point[Append[#, 0]& /@ pts]]]]

二维凸包网格：

Wolfram Language code: pts = RandomReal[{-1, 1}, {50, 2}];
Wolfram Language code: ConvexHullMesh[pts]

区域是包括点的最小凸域：

Wolfram Language code: Show[%, Graphics[Point[pts]]]

三维凸包网格：

Wolfram Language code: pts = RandomReal[{-1, 1}, {50, 3}];
Wolfram Language code: ConvexHullMesh[pts]

区域是包括点的最小凸域：

Wolfram Language code: Show[HighlightMesh[%, Style[2, Opacity[0.5]]], Graphics3D[Point[pts]]]

范围  (3)

由一组点创建一维凸包网格：

Wolfram Language code: pts = RandomReal[{-1, 1}, {50, 1}];
Wolfram Language code: ℛ = ConvexHullMesh[pts]

基本属性：

Wolfram Language code: {RegionQ[ℛ], BoundaryMeshRegionQ[ℛ]}

凸包网格是有界的：

Wolfram Language code: {BoundedRegionQ[ℛ], RegionBounds[ℛ]}

凸包网格是全维的：

Wolfram Language code: {RegionDimension[ℛ], RegionEmbeddingDimension[ℛ]}

求它的面积和形心：

Wolfram Language code: {RegionMeasure[ℛ], RegionCentroid[ℛ]}

检验点的成员属性：

Wolfram Language code: RegionMember[ℛ, {0}]

求最近的点及其距离：

Wolfram Language code: {RegionDistance[ℛ, {2}], RegionNearest[ℛ, {2}]}

由一组点创建二维凸包网格：

Wolfram Language code: pts = RandomReal[{-1, 1}, {50, 2}];
Wolfram Language code: ℛ = ConvexHullMesh[pts]

基本属性：

Wolfram Language code: {RegionQ[ℛ], BoundaryMeshRegionQ[ℛ]}

凸包网格是有界的：

Wolfram Language code: {BoundedRegionQ[ℛ], RegionBounds[ℛ]}

凸包网格是全维的：

Wolfram Language code: {RegionDimension[ℛ], RegionEmbeddingDimension[ℛ]}

求它的面积和形心：

Wolfram Language code: {RegionMeasure[ℛ], RegionCentroid[ℛ]}

检验点的成员属性：

Wolfram Language code: RegionMember[ℛ, {0, 0}]

求最近的点及其距离：

Wolfram Language code: {RegionDistance[ℛ, {2, 2}], RegionNearest[ℛ, {2, 2}]}

由一组点创建三维凸包网格：

Wolfram Language code: pts = RandomReal[{-1, 1}, {50, 3}];
Wolfram Language code: ℛ = ConvexHullMesh[pts]

基本属性：

Wolfram Language code: {RegionQ[ℛ], BoundaryMeshRegionQ[ℛ]}

凸包网格是有界的：

Wolfram Language code: {BoundedRegionQ[ℛ], RegionBounds[ℛ]}

凸包网格是全维的：

Wolfram Language code: {RegionDimension[ℛ], RegionEmbeddingDimension[ℛ]}

求它的体积和形心：

Wolfram Language code: {RegionMeasure[ℛ], RegionCentroid[ℛ]}

求它的表面积：

Wolfram Language code: Area[RegionBoundary[ℛ]]
Wolfram Language code: RegionMember[ℛ, {0, 0, 0}]

求最近的点及其距离：

Wolfram Language code: {RegionDistance[ℛ, {2, 2, 2}], RegionNearest[ℛ, {2, 2, 2}]}

选项  (13)

MeshCellHighlight  (3)

MeshCellHighlight 允许指定 ConvexHullMesh 的高亮部分：

Wolfram Language code: ConvexHullMesh[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, MeshCellHighlight -> {{1, All} -> Orange, {0, All} -> Green}]

通过使表面透明，可以看见三维 ConvexHullMesh 的内部结构：

Wolfram Language code: ConvexHullMesh[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {1, 1, 0}}, MeshCellHighlight -> {{2, All} -> Opacity[0.5, Orange]}]

单个单元可以使用它们的索引加以强调：

Wolfram Language code: ConvexHullMesh[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, MeshCellHighlight -> {{1, 1} -> {Thick, Orange}, {1, 2} -> {Dashed, Green}}]

或者通过单元自身：

Wolfram Language code: ConvexHullMesh[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, MeshCellHighlight -> {Line[{1, 2}] -> {Thick, Orange}, Line[{2, 4}] -> {Dashed, Green}}]

MeshCellLabel  (2)

MeshCellLabel 可用于标记部分 ConvexHullMesh：

Wolfram Language code: ConvexHullMesh[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, MeshCellLabel -> {0 -> "Index"}]

单个单元可以通过它们的单元索引进行标记：

Wolfram Language code: ConvexHullMesh[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, MeshCellLabel -> {{1, 1} -> "x", {1, 2} -> "y"}]

或者通过单元自身：

Wolfram Language code: ConvexHullMesh[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, MeshCellLabel -> {Line[{1, 2}] -> "x", Line[{2, 4}] -> "y"}]

MeshCellMarker  (1)

MeshCellMarker 可用于给部分 ConvexHullMesh 进行赋值：

Wolfram Language code: ConvexHullMesh[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, MeshCellMarker -> {{0, 1} -> 1, {0, 2} -> 2, {0, 3} -> 3, {0, 4} -> 4}]

使用 MeshCellLabel 显示标记：

Wolfram Language code: ConvexHullMesh[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, MeshCellMarker -> {{0, 1} -> 1, {0, 2} -> 2, {0, 3} -> 3, {0, 4} -> 4}, MeshCellLabel -> {0 -> "Marker"}]

MeshCellShapeFunction  (2)

MeshCellShapeFunction 允许指定部分 ConvexHullMesh 的函数：

Wolfram Language code: ConvexHullMesh[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, MeshCellShapeFunction -> {0 -> (Disk[#, .1]&)}]

个体单元可以使用它们的单元索引绘制：

Wolfram Language code: ConvexHullMesh[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, MeshCellShapeFunction -> {{0, 1} -> (Disk[#, .1]&), {0, 2} -> (Disk[#, {.1, .2}]&)}]

或者通过单元自身：

Wolfram Language code: ConvexHullMesh[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, MeshCellShapeFunction -> {Point[1] -> (Disk[#, .1]&), Point[2] -> (Disk[#, {.1, .2}]&)}]

MeshCellStyle  (3)

MeshCellStyle 允许指定部分 ConvexHullMesh 的样式：

Wolfram Language code: ConvexHullMesh[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, MeshCellStyle -> {{1, All} -> Orange, {0, All} -> Green}]

通过使表面透明，可以看见三维 ConvexHullMesh 的内部结构：

Wolfram Language code: ConvexHullMesh[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {1, 1, 0}}, MeshCellStyle -> {{2, All} -> Opacity[0.5, Orange]}]

个体单元可以使用它们的单元索引强调：

Wolfram Language code: ConvexHullMesh[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, MeshCellStyle -> {{1, 1} -> {Thick, Orange}, {1, 2} -> {Dashed, Green}}]

或者通过单元自身：

Wolfram Language code: ConvexHullMesh[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, MeshCellStyle -> {Line[{1, 2}] -> {Thick, Orange}, Line[{2, 4}] -> {Dashed, Green}}]

PlotTheme  (2)

使用具有网格线和图例的主题：

Wolfram Language code: ConvexHullMesh[ExampleData[{"Geometry3D", "UtahTeapot"}, "VertexData"], PlotTheme -> "Detailed"]

使用一个主题绘制线框：

Wolfram Language code: ConvexHullMesh[ExampleData[{"Geometry3D", "UtahTeapot"}, "VertexData"], PlotTheme -> "Lines"]

应用  (2)

五个四面体复合的凸包是一个十二面体：

Wolfram Language code: ℛ = DiscretizeGraphics[PolyhedronData["TetrahedronFiveCompound"]]
Wolfram Language code: ConvexHullMesh[MeshCoordinates[ℛ]]

计算一头牛的凸包：

Wolfram Language code: cowPoints = ExampleData[{"Geometry3D", "Cow"}, "VertexData"];
Wolfram Language code: cowvexHull = ConvexHullMesh[cowPoints];

可视化凸包和牛：

Wolfram Language code: cow = ExampleData[{"Geometry3D", "Cow"}, "Graphics3D"];
Wolfram Language code: Show[HighlightMesh[cowvexHull, {Style[1, {Brown}], Style[2, Opacity[0.3, Brown]]}], cow]

属性和关系  (3)

ConvexHullMesh 实际上是 DelaunayMesh 的 BoundaryMesh：

Wolfram Language code: pts = RandomReal[1, {5, 2}];
Wolfram Language code: {BoundaryMesh[DelaunayMesh[pts]], ConvexHullMesh[pts]}

在三维中：

Wolfram Language code: pts = RandomReal[{-1, 1}, {50, 3}];
Wolfram Language code: {BoundaryMesh[DelaunayMesh[pts]], ConvexHullMesh[pts]}

使用 DelaunayMesh 得到凸包内部的德劳内三角化：

Wolfram Language code: DelaunayMesh[RandomReal[1, {25, 2}]]

使用 TriangulateMesh 控制内部的三角化：

Wolfram Language code: ℛ = ConvexHullMesh[RandomReal[1, {25, 2}]];
Wolfram Language code: {TriangulateMesh[ℛ], TriangulateMesh[ℛ, MaxCellMeasure -> ∞]}

可能存在的问题  (1)

ConvexHullMesh 仅返回全维度网格区域：

Wolfram Language code: ConvexHullMesh[{{0., 0.}, {1., 0.}}]

使用 ConvexHullRegion 获取凸包：

Wolfram Language code: ConvexHullRegion[{{0., 0.}, {1., 0.}}]
Wolfram Research (2014)，ConvexHullMesh，Wolfram 语言函数，https://reference.wolfram.com/language/ref/ConvexHullMesh.html （更新于 2020 年）.

文本

Wolfram Research (2014)，ConvexHullMesh，Wolfram 语言函数，https://reference.wolfram.com/language/ref/ConvexHullMesh.html （更新于 2020 年）.

CMS

Wolfram 语言. 2014. "ConvexHullMesh." Wolfram 语言与系统参考资料中心. Wolfram Research. 最新版本 2020. https://reference.wolfram.com/language/ref/ConvexHullMesh.html.

APA

Wolfram 语言. (2014). ConvexHullMesh. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/ConvexHullMesh.html 年

BibTeX

@misc{reference.wolfram_2026_convexhullmesh, author="Wolfram Research", title="{ConvexHullMesh}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/ConvexHullMesh.html}", note=[Accessed: 17-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_convexhullmesh, organization={Wolfram Research}, title={ConvexHullMesh}, year={2020}, url={https://reference.wolfram.com/language/ref/ConvexHullMesh.html}, note=[Accessed: 17-August-2026]}