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AdjacentMeshCells[mr,cellspec,d]

给出维度为 d 的单元，该单元与网格 mr 中 cellspec 指定的单元相邻.

更多信息
Details and Options Details and Options
范例  
基本范例  
范围  
基本用法  
网格区域  
多边形和多面体  
应用  
基本应用  
邻接查询  
多面体运算  
拓扑运算  
属性和关系  
巧妙范例  
参见
相关指南
历史
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AdjacentMeshCells

AdjacentMeshCells[mr,cellspec,d]

给出维度为 d 的单元，该单元与网格 mr 中 cellspec 指定的单元相邻.

更多信息

  • AdjacentMeshCells 也称为邻近（neighboring）单元.
  • 典型用途包括在网格中获取单元邻接关系和拓扑信息.
  • AdjacentMeshCells[mr,cellspec,d] 返回一个单元指标列表，该列表与由 cellspec 指定的单元相邻的 d 维单元相关.
  • 可以使用以下单元规范 cellspec：
  • {d,i}维度为 d、索引为 i 的单元
    {d,ispec}维度为 d、索引规范为 ispec 的单元
    {dspec,…}维度由 dspec 给定的单元
    h[{i1,…}]头为 h、顶点索引为 i1, … 的显式单元
    {c1,c2,…}显式单元 ci 的列表
  • 索引规范 ispec 可以采用以下形式：
  • i单元索引 i
    {i1,i2,…}索引为 ik 的单元
    All所有单元
    patt索引与模式 patt 匹配的单元
  • 维度规范 dspec 可以采用以下形式：
  • d显式维度 d
    All从0到区域的几何维度的所有维度
    patt与模式 patt 匹配的维度

范例

打开所有单元 关闭所有单元

基本范例  (2)

与单元 {0,2} 相邻的直线的列表：

Wolfram Language code: ℛ = MengerMesh[1, MeshCellStyle -> {{0, 2} -> Red}]
Wolfram Language code: AdjacentMeshCells[ℛ, {0, 2}, 1]
Wolfram Language code: HighlightMesh[ℛ, %]

找出与模式匹配的单元相邻的所有面：

Wolfram Language code: pattern = {0, _ ? (# < 3&)}; ℛ = VoronoiMesh[RandomReal[1, {10, 2}], MeshCellStyle -> {pattern -> Red}];
Wolfram Language code: AdjacentMeshCells[ℛ, pattern, 2]
Wolfram Language code: HighlightMesh[ℛ, %]

范围  (5)

基本用法  (2)

使用索引和维度指定单元：

Wolfram Language code: ℛ = MeshRegion[{{0, 0, 0}, {2, 0, 0}, {2, 2, 0}, {0, 2, 0}, {1, 1, 2}}, {Tetrahedron[{{1, 2, 3, 5}, {1, 3, 4, 5}}]}]
Wolfram Language code: AdjacentMeshCells[ℛ, {0, 1}, 2]

模式：

Wolfram Language code: AdjacentMeshCells[ℛ, {_, 1}, 2]

显式单元：

Wolfram Language code: AdjacentMeshCells[ℛ, Line[{1, 2}], 2]

单元列表：

Wolfram Language code: AdjacentMeshCells[ℛ, {{0, 1}, {1, 2}}, 2]

查找与单元 {0, 1} 相邻的不同维度的单元：

Wolfram Language code: Table[AdjacentMeshCells[[image], {0, 1}, d], {d, {0, 1, 2, 3}}]

网格区域  (2)

二维 MeshRegion 的 AdjacentMeshCells：

Wolfram Language code: mesh = DelaunayMesh[RandomReal[1, {10, 2}], MeshCellStyle -> {{0, 1} -> Green}]
Wolfram Language code: AdjacentMeshCells[mesh, {0, 1}, 1]

突出显示单元：

Wolfram Language code: HighlightMesh[mesh, %]

一维：

Wolfram Language code: AdjacentMeshCells[[image], {0, 1}, 1]

三维：

Wolfram Language code: mesh = [image];
Wolfram Language code: AdjacentMeshCells[mesh, {0, 1}, 1]

突出显示单元：

Wolfram Language code: HighlightMesh[mesh, %]

BoundaryMeshRegion 的 AdjacentMeshCells：

Wolfram Language code: mesh = BoundaryMeshRegion[{{0, 0}, {3, 0}, {3, 3}, {0, 3}, {1, 1}, {2, 1}, {2, 2}, {1, 2}}, Line[{1, 2, 3, 4, 1}], Line[{5, 6, 7, 8, 5}], MeshCellStyle -> {{0, 1} -> Green}]
Wolfram Language code: AdjacentMeshCells[mesh, {0, 1}, 1]

突出显示单元：

Wolfram Language code: HighlightMesh[mesh, %]

一维：

Wolfram Language code: AdjacentMeshCells[[image], {0, 1}, 0]

三维：

Wolfram Language code: mesh = [image];
Wolfram Language code: AdjacentMeshCells[mesh, {0, 1}, 1]

突出显示单元：

Wolfram Language code: HighlightMesh[mesh, %]

多边形和多面体  (1)

Cube 的 AdjacentMeshCells：

Wolfram Language code: ℛ = Cube[];
Wolfram Language code: AdjacentMeshCells[ℛ, {0, 1}, 1]
Wolfram Language code: HighlightMesh[ℛ, %]

Simplex：

Wolfram Language code: ℛ = Simplex[{{0, 0, 1}, {1, 0, 0}, {1, 0, 1}, {1, 1, 1}}];
Wolfram Language code: AdjacentMeshCells[ℛ, {0, 1}, 1]
Wolfram Language code: HighlightMesh[ℛ, %]

Polyhedron：

Wolfram Language code: ℛ = Polyhedron[{{-0.85065080835204, 0., 1.1135163644116066}, {-0.2628655560595668, 0.8090169943749475, 1.1135163644116066}, {-0.42532540417602, 1.3090169943749475, 0.2628655560595668}, {-1.1135163644116066, 0.8090169943749475, -0.262865556059566 ... {{1, 2, 3, 4, 5}, {6, 7, 1, 5, 8}, {9, 10, 6, 8, 11}, {12, 13, 9, 11, 14}, {4, 14, 11, 8, 5}, {3, 15, 12, 14, 4}, {16, 17, 10, 9, 13}, {18, 16, 13, 12, 15}, {19, 18, 15, 3, 2}, {20, 19, 2, 1, 7}, {17, 20, 7, 6, 10}, {16, 18, 19, 20, 17}}];
Wolfram Language code: AdjacentMeshCells[ℛ, {0, 1}, 1]
Wolfram Language code: HighlightMesh[ℛ, %]

Triangle：

Wolfram Language code: ℛ = Triangle[{{0, 0}, {1, 1}, {2, 0}}];
Wolfram Language code: AdjacentMeshCells[ℛ, {0, 1}, 1]
Wolfram Language code: HighlightMesh[ℛ, %]

Polygon：

Wolfram Language code: ℛ = Polygon[{{1, 0}, {1/2, Sqrt[3]/2}, {-1/2, Sqrt[3]/2}, {-1, 0}, {-1/2, -1/2*Sqrt[3]}, {1/2, -1/2*Sqrt[3]}}];
Wolfram Language code: AdjacentMeshCells[ℛ, {0, 1}, 1]
Wolfram Language code: HighlightMesh[ℛ, %]

Line：

Wolfram Language code: ℛ = Line[{{1, 0}, {2, 1}, {3, 0}, {4, 1}}];
Wolfram Language code: AdjacentMeshCells[ℛ, {0, 1}, 1]
Wolfram Language code: HighlightMesh[ℛ, %]

应用  (8)

基本应用  (5)

Triangle 的邻接网格单元：

Wolfram Language code: mesh = [image];
Wolfram Language code: cells = AdjacentMeshCells[mesh, {0, 2}, 0]
Wolfram Language code: HighlightMesh[mesh, cells]

Cube 的邻接网格单元：

Wolfram Language code: mesh = [image];
Wolfram Language code: cells = AdjacentMeshCells[mesh, {0, 6}, 0]
Wolfram Language code: HighlightMesh[mesh, cells]

MengerMesh 的邻接网格单元：

Wolfram Language code: mesh = MengerMesh[2, MeshCellStyle -> {{0, 6} -> Red}];
Wolfram Language code: cells = AdjacentMeshCells[mesh, {0, 6}, 0]
Wolfram Language code: HighlightMesh[mesh, cells]

三维边界网格的邻接网格单元：

Wolfram Language code: mesh = [image];
Wolfram Language code: cells = AdjacentMeshCells[mesh, {0, 12}, 0]
Wolfram Language code: HighlightMesh[mesh, cells]

获取沃罗诺伊网格的邻接点：

Wolfram Language code: pts = RandomReal[1, {10, 2}];
Wolfram Language code: mesh = VoronoiMesh[pts, MeshCellStyle -> {{0, 12} -> Red}];
Wolfram Language code: cells = AdjacentMeshCells[mesh, {0, 12}, 0]
Wolfram Language code: HighlightMesh[mesh, cells]

邻接查询  (1)

使用 AdjacentMeshCells 查找与单元索引为 {0,1} 的点连接的所有点：

Wolfram Language code: AdjacentMeshCells[[image], {0, 1}, 0]

多面体运算  (1)

使用 AdjacentMeshCells 计算长方体的 DualPolyhedron：

Wolfram Language code: cube = [image];

获取每个点的相邻面：

Wolfram Language code: faces = (Last /@ AdjacentMeshCells[cube, {0, #}, 2])& /@ Range[MeshCellCount[cube, 0]]

计算对偶的坐标：

Wolfram Language code: pts = MeshCoordinates[cube]; fs = And@@@ MeshCells[cube, 2]; coords = Table[Mean[pts[[i]]], {i, fs}]

构造立方体的对偶：

Wolfram Language code: dual = Polyhedron[coords, faces]
Wolfram Language code: Graphics3D[{Opacity[0.2], cube, dual}]

拓扑运算  (1)

使用 MeshConnectivityGraph 检测网格是否相连：

Wolfram Language code: ConnectedMeshQ[mesh_] := Block[{a = {{0, 1}}, b}, While[b = Union[Join[a, AdjacentMeshCells[mesh, a, 0]]];b =!= a, a = b]; Length[a] == MeshCellCount[mesh, 0] ]
Wolfram Language code: Table[ConnectedMeshQ[i], {i, {[image], [image], [image], [image]}}]

属性和关系  (2)

单元索引 {d, k} 对应于维度为 d 的第 k 组单元：

Wolfram Language code: mesh = MeshRegion[{{0, 0}, {1, 0}, {2, 1 / 2}, {2, -1 / 2}}, {Line[{1, 2}], Line[{2, 3}], Line[{3, 4}], Line[{4, 2}]}]
Wolfram Language code: AdjacentMeshCells[mesh, {1, 2}, 1]

AdjacentMeshCells 可以使用 MeshConnectivityGraph 得到：

Wolfram Language code: mesh = MeshRegion[{{0, 0, 0}, {2, 0, 0}, {2, 2, 0}, {0, 2, 0}, {1, 1, 2}}, {Tetrahedron[{1, 2, 3, 5}], Tetrahedron[{1, 3, 4, 5}]}]
Wolfram Language code: MeshConnectivityGraph[mesh, {0, 2}]
Wolfram Language code: AdjacencyList[%, {0, 1}]
Wolfram Language code: AdjacentMeshCells[mesh, {0, 1}, 2]

巧妙范例  (1)

门格网格的 AdjacentMeshCells：

Wolfram Language code: g = MengerMesh[4]; spec = Thread[List[0, RandomSample[Range[MeshCellCount[g, 0]], 35]]]; cells = AdjacentMeshCells[g, spec, 0];
Wolfram Language code: MeshRegion[g, MeshCellStyle -> Join[{spec -> Red}, Thread[cells -> Green], {{_ ? (# > 0&), All} -> White}], ImageSize -> 200]
Wolfram Research (2020)，AdjacentMeshCells，Wolfram 语言函数，https://reference.wolfram.com/language/ref/AdjacentMeshCells.html.

文本

Wolfram Research (2020)，AdjacentMeshCells，Wolfram 语言函数，https://reference.wolfram.com/language/ref/AdjacentMeshCells.html.

CMS

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

APA

Wolfram 语言. (2020). AdjacentMeshCells. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/AdjacentMeshCells.html 年

BibTeX

@misc{reference.wolfram_2026_adjacentmeshcells, author="Wolfram Research", title="{AdjacentMeshCells}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/AdjacentMeshCells.html}", note=[Accessed: 08-September-2026]}

BibLaTeX

@online{reference.wolfram_2026_adjacentmeshcells, organization={Wolfram Research}, title={AdjacentMeshCells}, year={2020}, url={https://reference.wolfram.com/language/ref/AdjacentMeshCells.html}, note=[Accessed: 08-September-2026]}