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ArrayMesh[array]

由秩为 d 的数组生成网格区域，其中各个单元具有几何维度 d，表示数组的非零值.

更多信息和选项
Details and Options Details and Options
范例  
基本范例  
范围  
选项  
DataRange  
DataReversed  
MeshCellHighlight  
Show More Show More
MeshCellLabel  
MeshCellMarker  
MeshCellShapeFunction  
MeshCellStyle  
PlotTheme  
应用  
Cellular Automaton  
Image  
Pattern  
SubstitutionSystem  
Game Design  
属性和关系  
参见
相关指南
历史
按以下格式引用：

ArrayMesh

ArrayMesh[array]

由秩为 d 的数组生成网格区域，其中各个单元具有几何维度 d，表示数组的非零值.

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)

一维数组网格：

Wolfram Language code: ArrayMesh[{1, 0, 1, 1, 0, 1}]

二维数组网格：

Wolfram Language code: ArrayMesh[{{1, 1, 0, 1}, {1, 1, 1, 1}, {0, 1, 0, 1}}]

三维数组网格：

Wolfram Language code: ArrayMesh[{{{1, 1}, {1, 1}, {1, 0}}, {{0, 1}, {1, 1}, {0, 0}}}]

范围  (2)

创建一维数组网格：

Wolfram Language code: ArrayMesh[{1, 1, 0, 0, 1}]

二维数组网格：

Wolfram Language code: ArrayMesh[{{1, 1, 0, 1}, {1, 1, 1, 1}, {0, 1, 0, 1}}]

三维数组网格：

Wolfram Language code: ArrayMesh[{{{1, 1}, {1, 1}, {1, 0}}, {{0, 1}, {1, 1}, {0, 0}}}]

ArrayMesh 作用于 SparseArray：

Wolfram Language code: ArrayMesh[SparseArray[{{x_, y_} /; Abs[x - y] < 2 -> 1}, {3, 3}]]

选项  (14)

DataRange  (1)

DataRange 允许指定所要生成网格的坐标范围：

Wolfram Language code: ArrayMesh[{{1, 0}, {1, 1}}]
Wolfram Language code: MeshCoordinates[%]

指定不同范围：

Wolfram Language code: ArrayMesh[{{1, 0}, {1, 1}}, DataRange -> {{0, 1}, {0, 2}}]
Wolfram Language code: MeshCoordinates[%]

DataReversed  (1)

DataReversed 允许颠倒行序：

Wolfram Language code: ArrayMesh[{{1, 0, 0}, {1, 1, 0}, {1, 0, 1}, {1, 1, 1}}]

颠倒行序：

Wolfram Language code: ArrayMesh[{{1, 0, 0}, {1, 1, 0}, {1, 0, 1}, {1, 1, 1}}, DataReversed -> True]

MeshCellHighlight  (2)

MeshCellHighlight 允许突出显示 ArrayMesh 的一部分：

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

个体单元可以使用其单元索引进行突出显示：

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

或者通过单元自身：

Wolfram Language code: ArrayMesh[{{1, 0}, {1, 1}}, MeshCellHighlight -> {Line[{4, 6}] -> {Thick, Red}, Line[{5, 6}] -> {Dashed, Green}}]

MeshCellLabel  (2)

MeshCellLabel 可用于对 ArrayMesh 的一部分添加标签：

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

个体单元可以使用其单元索引添加标签：

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

或者通过单元自身：

Wolfram Language code: ArrayMesh[{{1, 0}, {1, 1}}, MeshCellLabel -> {Line[{5, 6}] -> "x", Line[{4, 6}] -> "y"}]

MeshCellMarker  (1)

MeshCellMarker 可用于对 ArrayMesh 的一部分进行赋值：

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

使用 MeshCellLabel 显示标记：

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

MeshCellShapeFunction  (2)

MeshCellShapeFunction 可用于对 ArrayMesh 的一部分进行赋值：

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

个体单元可以使用其单元索引绘制：

Wolfram Language code: ArrayMesh[{{{1, 0}}}, MeshCellShapeFunction -> {{1, 4} -> (Tube[#1, .1]&)}]

或通过单元自身：

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

MeshCellStyle  (3)

MeshCellStyle 允许指定一部分 ArrayMesh 的样式化：

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

个体单元可以使用其单元索引突出显示：

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

或通过单元自身：

Wolfram Language code: ArrayMesh[{{1, 0}}, MeshCellStyle -> {Line[{3, 4}] -> {Thick, Red}, Line[{2, 4}] -> {Dashed, Green}}]

给出显式颜色指令来指定个体单元的颜色：

Wolfram Language code: ArrayMesh[{{1, 0, 0, 1}, {1, 1, 0, 1}, {1, 0, 1, 1}}, MeshCellStyle -> {{2, All} -> Black, {2, 1} -> Red, {2, {2, 3}} -> Pink}]

PlotTheme  (2)

使用带有网格线的主题和图例：

Wolfram Language code: ArrayMesh[{{1, 0}, {1, 1}}, PlotTheme -> "Detailed"]

使用主题绘制线框：

Wolfram Language code: ArrayMesh[{{1, 0}, {1, 1}}, PlotTheme -> "Lines"]

应用  (15)

Cellular Automaton  (5)

二维元胞自动机的演化：

Wolfram Language code: ArrayMesh[CellularAutomaton[30, {{1}, 0}, 50]]

显示三维元胞自动机演化的步骤序列：

Wolfram Language code: ArrayMesh /@ CellularAutomaton[{14, {2, 1}, {1, 1, 1}}, {{{{1}}}, 0}, 10]

使用外部加总（Outer-totalistic）二维元胞自动机生成类似迷宫的模式：

Wolfram Language code: ArrayMesh[CellularAutomaton[{746, {2, {{2, 2, 2}, {2, 1, 2}, {2, 2, 2}}}, {1, 1}}, {{Table[1, {7}]}, 0}, {{{150}}}]]

显示 Game of Life 中的滑翔机：

Wolfram Language code: c = CellularAutomaton[{224, {2, {{2, 2, 2}, {2, 1, 2}, {2, 2, 2}}}, {1, 1}}, {{{0, 1, 0}, {0, 0, 1}, {1, 1, 1}}, 0}, 8];
Wolfram Language code: glider = (First /@ Position[Flatten[#], 1])& /@ c;
Wolfram Language code: ArrayMesh[ConstantArray[1, {5, 5}], MeshCellStyle -> {{1, All} -> Black, {2, All} -> White, {2, #} -> Black}]& /@ glider

由二维9邻域规则生成的模式：

Wolfram Language code: Table[ArrayMesh[CellularAutomaton[{i, {2, 1}, {1, 1}}, {{{1}}, 0}, {{{30}}}]], {i, 2, 20, 4}]

平均单元值：

Wolfram Language code: Table[ArrayMesh[Mean[CellularAutomaton[{i, {2, 1}, {1, 1}}, {{{1}}, 0}, 10]]], {i, 2, 20, 4}]

Image  (2)

将二维图像转换为 MeshRegion：

Wolfram Language code: img = [image];

单元和样式：

Wolfram Language code: cells = ImageData[img];
Wolfram Language code: style = MapIndexed[{2, First[#2]} -> GrayLevel[#1] &, Flatten[cells]];

网格：

Wolfram Language code: ArrayMesh[cells, MeshCellStyle -> style]

转换为三维图像：

Wolfram Language code: img = Image3D[RandomReal[1, {2, 3, 4}], ColorFunction -> GrayLevel]

单元和样式：

Wolfram Language code: cells = Transpose[ImageData[img], {2, 3, 1}];
Wolfram Language code: style = MapIndexed[{3, First[#2]} -> GrayLevel[#1] &, Flatten[cells]];

网格：

Wolfram Language code: ArrayMesh[cells, MeshCellStyle -> style]

Pattern  (2)

生成简单的二维模式：

Wolfram Language code: ArrayMesh[Table[If[Mod[i, 4] == 2 && Mod[j, 4] == 2, 0, 1], {i, 11}, {j, 11}]]

三维模式：

Wolfram Language code: ArrayMesh[{{{1, 1, 1}, {1, 0, 1}, {1, 1, 1}}, {{1, 1, 1}, {1, 0, 1}, {1, 1, 1}}, {{1, 1, 1}, {1, 0, 1}, {1, 1, 1}}}]

涉及更多的模式：

Wolfram Language code: ArrayMesh[CellularAutomaton[{14, {2, 1}, {1, 1}}, {{{1}}, 0}, 10]]

构建 Seidel 网格，具有各个方向的隧道而不交叉：

Wolfram Language code: SeidelMesh[{r_, s_, t_}] := ArrayMesh[Table[If[Mod[i, 4] == 2 && Mod[j, 4] == 2 || Mod[i, 4] == 0 && Mod[k, 4] == 0 || Mod[j, 4] == 0 && Mod[k, 4] == 2, 0, 1], {i, 3 + r 4}, {j, 3 + s 4}, {k, 3 + t 4}]]
Wolfram Language code: SeidelMesh[{1, 1, 1}]

通过转换为边界网格并对其样式化，它变得易于理解：

Wolfram Language code: HighlightMesh[BoundaryMesh[%], {Style[1, None], Style[2, Opacity[0.5]]}]

SubstitutionSystem  (4)

一维康托尔网格：

Wolfram Language code: ArrayMesh[{1, 0, 1, 0, 0, 0, 1, 0, 1}]

每个阶段康托尔集合的长度：

Wolfram Language code: Table[Rationalize[RegionMeasure[ArrayMesh[n]]], {n, SubstitutionSystem[{1 -> {1, 0, 1}, 0 -> {0, 0, 0}}, {1}, 5]}]

公式：

Wolfram Language code: FindSequenceFunction[%, n]

建立康托尔集合的步骤：

Wolfram Language code: ArrayMesh[{#}]& /@ SubstitutionSystem[{1 -> {1, 0, 1}, 0 -> {0, 0, 0}}, {1}, 3]

创建一个类似的二维嵌套对象：

Wolfram Language code: ArrayMesh /@ SubstitutionSystem[{1 -> {{1, 1, 1}, {1, 0, 1}, {1, 1, 1}}, 0 -> ConstantArray[0, {3, 3}]}, {{1}}, 3]

三维 Menger 海绵：

Wolfram Language code: ArrayMesh /@ SubstitutionSystem[{1 -> 1 - CrossMatrix[{1, 1, 1}], 0 -> ConstantArray[0, {3, 3, 3}]}, {{{1}}}, 3]

Game Design  (2)

建立二维国际象棋棋盘：

Wolfram Language code: m = Join@@ConstantArray[{{0, 1, 0, 1, 0, 1, 0, 1}, {1, 0, 1, 0, 1, 0, 1, 0}}, 4];
Wolfram Language code: p = First /@ Position[Flatten[m], 1];
Wolfram Language code: style = {{1, All} -> {Thick, Black}, {2, All} -> White, {2, #}& /@ p -> Black};
Wolfram Language code: r = ArrayMesh[ConstantArray[1, {8, 8}], MeshCellStyle -> style]

三维棋盘：

Wolfram Language code: m = Join@@ConstantArray[{{{0}, {1}, {0}, {1}, {0}, {1}, {0}, {1}}, {{1}, {0}, {1}, {0}, {1}, {0}, {1}, {0}}}, 4];
Wolfram Language code: p = First /@ Position[Flatten[m], 1];
Wolfram Language code: style = {{1, All} -> {Thick, Black}, {3, All} -> White, {3, #}& /@ p -> Black};
Wolfram Language code: r = ArrayMesh[ConstantArray[1, {8, 8, 1}], MeshCellStyle -> style]

生成俄罗斯方块，每一个由四个正方形组成：

Wolfram Language code: reg = ArrayMesh /@ {(⁠| | | | | | - | - | - | - | | 1 | 0 | 0 | 0 | | 1 | 0 | 0 | 0 | | 1 | 0 | 0 | 0 | | 1 | 0 | 0 | 0 |⁠), (⁠| | | | | | - | - | - | - | | 1 | 1 | 0 | 0 | | 0 | 1 | 0 | 0 | | 0 | 1 | 0 | 0 | | 0 | 0 | 0 | 0 |⁠), (⁠| | | | | | - | - | - | - | | 1 | 1 | 0 | 0 | | 1 | 0 | 0 | 0 | | 1 | 0 | 0 | 0 | | 0 | 0 | 0 | 0 |⁠), (⁠| | | | | | - | - | - | - | | 0 | 1 | 0 | 0 | | 1 | 1 | 0 | 0 | | 0 | 1 | 0 | 0 | | 0 | 0 | 0 | 0 |⁠), (⁠| | | | | | - | - | - | - | | 1 | 0 | 0 | 0 | | 1 | 1 | 0 | 0 | | 0 | 1 | 0 | 0 | | 0 | 0 | 0 | 0 |⁠), (⁠| | | | | | - | - | - | - | | 1 | 1 | 0 | 0 | | 1 | 1 | 0 | 0 | | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 0 |⁠), (⁠| | | | | | - | - | - | - | | 1 | 1 | 0 | 0 | | 0 | 1 | 1 | 0 | | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 0 |⁠)}

对俄罗斯方块上色：

Wolfram Language code: col = ColorData[97, "ColorList"];
Wolfram Language code: Table[MeshRegion[reg[[i]], MeshCellStyle -> {2 -> col[[i]]}], {i, 7}]

属性和关系  (6)

ArrayMesh 的输出恒为全维的 MeshRegion：

Wolfram Language code: ArrayMesh[RandomInteger[1, {3, 4}]]
Wolfram Language code: {MeshRegionQ[%], RegionDimension[%]}

ArrayMesh 在一维中由区间组成：

Wolfram Language code: ArrayMesh[{1, 1, 0, 0, 1}]
Wolfram Language code: MeshCells[%, RegionDimension[%]]

二维矩形：

Wolfram Language code: ArrayMesh[{{0, 0, 1, 1}, {0, 1, 1, 0}, {1, 0, 0, 0}}]
Wolfram Language code: MeshCells[%, RegionDimension[%]]

三维六面体：

Wolfram Language code: ArrayMesh[{{{1, 0}, {0, 1}}}]
Wolfram Language code: MeshCells[%, RegionDimension[%]]

ArrayPlot 可用于生成图形：

Wolfram Language code: arr = {{0, 1, 1, 0}, {1, 0, 1, 0}, {1, 1, 0, 1}};
Wolfram Language code: ArrayMesh[arr]

显示图形：

Wolfram Language code: ArrayPlot[arr]

MatrixPlot 可用于生成图形：

Wolfram Language code: arr = {{0, 1, 1, 0}, {1, 0, 1, 0}, {1, 1, 0, 1}};
Wolfram Language code: ArrayMesh[arr]

显示图形：

Wolfram Language code: MatrixPlot[arr]

通过使用 BoundaryMesh 求边界网格区域：

Wolfram Language code: BoundaryMesh[ArrayMesh[{{0, 1, 1, 0}, {1, 0, 1, 0}, {1, 1, 0, 1}}]]

DataRange range 等价于使用 RescalingTransform[{...},range]：

Wolfram Language code: ArrayMesh[{{1, 0}, {1, 1}}, DataRange -> {{1, 2}, {1, 3}}, Frame -> True]

使用 RescalingTransform：

Wolfram Language code: box = TransformedRegion[ArrayMesh[{{1, 0}, {1, 1}}], RescalingTransform[{{0, 2}, {0, 2}}, {{1, 2}, {1, 3}}]];
Wolfram Language code: MeshRegion[box, Frame -> True]
Wolfram Research (2016)，ArrayMesh，Wolfram 语言函数，https://reference.wolfram.com/language/ref/ArrayMesh.html.

文本

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_arraymesh, author="Wolfram Research", title="{ArrayMesh}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/ArrayMesh.html}", note=[Accessed: 17-July-2026]}

BibLaTeX

@online{reference.wolfram_2026_arraymesh, organization={Wolfram Research}, title={ArrayMesh}, year={2016}, url={https://reference.wolfram.com/language/ref/ArrayMesh.html}, note=[Accessed: 17-July-2026]}