2D-Netze 

Erzeugen Sie zweidimensionale Netze und Begrenzungsflächenmodelle (BReps).

Die gesamte Wolfram-Language Eingabe zeigenEingabe verbergen

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X pointMesh2d = MeshRegion[Tuples[Range[4], 2], Point[Range[16]]];

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X lineMesh2d = MeshRegion[{{0, 0}, {1, 0}, {2, -1}, {2, 1}}, Line[{1, 2, 3, 4, 2}]];

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X polygonMesh2d = MeshRegion[{{2, 0}, {1, 2}, {-1, 2}, {-2, 0}, {-1, -2}, {1, -2}, {0, 0}}, Polygon[{{1, 2, 7}, {2, 3, 7}, {3, 4, 7}, {4, 5, 7}, {5, 6, 7}, {6, 1, 7}}]];

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X mixedMesh2d = MeshRegion[{{0, 0}, {0, 1}, {0, -1}, {1, 0}, {2, -1}, {2, 1}}, {Point[{2, 3}], Line[{1, 4}], Polygon[{4, 5, 6}]}];

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X boundaryMesh2d = BoundaryMeshRegion[{{2, 0}, {1, 2}, {-1, 2}, {-2, 0}, {-1, -2}, {1, -2}}, Line[{1, 2, 3, 4, 5, 6, 1}]];

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X boundaryMeshHoles2d = BoundaryMeshRegion[{{2, 0}, {1, 2}, {-1, 2}, {-2, 0}, {-1, -2}, {1, -2}, {-1, -1}, {1, -1}, {1, 1}, {-1, 1}}, Line[{1, 2, 3, 4, 5, 6, 1}], Line[{7, 8, 9, 10, 7}]];

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X $ImagePadding = 20; ExampleFrame2D[expr_, label_] := Framed[Grid[ List /@ {label, Show[expr, ImagePadding -> $ImagePadding]}, ItemSize -> {15, Automatic}, BaseStyle -> {Gray, FontFamily -> "Helvetica"}, Alignment -> Top], FrameStyle -> Directive[Thickness[4], Gray], RoundingRadius -> 5];

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X Grid[Partition[{ExampleFrame2D[pointMesh2d, "Point Mesh"], ExampleFrame2D[lineMesh2d, "Line Mesh"], ExampleFrame2D[polygonMesh2d, "Polygon Mesh"], ExampleFrame2D[mixedMesh2d, "Mixed Dimension Mesh"], ExampleFrame2D[boundaryMesh2d, "Boundary Mesh"], ExampleFrame2D[boundaryMeshHoles2d, "Boundary Mesh w/ Hole"]}, 3]]

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Komplexe Netze können programmatisch erzeugt werden.

Die gesamte Wolfram-Language Eingabe zeigenEingabe verbergen

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X ArrayPatternMesh[a_?ArrayQ] := Module[{mp, pos, fpos, dims = Dimensions[a], cdims}, mp = RegionProduct @@ Map[MeshRegion[Partition[N[Range[0, #]]/#, 1], Line[Range[1, # + 1]]] &, dims]; pos = ArrayRules[a][[1 ;; -2, 1]]; cdims = Reverse[FoldList[Times, 1, dims[[2 ;; -1]]]]; fpos = 1 + (pos - 1).cdims; MeshRegion[MeshCoordinates[mp], MeshCells[mp, {Length[dims], fpos}]]]; drill[s_, t_] := Block[{sp, d = ArrayDepth[t], r = Length[s]/Length[t]}, If[r == 1, Mod[t s, 2], sp = Partition[s, Dimensions[s]/Dimensions[t]]; Flatten[MapThread[If[#1 == 0, #2 0, drill[#2, t]] &, {t, sp}, d], Transpose[Partition[Range[2 d], d]]]]]; SierpinskiArray[t_, k_] := Module[{s, dims = Dimensions[t]}, s = ConstantArray[1, dims^k]; drill[s, t]];

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X ArrayPatternMesh[SierpinskiArray[{{1, 1}, {1, 0}}, 6]]

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