3D-Netze 

Erzeugen Sie dreidimensionale Netze und Begrenzungsflächenmodelle (BReps).

Die gesamte Wolfram-Language Eingabe zeigenEingabe verbergen

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X pointMesh3d = MeshRegion[Tuples[Range[4], 3], Point[Range[64]]];

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X lineMesh3d = MeshRegion[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, Line[Union[Sort /@ Permutations[Range[4], {2}]]]];

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X polygonMesh3d = MeshRegion[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, Polygon[{{1, 3, 2}, {4, 2, 3}, {3, 1, 4}}]];

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X solidMesh3d = MeshRegion[{{0, 0, 0}, {1, 0, 0}, {1, 1, 0}, {0, 1, 0}, {0, 0, 1}, {1, 0, 1}, {1, 1, 1}, {0, 1, 1}, {0.5, 0.5, 1.5}, {1.5, 0, 0}, {1.5, 1, 0}, {1, -0.5, 0}}, {Hexahedron[{1, 2, 3, 4, 5, 6, 7, 8}], Pyramid[{5, 6, 7, 8, 9}], Prism[{2, 10, 6, 3, 11, 7}], Tetrahedron[{2, 10, 6, 12}]}];

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X boundaryMesh3d = BoundaryMeshRegion[{{0, 0, 0}, {4, 0, 0}, {0, 4, 0}, {0, 0, 4}}, Polygon[{{1, 2, 3}, {1, 2, 4}, {2, 3, 4}, {1, 3, 4}}]];

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X pts = {{0, 0, 0}, {0, 1, 0}, {1, 1, 0}, {1, 0, 0}, {0, 0, 1}, {0, 1, 1}, {1, 1, 1}, {1, 0, 1}}; pts1 = ScalingTransform[{3, 3, 3}][pts]; pts2 = TranslationTransform[{1, 1, 1}][pts]; hex = {{2, 3, 4, 1}, {1, 4, 8, 5}, {4, 3, 7, 8}, {3, 2, 6, 7}, {2, 1, 5, 6}, {5, 8, 7, 6}}; boundaryMeshHoles3d = BoundaryMeshRegion[Join[pts1, pts2], Polygon[hex], Polygon[hex + 8], MeshCellStyle -> Opacity[0.35]];

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X $ImageSize = 100; ExampleFrame3D[expr_, label_] := Framed[Grid[List /@ {label, Show[expr, ImageSize -> $ImageSize]}, ItemSize -> {12, 3}, BaseStyle -> {Gray, FontFamily -> "Helvetica"}, Alignment -> Top], FrameStyle -> Directive[Thickness[4], Gray], RoundingRadius -> 5]

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X Grid[Partition[{ExampleFrame3D[pointMesh3d, "Point Mesh"], ExampleFrame3D[lineMesh3d, "Line Mesh"], ExampleFrame3D[polygonMesh3d, "Polygon Mesh"], ExampleFrame3D[solidMesh3d, "Solid Mesh"], ExampleFrame3D[boundaryMesh3d, "Boundary Mesh"], ExampleFrame3D[Rasterize[boundaryMeshHoles3d], "Boundary Mesh v/ Void"]}, 3]]

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Komplexe Netze können programmatisch erzeugt werden.

Die gesamte Wolfram-Language Eingabe zeigenEingabe verbergen

In[9]:=

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 t = {{{1, 1, 1}, {1, 0, 1}, {1, 1, 1}}, {{1, 0, 1}, {0, 0, 0}, {1, 0, 1}}, {{1, 1, 1}, {1, 0, 1}, {1, 1, 1}}}; mr = ArrayPatternMesh[SierpinskiArray[t, 3]]

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