Formelbasierte Regionen in 3D 

Verwenden Sie ImplicitRegion und ParametricRegion zur Beschreibung von Regionen, die in den dreidimensionalen Raum eingebettet sind.

Die gesamte Wolfram-Language Eingabe zeigenEingabe verbergen

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X region["Parametric Curve"] = ParametricRegion[{Cos[t], Sin[t], t/16}, {{t, 0, 10 \[Pi]}}];

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X region["Implicit Curve"] = ImplicitRegion[ 5 y - 20 y^3 + 16 y^5 - z == 0 && x^2 + y^2 == 1, {x, y, z}];

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X region["Sphere"] = ImplicitRegion[x^2 + y^2 + z^2 == 1, {x, y, z}];

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X region["Saddle"] = ParametricRegion[{u, v, u^2 - v^2}, {{u, -1, 1}, {v, -1, 1}}];

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X region["Torus"] = ParametricRegion[{Cos[u] (2 + Sin[v]), Sin[u] (2 + Sin[v]), Cos[v]}, {{u, 0, 2 \[Pi]}, {v, 0, 2 \[Pi]}}];

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X region["Astroidal Ellipsoid"] = ImplicitRegion[(x^2)^(1/3)/3^(2/3) + (y^2)^(1/3)/2^(2/3) + (z^2)^( 1/3)/3^(2/3) == 1, {x, y, z}];

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X region["Cylindrical Shell"] = ImplicitRegion[4 <= x^2 + y^2 <= 9 && -3 <= z <= 3, {x, y, z}];

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X region["Steinmetz 3\[Dash]solid"] = ImplicitRegion[ x^2 + z^2 < 9 && x^2 + y^2 < 9 && y^2 + z^2 < 9, {x, y, z}];

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X region["Eight Solid"] = ImplicitRegion[4 z^4 + 9 (x^2 + y^2 - 4 z^2) <= 1, {x, y, z}];

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X names = {"Parametric Curve", "Implicit Curve", "Sphere", "Saddle", "Torus", "Astroidal Ellipsoid", "Cylindrical Shell", "Steinmetz 3\[Dash]solid", "Eight Solid"};

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

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X plots = { ParametricPlot3D[ Evaluate[region["Parametric Curve"][[1]]], {t, 0, 10 Pi}, Ticks -> None], DiscretizeRegion[Evaluate@region["Implicit Curve"]], ContourPlot3D[ Evaluate[region["Sphere"][[1]]], {x, -1.1, 1.1}, {y, -1.1, 1.1}, {z, -1.1, 1.1}, Mesh -> None, Ticks -> None], ParametricPlot3D[ Evaluate[region["Saddle"][[1]]], {u, -1, 1}, {v, -1, 1}, Mesh -> None, Ticks -> None], ParametricPlot3D[ Evaluate[region["Torus"][[1]]], {u, 0, 2 Pi}, {v, 0, 2 Pi}, Mesh -> None, Ticks -> None, PlotRange -> {-3, 3}], ContourPlot3D[ Evaluate[region["Astroidal Ellipsoid"][[1]]], {x, -2.5, 2.5}, {y, -2.5, 2.5}, {z, -2.5, 2.5}, Mesh -> None, Ticks -> None], RegionPlot3D[Evaluate@region["Cylindrical Shell"], PlotPoints -> 50], RegionPlot3D[Evaluate@region["Steinmetz 3\[Dash]solid"], PlotPoints -> 100], RegionPlot3D[Evaluate@region["Eight Solid"], PlotRange -> {{-3, 3}, {-3, 3}, {-3, 3}}, PlotPoints -> 100]};

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X Grid[Partition[MapThread[FrameExample, {plots, names}], 3]]

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