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ListDensityPlot3D

ListDensityPlot3D[farr]

根据数值数组 farr 生成平滑的密度图.

ListDensityPlot3D[{{x₁,y₁,z₁,f₁},…,{x_n,y_n,z_n,f_n}}]

在指定的点 {x_i,y_i,z_i} 生成值为 f_i 的密度图.

范例

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基本范例 (2)

画出一个数值数组的密度图：

Wolfram Language code: data = Table[x y z, {z, -1, 1, 2 / 40.}, {y, -1, 1, 2 / 40.}, {x, -1, 1, 2 / 40.}];

Wolfram Language code: ListDensityPlot3D[data]

选用不同的颜色方案和图例：

Wolfram Language code: data = Table[Sin[x]Cos[y]Sin[z], {z, -5, 5, 0.1}, {y, -5, 5, 0.1}, {x, -5, 5, 0.1}];

Wolfram Language code: ListDensityPlot3D[data, ColorFunction -> "TemperatureMap", PlotLegends -> Automatic]

范围 (16)

数据 (7)

对于由值组成的规则数据，、和数据反映了它们在数组中的位置：

Wolfram Language code: data = Table[Sin[x]Cos[y]Sin[z], {z, 0, 2 Pi, 2Pi / 30}, {y, 0, 2Pi, 2Pi / 30}, {x, 0, 2Pi, 2Pi / 30}];

Wolfram Language code: ListDensityPlot3D[data]

利用 DataRange 显式指定、和数据的范围：

Wolfram Language code: ListDensityPlot3D[data, DataRange -> {{0, 2Pi}, {0, 2Pi}, {0, 2Pi}}]

对密度点给出显式的 , , , 坐标：

Wolfram Language code:

data = Flatten[Table[{x, y, z, ChessboardDistance[{x, y, z}, {0, 0, 0}]}, {z, -1, 1, 2 / 9}, {y, -1, 1, 2 / 9}, {x, -1, 1, 2 / 9}], 2];

Wolfram Language code: ListDensityPlot3D[data]

对于这样的不规则数据，则从数据中推断得出、和的数据范围：

Wolfram Language code:

pts = RandomPoint[Cuboid[], 10 ^ 3];
data = Table[Append[p, Sqrt[p[[1]] ^ 2 + p[[2]] ^ 2 + p[[3]] ^ 2]], {p, pts}];

Wolfram Language code: ListDensityPlot3D[data]

用 RegionFunction 来限制数据范围：

Wolfram Language code: data = Table[x y z, {z, -1, 1, 2 / 40.}, {y, -1, 1, 2 / 40.}, {x, -1, 1, 2 / 40.}];

Wolfram Language code:

ListDensityPlot3D[data, RegionFunction -> Function[{x, y, z}, x ^ 2 + y ^ 2 + z ^ 2 ≤ 1], DataRange -> {{-1, 1}, {-1, 1}, {-1, 1}}]

绘制由 SparseArray 给出的值数组的密度：

Wolfram Language code: data = SparseArray[Flatten[Table[{i ^ 2, j ^ 2, k ^ 2} -> i j k, {i, 1, 4}, {j, 1, 4}, {k, 1, 4}]]];

Wolfram Language code: ListDensityPlot3D[data]

绘制由 QuantityArray 给出的值数组的密度：

Wolfram Language code: data = QuantityArray[Table[x y z, {z, -1, 1, .05}, {y, -1, 1, .05}, {x, -1, 1, .05}], "kg/m^3"];

Wolfram Language code:

ListDensityPlot3D[data, AxesLabel -> Automatic, PlotLegends -> Automatic, TargetUnits -> {"Feet", "Feet", "Feet", "g/ft^3"}]

用 ClipPlanes 指定一个或几个剪切平面. 下例中，剪切平面为：

Wolfram Language code: data = Table[Sin[x]Cos[y]Sin[z], {z, 0, 2 Pi, 2Pi / 30}, {y, 0, 2Pi, 2Pi / 30}, {x, 0, 2Pi, 2Pi / 30}];

Wolfram Language code:

ListDensityPlot3D[data, ClipPlanes -> {{-1, 1, -1, 2}}, OpacityFunction -> None, DataRange -> {{0, 2Pi}, {0, 2Pi}, {0, 2Pi}}]

表格数据 (1)

获取表格数据：

Wolfram Language code: tabular = Tabular[IconizedObject[«data»], {"f", "x", "y", "z"}]

绘制表格数据，其中每列表示 {x,y,z,f} 形式的数据：

Wolfram Language code: ListDensityPlot3D[tabular -> {"x", "y", "z", "f"}]

为绘图添加图例：

Wolfram Language code: ListDensityPlot3D[tabular -> {"x", "y", "z", "f"}, PlotLegends -> Automatic]

演示 (8)

用 PlotTheme 对整体样式进行配置：

Wolfram Language code: data = Table[x y z, {z, -1, 1, .05}, {y, -1, 1, .05}, {x, -1, 1, .05}];

Wolfram Language code: Table[ListDensityPlot3D[data, PlotLabel -> t, PlotTheme -> t], {t, {"Minimal", "Scientific", "Marketing"}}]

用 PlotLegends 显示不同数值对应的颜色条：

Wolfram Language code: data = Table[x y z, {z, -1, 1, .05}, {y, -1, 1, .05}, {x, -1, 1, .05}];

Wolfram Language code: ListDensityPlot3D[data, PlotLegends -> Automatic]

用 Axes 控制坐标轴的显示：

Wolfram Language code: data = Table[x y z, {z, -1, 1, .05}, {y, -1, 1, .05}, {x, -1, 1, .05}];

Wolfram Language code: Table[ListDensityPlot3D[data, PlotLabel -> a, Axes -> a], {a, {True, False, {True, False, True}}}]

用 AxesLabel 对坐标轴进行标注，用 PlotLabel 对整个图线进行标注：

Wolfram Language code: data = Table[x y z, {z, -1, 1, .05}, {y, -1, 1, .05}, {x, -1, 1, .05}];

Wolfram Language code: ListDensityPlot3D[data, Ticks -> None, AxesLabel -> {x, y, z}, PlotLabel -> x y z]

用 ColorFunction 根据函数值对图线着色：

Wolfram Language code: data = Table[x y z, {z, -1, 1, .05}, {y, -1, 1, .05}, {x, -1, 1, .05}];

Wolfram Language code: Table[ListDensityPlot3D[data, PlotLabel -> c, ColorFunction -> c], {c, {Hue, "BlueGreenYellow"}}]

用自定义不透明度函数指定每个体积点的不透明度：

Wolfram Language code: data = Table[Sin[π x]Sin[π (y + z)], {z, -2, 2, 0.1}, {y, -2, 2, 0.1}, {x, -2, 2, 0.1}];

Wolfram Language code: ListDensityPlot3D[data, OpacityFunction -> (If[# < 0.7, 1, 0]&)]

TargetUnits 指定可视化时用什么单位：

Wolfram Language code: data = QuantityArray[Table[x y z, {z, -1, 1, .05}, {y, -1, 1, .05}, {x, -1, 1, .05}], "kg/m^3"];

Wolfram Language code:

ListDensityPlot3D[data, AxesLabel -> Automatic, PlotLegends -> Automatic, TargetUnits -> {"Feet", "Feet", "Feet", "g/ft^3"}]

在 x 方向使用 ScalingFunctions：

Wolfram Language code:

ListDensityPlot3D[Table[Sin[π x]Sin[π (y + z)], {z, -2, 2, 0.05}, {y, -2, 2, 0.05}, {x, -2, 2, 0.05}], ScalingFunctions -> {"Log", None, None}]

选项 (38)

BoxRatios (3)

默认边框的边有相同长度：

Wolfram Language code: data = Table[Sin[2π x]Sin[2π y]Sin[2π z], {z, -Pi, Pi, 0.1}, {y, -1, 1, 0.1}, {x, -1, 1, 0.1}];

Wolfram Language code: ListDensityPlot3D[data]

用 BoxRatiosAutomatic 显示三维坐标值的自然缩放：

Wolfram Language code: data = Table[Sin[2π x]Sin[2π y]Sin[2π z], {z, -Pi, Pi, 0.1}, {y, -1, 1, 0.1}, {x, -1, 1, 0.1}];

Wolfram Language code: ListDensityPlot3D[data, BoxRatios -> Automatic]

指定边框长度间的比例：

Wolfram Language code: data = Table[Sin[2π x]Sin[2π y]Sin[2π z], {z, -Pi, Pi, 0.1}, {y, -1, 1, 0.1}, {x, -1, 1, 0.1}];

Wolfram Language code: ListDensityPlot3D[data, BoxRatios -> {5, 2, 3}]

ClipPlanes (3)

用 ClipPlanes 指定一个或几个剪切面. 此处，我们剪切：

Wolfram Language code: data = Table[Sin[x + y + z] / 10, {z, 0, 10, .5}, {y, 0, 10, .5}, {x, 0, 10, .5}];

Wolfram Language code:

ListDensityPlot3D[data, DataRange -> {{0, 10}, {0, 10}, {0, 10}}, OpacityFunction -> None, ClipPlanes -> {{1, 1, -1, 0}}]

指定几个剪切面，这里剪切和：

Wolfram Language code: data = Table[Sin[x + y + z] / 10, {z, 0, 10, .5}, {y, 0, 10, .5}, {x, 0, 10, .5}];

Wolfram Language code:

ListDensityPlot3D[data, OpacityFunction -> None, ClipPlanes -> {{1, 1, -1, 0}, {0, 1, 0, -4}}, DataRange -> {{0, 10}, {0, 10}, {0, 10}}]

与一般的 RegionFunction 比较：

Wolfram Language code: data = Table[Sin[x + y + z] / 10, {z, 0, 10, .5}, {y, 0, 10, .5}, {x, 0, 10, .5}];

Wolfram Language code:

ListDensityPlot3D[data, OpacityFunction -> None, RegionFunction -> Function[{x, y, z}, x + y - z ≤ 0], DataRange -> {{0, 10}, {0, 10}, {0, 10}}]

ColorFunction (2)

在 x， y， z 坐标按 f 缩放值着色：

Wolfram Language code: data = Table[Sin[(i + j + k) / 20], {i, 0, 20}, {j, 0, 20}, {k, 0, 20}];

Wolfram Language code: ListDensityPlot3D[data, ColorFunction -> Hue]

使用 ColorData 中的着色函数：

Wolfram Language code: data = Table[PDF[DirichletDistribution[{1, 2, 3, 4}], {x, y, z}], {z, 0, 1, 0.05}, {y, 0, 1, 0.05}, {x, 0, 1, 0.05}];

Wolfram Language code:

Table[ListDensityPlot3D[data, ColorFunction -> cf, DataRange -> {{0, 1}, {0, 1}, {0, 1}}], {cf, {"AlpineColors", "Aquamarine", "ArmyColors", "AtlanticColors"}}]

ColorFunctionScaling (2)

ColorFunction 的参数通常被缩放至0到1之间：

Wolfram Language code: ListDensityPlot3D[Table[x + y + z, {z, 0, 3, 0.2}, {y, 0, 3, 0.2}, {x, 0, 3, 0.2}], ColorFunction -> Hue]

设置 ColorFunctionScaling 为 False，使用未经缩放的坐标：

Wolfram Language code: data = Table[x + y + z, {z, 0, 3, 0.2}, {y, 0, 3, 0.2}, {x, 0, 3, 0.2}];

Wolfram Language code: ListDensityPlot3D[data, ColorFunction -> Hue, ColorFunctionScaling -> False]

DataRange (2)

默认情况下，数据范围采用数组的维度：

Wolfram Language code: data = Table[Exp[-(x ^ 2 + y ^ 2 + z ^ 2)], {z, -1, 1, 1 / 10}, {y, -1, 1, 1 / 20}, {x, -1, 1, 1 / 30}];

Wolfram Language code: ListDensityPlot3D[data, DataRange -> Automatic]

显式指定数据范围：

Wolfram Language code: data = Table[Exp[-(x ^ 2 + y ^ 2 + z ^ 2)], {z, -1, 1, 1 / 10}, {y, -1, 1, 1 / 20}, {x, -1, 1, 1 / 30}];

Wolfram Language code: ListDensityPlot3D[data, DataRange -> {{-1, 1}, {-1, 1}, {-1, 1}}]

MaxPlotPoints (1)

指定数据点的最大个数：

Wolfram Language code:

data = Table[PDF[DirichletDistribution[{1, 2, 3, 4}], {x, y, z}], {z, 0, 1, 1 / 40.}, {y, 0, 1, 1 / 40.}, {x, 0, 1, 1 / 40.}];

默认情况下，使用所有数据：

Wolfram Language code: ListDensityPlot3D[data, DataRange -> Automatic, MaxPlotPoints -> Automatic]

OpacityFunction (5)

默认情况下，OpacityFunction 设为 Automatic：

Wolfram Language code: data = Table[x ^ 2 + y ^ 2 + z ^ 2, {z, -2, 2, 0.1}, {y, -2, 2, 0.1}, {x, -2, 2, 0.1}];

Wolfram Language code: ListDensityPlot3D[data]

用 None 使整个图不透明：

Wolfram Language code: data = Table[Sin[π x]Sin[π (y + z)], {z, -2, 2, 0.1}, {y, -2, 2, 0.1}, {x, -2, 2, 0.1}];

Wolfram Language code: ListDensityPlot3D[data, OpacityFunction -> None]

用自定义的不透明透明度函数指定每个体积点的不透明度：

Wolfram Language code: data = Table[Sin[π x]Sin[π (y + z)], {z, -2, 2, 0.1}, {y, -2, 2, 0.1}, {x, -2, 2, 0.1}];

Wolfram Language code: ListDensityPlot3D[data, OpacityFunction -> (If[# < 0.4, 1, 0]&)]

令区间和上的值更不透明：

Wolfram Language code: data = Table[Sin[π x]Sin[π y] Sin[π z], {z, -1, 1, 0.05}, {y, -1, 1, 0.05}, {x, -1, 1, 0.05}];

Wolfram Language code:

ListDensityPlot3D[data, OpacityFunction -> Interval[{-1, -0.6}, {0.6, 1}], OpacityFunctionScaling -> False, PlotLegends -> Automatic, DataRange -> {{-1, 1}, {-1, 1}, {-1, 1}}]

不透明度为常数 Opacity[0.05]：

Wolfram Language code: data = Table[Sin[π x]Sin[π y] Sin[π z], {z, -1, 1, 0.05}, {y, -1, 1, 0.05}, {x, -1, 1, 0.05}];

Wolfram Language code: ListDensityPlot3D[data, OpacityFunction -> 0.05, PlotLegends -> Automatic, DataRange -> {{-1, 1}, {-1, 1}, {-1, 1}}]

OpacityFunctionScaling (2)

默认情况下，使用缩放过的值：

Wolfram Language code: data = Table[x y z, {z, -5, 5}, {y, -5, 5}, {x, -5, 5}];

Wolfram Language code: ListDensityPlot3D[data, OpacityFunction -> Function[f, If[f > 0, 1, 0]]]

将 OpacityFunctionScaling 设为 False，使用未经缩放的密度值：

Wolfram Language code: data = Table[x y z, {z, -5, 5}, {y, -5, 5}, {x, -5, 5}];

Wolfram Language code: ListDensityPlot3D[data, OpacityFunction -> Function[f, If[f > 0, 1, 0]], OpacityFunctionScaling -> False]

PerformanceGoal (2)

生成高品质的图线：

Wolfram Language code: data = Table[x y z, {z, -1, 1, .1}, {y, -1, 1, .1}, {x, -1, 1, .1}];

Wolfram Language code: Timing[ListDensityPlot3D[data, PerformanceGoal -> "Quality"]]

以提高速度为主，可能会牺牲质量：

Wolfram Language code: data = Table[x y z, {z, -1, 1, .1}, {y, -1, 1, .1}, {x, -1, 1, .1}];

Wolfram Language code: Timing[ListDensityPlot3D[data, PerformanceGoal -> "Speed"]]

PlotLegends (2)

默认不使用图例：

Wolfram Language code: data = Table[x y z, {x, -1, 1, 2 / 40.}, {y, -1, 1, 2 / 40.}, {z, -1, 1, 2 / 40.}];

Wolfram Language code: ListDensityPlot3D[data]

用 PlotLegends->Automatic 显示图例：

Wolfram Language code: data = Table[x y z, {z, -1, 1, 2 / 40.}, {y, -1, 1, 2 / 40.}, {x, -1, 1, 2 / 40.}];

Wolfram Language code: ListDensityPlot3D[data, PlotLegends -> Automatic]

PlotRange (3)

默认情况下，显示图线的全部范围：

Wolfram Language code: data = Table[Exp[-(x ^ 2 + y ^ 2 + z ^ 2)], {z, -1, 1, 1 / 20}, {y, -1, 1, 1 / 20}, {x, -1, 1, 1 / 20}];

Wolfram Language code: ListDensityPlot3D[data, DataRange -> {{-1, 1}, {-1, 1}, {-1, 1}}]

指定范围以显示更多细节：

Wolfram Language code: data = Table[Exp[-(x ^ 2 + y ^ 2 + z ^ 2)], {z, -1, 1, 1 / 20}, {y, -1, 1, 1 / 20}, {x, -1, 1, 1 / 20}];

Wolfram Language code:

ListDensityPlot3D[data, DataRange -> {{-1, 1}, {-1, 1}, {-1, 1}}, PlotRange -> {{-1, 0}, All, All}, BoxRatios -> Automatic]

只显示0到0.2之间的函数值：

Wolfram Language code: data = Table[Exp[-(x ^ 2 + y ^ 2 + z ^ 2)], {z, -1, 1, 0.05}, {y, -1, 1, 0.05}, {x, -1, 1, 0.05}];

Wolfram Language code: ListDensityPlot3D[data, PlotRange -> {All, All, All, {0, 0.2}}]

替代形式：

Wolfram Language code: ListDensityPlot3D[data, PlotRange -> {0, 0.2}]

PlotTheme (3)

选用带有详细刻度、网格线和图例的主题样式：

Wolfram Language code: data = Table[x y z, {z, -1, 1, 2 / 40.}, {y, -1, 1, 2 / 40.}, {x, -1, 1, 2 / 40.}];

Wolfram Language code: ListDensityPlot3D[data, PlotTheme -> "Detailed"]

不显示网格线：

Wolfram Language code: data = Table[x y z, {z, -1, 1, 2 / 40.}, {y, -1, 1, 2 / 40.}, {x, -1, 1, 2 / 40.}];

Wolfram Language code: ListDensityPlot3D[data, PlotTheme -> "Detailed", FaceGrids -> None]

比较不同的主题样式：

Wolfram Language code: data = Table[x y z, {z, -1, 1, 2 / 40.}, {y, -1, 1, 2 / 40.}, {x, -1, 1, 2 / 40.}];

Wolfram Language code:

Table[ListDensityPlot3D[data, PlotLabel -> t, PlotTheme -> t, ImageSize -> 130], {t, {"Scientific", "Monochrome", "Minimal", "Web", "Working", "Classic", "Business", "Marketing", "Detailed"}}]

RegionFunction (3)

在球上绘制、和：

Wolfram Language code: data = Table[x y z, {z, -1, 1, 2 / 40.}, {y, -1, 1, 2 / 40.}, {x, -1, 1, 2 / 40.}];

Wolfram Language code:

ListDensityPlot3D[data, RegionFunction -> Function[{x, y, z}, x ^ 2 + y ^ 2 + z ^ 2 ≤ 1], DataRange -> {{-1, 1}, {-1, 1}, {-1, 1}}]

只显示的区域：

Wolfram Language code: data = Table[x ^ 2 + y ^ 2 - z ^ 2, {z, -2, 2, .2}, {y, -2, 2, .2}, {x, -2, 2, .2}];

Wolfram Language code: ListDensityPlot3D[data, RegionFunction -> Function[{x, y, z, f}, f < 2], DataRange -> {{-2, 2}, {-2, 2}, {-2, 2}}]

各区域之间不必相连：

Wolfram Language code: data = Table[x ^ 2 + y ^ 2 - z ^ 2, {z, -2, 2, .2}, {y, -2, 2, .2}, {x, -2, 2, .2}];

Wolfram Language code:

ListDensityPlot3D[data, RegionFunction -> Function[{x, y, z, f}, x < -1 || x > 1], DataRange -> {{-2, 2}, {-2, 2}, {-2, 2}}]

ScalingFunctions (4)

默认情况下，在所有方向上采用线性刻度：

Wolfram Language code: ListDensityPlot3D[Table[Cos[x + y + z] / 10, {z, 0, 10, .25}, {y, 0, 10, .25}, {x, 0, 10, .25}]]

生成轴为对数刻度的图：

Wolfram Language code:

ListDensityPlot3D[Table[Cos[x + y + z] / 10, {z, 0, 10, .25}, {y, 0, 10, .25}, {x, 0, 10, .25}], ScalingFunctions -> {"Log", None, None}]

用 ScalingFunctions 反转轴坐标的方向：

Wolfram Language code:

ListDensityPlot3D[Table[Cos[x + y + z] / 10, {z, 0, 10, .25}, {y, 0, 10, .25}, {x, 0, 10, .25}], ScalingFunctions -> {None, None, "Reverse"}]

使用函数及其逆定义的刻度：

Wolfram Language code:

ListDensityPlot3D[Table[Cos[x + y + z] / 10, {z, 0, 10, .25}, {y, 0, 10, .25}, {x, 0, 10, .25}], ScalingFunctions -> {None, None, {-Log[#]&, Exp[-#]&}}]

TargetUnits (1)

指定在图线中显示的单位：

Wolfram Language code: data = QuantityArray[Table[Exp[-(x ^ 2 + y ^ 2 + z ^ 2)], {z, -2, 2, 0.1}, {y, -2, 2, 0.1}, {x, -2, 2, 0.1}], "Feet"];

Wolfram Language code:

ListDensityPlot3D[data, TargetUnits -> {"Meters", "Meters", "Meters", "Meters"}, PlotLegends -> Automatic, AxesLabel -> Automatic]

应用 (13)

初等函数 (4)

绘制函数：

Wolfram Language code: data = Table[x, {z, -2, 2}, {y, -2, 2}, {x, -2, 2, 0.25}];

Wolfram Language code: ListDensityPlot3D[data]

绘制函数和：

Wolfram Language code:

{ListDensityPlot3D[Table[y, {z, -2, 2}, {y, -2, 2, 0.25}, {x, -2, 2}]], 
	ListDensityPlot3D[Table[z, {z, -2, 2, 0.25}, {y, -2, 2}, {x, -2, 2}]]}

绘制函数和：

Wolfram Language code:

{ListDensityPlot3D[Table[x + y, {z, -2, 2}, {y, -2, 2, 0.25}, {x, -2, 2, 0.25}]], 
	ListDensityPlot3D[Table[y + z, {z, -2, 2, 0.25}, {y, -2, 2, 0.25}, {x, -2, 2}]]}

绘制函数和：

Wolfram Language code:

{ListDensityPlot3D[Table[x + y + z, {z, -2, 2, 0.25}, {y, -2, 2, 0.25}, {x, -2, 2, 0.25}]], 
	ListDensityPlot3D[Table[x - y + z, {x, -2, 2, 0.2}, {y, -2, 2, 0.2}, {z, -2, 2, 0.2}]]}

绘制函数和：

Wolfram Language code:

{ListDensityPlot3D[Table[x ^ 2 + y ^ 2, {z, -2, 2}, {y, -2, 2, 0.25}, {x, -2, 2, 0.25}]], ListDensityPlot3D[Table[y ^ 2 + z ^ 2, {z, -2, 2, 0.25}, {y, -2, 2, 0.25}, {x, -2, 2}]]}

绘制函数和：

Wolfram Language code:

{ListDensityPlot3D[Table[x ^ 2 + y ^ 2 + z ^ 2, {z, -2, 2, 0.2}, {y, -2, 2, 0.2}, {x, -2, 2, 0.2}]], ListDensityPlot3D[Table[x ^ 2 + y ^ 2 + 2z ^ 2, {z, -2, 2, 0.2}, {y, -2, 2, 0.2}, {x, -2, 2, 0.2}]]}

绘制，单变量函数的乘积：

Wolfram Language code: ListDensityPlot3D[Table[Sin[π x]Sin[π y]Sin[π z], {z, -2, 2, 0.1}, {y, -2, 2, 0.1}, {x, -2, 2, 0.1}]]

绘制和，单变量函数和双变量函数：

Wolfram Language code:

{ListDensityPlot3D[Table[Sin[π x]Sin[π (y + z)], {z, -2, 2, 0.1}, {y, -2, 2, 0.1}, {x, -2, 2, 0.1}]], ListDensityPlot3D[Table[Sin[π (x + y)]Sin[π z], {z, -2, 2, 0.1}, {y, -2, 2, 0.1}, {x, -2, 2, 0.1}]]}

绘制三变量函数：

Wolfram Language code: ListDensityPlot3D[Table[Sin[π (x + y + z)], {z, -2, 2, 0.1}, {y, -2, 2, 0.1}, {x, -2, 2, 0.1}]]

绘制指数和 $sum_ialpha_i exp(-TemplateBox[{{p, -, {p, _, i}}}, Norm]^2)$ ：

Wolfram Language code: f = Exp[-Norm[{x, y, z} - {-1, -1, -1}]^2] + Exp[-Norm[{x, y, z} - {1, 1, 1}]^2];

Wolfram Language code: ListDensityPlot3D[Table[f, {z, -2, 2, 0.2}, {y, -2, 2, 0.2}, {x, -2, 2, 0.2}]]

从盒中随机选取点：

Wolfram Language code: f = Sum[Exp[-2Norm[{x, y, z} - pi]^2], {pi, RandomPoint[Cuboid[{-1, -1, -1}, {1, 1, 1}], 10]}];

Wolfram Language code: ListDensityPlot3D[Table[f, {x, -2, 2, 0.2}, {y, -2, 2, 0.2}, {z, -2, 2, 0.2}]]

模拟数据 (6)

绘制三变量概率密度函数：

Wolfram Language code:

𝒟 = ProductDistribution[{LogNormalDistribution[0, 1], 3}];
f = PDF[𝒟, {x, y, z}]

Wolfram Language code: ListDensityPlot3D[Table[f, {z, 0, 3, .1}, {y, 0, 3, .1}, {x, 0, 3, .1}], DataRange -> {{0, 3}, {0, 3}, {0, 3}}]

模拟分布并计算组数：

Wolfram Language code: data = Last@HistogramList[RandomVariate[𝒟, 10 ^ 6], {0, 3, 0.1}];

Wolfram Language code: ListDensityPlot3D[data]

模拟随机行走并显示路径：

Wolfram Language code: walk = Accumulate[RandomInteger[{-1, 1}, {10 ^ 5, 3}]];

Wolfram Language code: Graphics3D[Line[walk], BoxRatios -> 1, Axes -> True]

对行走经过的空间位置进行分组并显示密度：

Wolfram Language code: data = Last@HistogramList[walk];

Wolfram Language code: ListDensityPlot3D[data, PlotLegends -> Automatic, DataRange -> CoordinateBounds[walk]]

绘制二维元胞自动机的演化过程：

Wolfram Language code: data = CellularAutomaton[{2274, {2, 1}, {1, 1, 1}}, {{{{1}}}, 0}, {20, {{10}}}];

Wolfram Language code: ListDensityPlot3D[data]

生成门格海绵阵列：

Wolfram Language code: data = Last@SubstitutionSystem[{1 -> 1 - CrossMatrix[{1, 1, 1}], 0 -> ConstantArray[0, {3, 3, 3}]}, {{{1}}}, 3];

Wolfram Language code: ListDensityPlot3D[data, OpacityFunction -> (#&), ColorFunction -> GrayLevel]

绘制替换系统的演化：

Wolfram Language code:

data = Last@SubstitutionSystem[{1 -> ArrayReshape[IntegerDigits[45115427, 2, 27], {3, 3, 3}], 0 -> ConstantArray[0, {3, 3, 3}]}, {{{1}}}, 3];

Wolfram Language code: ListDensityPlot3D[data]

通过对数组中半径为1的范围取均值，模拟一个二维随机值数组的离散扩散模型：

Wolfram Language code: g[d_] := ArrayFilter[Total[#, 2] / 9&, d, 1];

Wolfram Language code: ListDensityPlot3D[NestList[g, RandomReal[1, {40, 40}], 40], PlotLegends -> Automatic, AxesLabel -> {None, None, "time"}]

数据模式 (3)

显示三维离散傅立叶变换的相位：

Wolfram Language code: data = Arg[Fourier[Table[1 / LCM[i, j, k], {i, 64}, {j, 64}, {k, 64}]]];

Wolfram Language code: ListDensityPlot3D[data]

对蛋白质中原子的位置进行分组并显示密度：

Wolfram Language code: positions = ProteinData["RAB21", "AtomPositions"];

Wolfram Language code: data = Last@HistogramList[positions];

Wolfram Language code: ListDensityPlot3D[data, PlotLegends -> Automatic]

与分子图进行比较：

Wolfram Language code: ProteinData["RAB21", "MoleculePlot"]

可视化大脑的 MRI 数据：

Wolfram Language code: data = ExampleData[{"TestImage3D", "MRbrain"}, "GrayLevels"];

Wolfram Language code: ListDensityPlot3D[data, BoxRatios -> Automatic]

如果想得到与 Image3D 定位一致的图像，使用选项 DataReversed：

Wolfram Language code: data = ImageData[ExampleData[{"TestImage3D", "MRbrain"}, "Image3D"], DataReversed -> True];

Wolfram Language code: ListDensityPlot3D[data, BoxRatios -> Automatic]

属性和关系 (6)

用 ListSliceDensityPlot3D 绘制切片曲面的密度图：

Wolfram Language code: data = Table[x y z, {z, -2, 2, .1}, {y, -2, 2, .1}, {x, -2, 2, .1}];

Wolfram Language code: {ListSliceDensityPlot3D[data, "BackPlanes"], ListDensityPlot3D[data]}

用 ListDensityPlot 绘制二维密度图：

Wolfram Language code: data = Table[x ^ 2 + y ^ 2, {z, -1, 1, .1}, {y, -1, 1, .1}, {x, -1, 1, .1}];

Wolfram Language code: {ListDensityPlot[First[data]], ListDensityPlot3D[data, OpacityFunction -> None]}

用 DensityPlot3D 绘制函数：

Wolfram Language code: data = Table[x y z, {z, -1, 1, 0.05}, {y, -1, 1, 0.05}, {x, -1, 1, 0.05}];

Wolfram Language code: {DensityPlot3D[x y z, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}], ListDensityPlot3D[data]}

用 ListSliceContourPlot3D 绘制切片曲面的等高线图：

Wolfram Language code: data = Table[x ^ 2 + y ^ 2 + z ^ 2, {z, -2, 2, .1}, {y, -2, 2, .1}, {x, -2, 2, .1}];

Wolfram Language code: {ListSliceContourPlot3D[data], ListDensityPlot3D[data]}

用 ListContourPlot3D 绘制常数值曲面：

Wolfram Language code: data = Table[x ^ 2 + y ^ 2 + z ^ 2, {z, -2, 2, .1}, {y, -2, 2, .1}, {x, -2, 2, .1}];

Wolfram Language code: {ListContourPlot3D[data], ListDensityPlot3D[data]}

用 ArrayPlot3D 绘制离散数据：

Wolfram Language code: data = Table[GCD[x, y, z] - 1, {z, -5, 5}, {y, -5, 5}, {x, -5, 5}];

Wolfram Language code: {ArrayPlot3D[data], ListDensityPlot3D[data]}

Top

	Automatic	自动确定
	None	不使用不透明度函数，完全不透明
	α	不透明度为常数 Opacity[α]
	Interval[…]	令区间内的值更不透明
	"Image3D"	Image3D 中使用的默认不透明函数
	func	一般不透明度函数

	"Log"		对数刻度，自动进行标记
	"Log10"		以 10 为底的对数刻度，用 10 的幂进行标记
	"SignedLog"		类似对数的刻度，包含 0 和负数
	"Reverse"		反转坐标的方向

AlignmentPoint	Center	在图形内对齐的缺省点
AspectRatio	Automatic	高与宽的比
Axes	True	是否绘制坐标轴
AxesEdge	Automatic	在哪条边上放置轴
AxesLabel	None	坐标轴标签
AxesOrigin	Automatic	坐标轴交叉的位置
AxesStyle	{}	指定坐标轴样式的图形指令
Background	None	图形背景色
BaselinePosition	Automatic	如何与环绕文本基线对齐
BaseStyle	{}	图形的基本样式指定
Boxed	True	是否绘制边框
BoxRatios	{1,1,1}	三维边框的比例
BoxStyle	{}	盒框的样式指定
ClipPlanes	None	剪切平面
ClipPlanesStyle	Automatic	剪切平面的样式指定
ColorFunction	Automatic	如何给图线着色
ColorFunctionScaling	True	是否缩放 ColorFunction 的参数
ContentSelectable	Automatic	是否允许内容选择
ControllerLinking	False	连接到外部旋转控制器的时间
ControllerPath	Automatic	尝试使用的外部控制器
DataRange	Automatic	假设的 x、 y 和 z 取值范围
Epilog	{}	在主图形显示后显示的二维图形基元
FaceGrids	None	在边框上绘制的网格线
FaceGridsStyle	{}	网格面的样式指定
FormatType	TraditionalForm	文本的缺省格式类型
ImageMargins	0.	图形周围预留的边幅
ImagePadding	All	允许为标签等设置的填充范围
ImageSize	Automatic	渲染图形的绝对尺寸
LabelStyle	{}	标签的样式指定
Lighting	Automatic	使用的模拟光照
MaxPlotPoints	Automatic	最多包含多少个点
Method	Automatic	使用的三维图形方法的详细信息
OpacityFunction	Automatic	如何计算各个点的不透明度
OpacityFunctionScaling	True	是否缩放 OpacityFunction 的参数
PerformanceGoal	$PerformanceGoal	优化的目标
PlotLabel	None	图形的标签
PlotLegends	None	颜色梯度的图例
PlotRange	{Full,Full,Full,Automatic}	要包括的 f 或其它值的范围
PlotRangePadding	Automatic	值域范围填充的程度
PlotRegion	Automatic	要填充的最终显示区域
PlotTheme	$PlotTheme	图线的整体主题
PreserveImageOptions	Automatic	当显示相同图形的一个新版本时，是否保留图像选项
Prolog	{}	在主图形之前渲染的二维图形基元
RegionFunction	(True&)	如何确定是否包含一个点
RotationAction	"Fit"	互动旋转后渲染的方式
ScalingFunctions	None	怎样缩放个别坐标
SphericalRegion	Automatic	是否将外切球体调整适合最后显示区域
TargetUnits	Automatic	要用的单位
Ticks	Automatic	指定刻度
TicksStyle	{}	刻度的样式指定
TouchscreenAutoZoom	False	当在一个触摸屏上激活时，是否放大为全屏
ViewAngle	Automatic	视图的角度
ViewCenter	Automatic	在中心显示的点
ViewMatrix	Automatic	显式转换矩阵
ViewPoint	{1.3,-2.4,2.}	观察位置
ViewProjection	Automatic	用于渲染远离观察者的对象的投影方法
ViewRange	All	要包含的观察距离范围
ViewVector	Automatic	模拟相机的位置和方向
ViewVertical	{0,0,1}	垂直的方向

ListDensityPlot3D

更多信息和选项

所有选项的列表

范例

基本范例 (2)

范围 (16)

数据 (7)

表格数据 (1)

演示 (8)

选项 (38)

BoxRatios (3)

ClipPlanes (3)

ColorFunction (2)

ColorFunctionScaling (2)

DataRange (2)

MaxPlotPoints (1)

OpacityFunction (5)

OpacityFunctionScaling (2)

PerformanceGoal (2)

PlotLegends (2)

PlotRange (3)

PlotTheme (3)

RegionFunction (3)

ScalingFunctions (4)

TargetUnits (1)

应用 (13)

初等函数 (4)

模拟数据 (6)

数据模式 (3)

属性和关系 (6)

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