SliceContourPlot3D
✖
SliceContourPlot3D
在切片曲面 surf 上,生成以 x、y、z 为函数的 f 的等高线图.
更多信息和选项




- SliceContourPlot3D 在曲面 surf 上构建等值线,对应于 f[x,y,z] 的值为常数 d1、d2 等的水平集. 默认情况下,曲线间的区域被着色,以便更容易识别值介于 di 和 di+1 之间的区域.
- 函数可视化区域
.
- 可以给出以下基本切片曲面 surfi:
-
Automatic 自动确定切片曲面 "CenterPlanes" 过中心点的坐标平面 "BackPlanes" 图形后面的坐标平面 "XStackedPlanes" 沿 轴叠放的坐标平面
"YStackedPlanes" 沿 轴叠放的坐标平面
"ZStackedPlanes" 沿 轴叠放的坐标平面
"DiagonalStackedPlanes" 沿对角线叠放的坐标平面 "CenterSphere" 位于中心的球面 "CenterCutSphere" 切去楔形块的球面 "CenterCutBox" 八分之一被切掉的盒子 - SliceContourPlot3D[f,{x,xmin,xmax},…] 等价于 SliceContourPlot3D[f,Automatic,{x,xmin,xmax},…] 等.
- 以下参数化可以用于基本切片曲面:
-
{"XStackedPlanes",n}, 生成 n 个等间隔平面 {"XStackedPlanes",{x1,x2,…}} 生成平面 {"CenterCutSphere",ϕopen} 正对视点处切去角 ϕopen {"CenterCutSphere",ϕopen,ϕcenter} 以 平面上的 ϕcenter 为中心角切去角 ϕopen
- "YStackedPlanes"、"ZStackedPlanes" 和 "XStackedPlanes" 的规范一样,在“范围”下面的例子中会展示更多的用法.
- 可以使用下列常见的切片曲面 surfi:
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expr0 以 x、y 和 z 表示的隐方程,如 x y z-10 surfaceregion 三维空间中的二维区域,如 Hyperplane volumeregion 三维空间中的三维区域,其中 surfi 为边界曲面,如 Cuboid - 可将下列封装用于切片曲面 surfi:
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Annotation[surf,label] 提供注释 Button[surf,action] 定义当曲面被点击时应执行的操作 EventHandler[surf,…] 为曲面定义通用事件处理程序 (general event handler) Hyperlink[surf,uri] 将曲面设置为超链接 PopupWindow[surf,cont] 为曲面添加弹出窗口 StatusArea[surf,label] 当鼠标悬停在曲面处时,在状态栏中显示的内容 Tooltip[surf,label] 为曲面添加任意提示条 - SliceContourPlot3D 与 Graphics3D 的选项相同,不同之处和更多选项如下所示: [所有选项的列表]
-
Axes True 是否绘制坐标轴 BoundaryStyle Automatic 如何设计曲面边界 BoxRatios {1,1,1} 三维边界盒的比例 ClippingStyle None 如何绘制用 PlotRange 修剪过的值 ColorFunction Automatic 如何为图上色 ColorFunctionScaling True 是否缩放传递给 ColorFunction 的参数 Contours Automatic 在每个曲面上显示多少个或显示什么样的等高线 ContourShading Automatic 如何为等高线间的区域做明暗处理 ContourStyle Automatic 等高线的样式 PerformanceGoal $PerformanceGoal 优化的目标 PlotLegends None 颜色梯度的图例 PlotPoints Automatic 每个方向上函数 f 和切片曲面 surfi 的初始样本数 PlotRange {Full,Full,Full,Automatic} 函数 f 的值域或要包括的其他值 PlotTheme $PlotTheme 图的整体主题 RegionFunction (True&) 如何决定是否要包括某个点 ScalingFunctions None 怎样缩放个别坐标 TargetUnits Automatic 想要使用的单位 WorkingPrecision MachinePrecision 内部计算时使用的精度 - 默认情况下,传递给 ColorFunction 的是经过缩放的 f 值.
- 默认情况下,RegionFunction 的变量由 x、y、z 和 f 提供.
- ScalingFunctions 的可能设置包括:
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sf 缩放 f 等值线的值 {sx,sy,sz} 缩放 x、y 和 z 坐标轴 {sx,sy,sz,sf} 缩放 x、y 和 z 坐标轴以及 f 等值线的值 - 常见内置缩放函数 s 包括:
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"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 "Infinite" 无穷刻度

所有选项的列表




范例
打开所有单元关闭所有单元基本范例 (2)常见实例总结
范围 (24)标准用法实例范围调查
曲面 (9)

https://wolfram.com/xid/0tp1gh65gqu1tk-y8d13b


https://wolfram.com/xid/0tp1gh65gqu1tk-g49ifo


https://wolfram.com/xid/0tp1gh65gqu1tk-t9j4z8


https://wolfram.com/xid/0tp1gh65gqu1tk-533t34

在基本几何体(volume primitive)上绘制等高线图相当于在 RegionBoundary[reg] 上绘制:

https://wolfram.com/xid/0tp1gh65gqu1tk-ldhqvm


https://wolfram.com/xid/0tp1gh65gqu1tk-7cse7o


https://wolfram.com/xid/0tp1gh65gqu1tk-cyajg1


https://wolfram.com/xid/0tp1gh65gqu1tk-5vavq1


https://wolfram.com/xid/0tp1gh65gqu1tk-7ng1gh

抽样 (4)
使用 Contours 指定等高线的数量:

https://wolfram.com/xid/0tp1gh65gqu1tk-bfpkkk


https://wolfram.com/xid/0tp1gh65gqu1tk-xuugwu


https://wolfram.com/xid/0tp1gh65gqu1tk-q5mv44

用 RegionFunction 来显示被遮挡的切片:

https://wolfram.com/xid/0tp1gh65gqu1tk-dhqoa

可以用包含 Cone 的区域来指定值域:

https://wolfram.com/xid/0tp1gh65gqu1tk-pu0wit

一个含有 ImplicitRegion 的公式区域(formula region):

https://wolfram.com/xid/0tp1gh65gqu1tk-j02kuu

https://wolfram.com/xid/0tp1gh65gqu1tk-fhzvnj

一个含有 BoundaryMeshRegion 的基于网格的区域:

https://wolfram.com/xid/0tp1gh65gqu1tk-mn7ny


https://wolfram.com/xid/0tp1gh65gqu1tk-bf1zwg

演示 (11)
使用 PlotTheme 对整体样式进行配置:

https://wolfram.com/xid/0tp1gh65gqu1tk-qpuqqo

用 PlotLegends 显示不同数值对应的颜色:

https://wolfram.com/xid/0tp1gh65gqu1tk-rhpvcf

用 Axes 控制坐标轴的显示:

https://wolfram.com/xid/0tp1gh65gqu1tk-nyudgi

可使用 AxesLabel 为坐标轴添加标签,使用 PlotLabel 为整个图添加标签:

https://wolfram.com/xid/0tp1gh65gqu1tk-j8uski

用 ColorFunction 根据函数值为图上色:

https://wolfram.com/xid/0tp1gh65gqu1tk-2bv1by

用 ContourShading 为等高线间的区域设计样式:

https://wolfram.com/xid/0tp1gh65gqu1tk-brwdo2

用 ContourStyle 为等高线设计样式:

https://wolfram.com/xid/0tp1gh65gqu1tk-m1arsj

用 BoundaryStyle 为切片曲面边界设计样式:

https://wolfram.com/xid/0tp1gh65gqu1tk-cyvpky

TargetUnits 指定在可视化时使用哪个单位:

https://wolfram.com/xid/0tp1gh65gqu1tk-t4u8b6


https://wolfram.com/xid/0tp1gh65gqu1tk-24omnx


https://wolfram.com/xid/0tp1gh65gqu1tk-l3ao9

选项 (43)各选项的常用值和功能
BoundaryStyle (1)
BoxRatios (3)
ClippingStyle (2)

https://wolfram.com/xid/0tp1gh65gqu1tk-m7ibeu

用 None 去掉剪切区域:

https://wolfram.com/xid/0tp1gh65gqu1tk-qa2soa

ColorFunction (3)
ColorFunctionScaling (2)

https://wolfram.com/xid/0tp1gh65gqu1tk-rrfrkq

用 ColorFunctionScalingFalse 来得到未经缩放的值:

https://wolfram.com/xid/0tp1gh65gqu1tk-g000x6

Contours (4)

https://wolfram.com/xid/0tp1gh65gqu1tk-8qd9h1


https://wolfram.com/xid/0tp1gh65gqu1tk-gsf8x7


https://wolfram.com/xid/0tp1gh65gqu1tk-rjmys1


https://wolfram.com/xid/0tp1gh65gqu1tk-ocd2kq

ContourShading (4)
ContourShadingAutomatic 根据 ColorFunction 计算等高线区域的色调:

https://wolfram.com/xid/0tp1gh65gqu1tk-52ac5a


https://wolfram.com/xid/0tp1gh65gqu1tk-u4k26q


https://wolfram.com/xid/0tp1gh65gqu1tk-858exy


https://wolfram.com/xid/0tp1gh65gqu1tk-3g9uou

PerformanceGoal (2)
PlotLegends (4)

https://wolfram.com/xid/0tp1gh65gqu1tk-hv5wme

PlotLegends 自动获取 Contours 和 ContourShading 的值:

https://wolfram.com/xid/0tp1gh65gqu1tk-3bop1e

设置 ContourShadingAutomatic,可从 ColorFunction 得到颜色:

https://wolfram.com/xid/0tp1gh65gqu1tk-6ppeoh

用 Placed 控制图例的位置:

https://wolfram.com/xid/0tp1gh65gqu1tk-pqj5ip

PlotRange (3)
默认情况下显示 All 等高线:

https://wolfram.com/xid/0tp1gh65gqu1tk-uhazyj


https://wolfram.com/xid/0tp1gh65gqu1tk-hwlvlp


https://wolfram.com/xid/0tp1gh65gqu1tk-hjax0p

其与完整形式(fully qualified form)等价:

https://wolfram.com/xid/0tp1gh65gqu1tk-m0kjnp

PlotTheme (3)

https://wolfram.com/xid/0tp1gh65gqu1tk-ygbqhf

任何选项设定都可以重写 PlotTheme 的设置,在以下情况中,移除了表面的网格:

https://wolfram.com/xid/0tp1gh65gqu1tk-2dqvd3


https://wolfram.com/xid/0tp1gh65gqu1tk-g0e9g0

RegionFunction (2)
ScalingFunctions (5)

https://wolfram.com/xid/0tp1gh65gqu1tk-52n5ur


https://wolfram.com/xid/0tp1gh65gqu1tk-rgmd7s

用 ScalingFunctions 缩放并反转 轴:

https://wolfram.com/xid/0tp1gh65gqu1tk-47658g


https://wolfram.com/xid/0tp1gh65gqu1tk-7lj6h6


https://wolfram.com/xid/0tp1gh65gqu1tk-vw38w5

TargetUnits (2)
坐标轴和图例的标签都使用 TargetUnits 指定的单位:

https://wolfram.com/xid/0tp1gh65gqu1tk-qo473z

将 Quantity 指定的单位转换成 TargetUnits 指定的单位:

https://wolfram.com/xid/0tp1gh65gqu1tk-6qstx3

应用 (17)用该函数可以解决的问题范例
基础函数 (4)

https://wolfram.com/xid/0tp1gh65gqu1tk-c1wwxq


https://wolfram.com/xid/0tp1gh65gqu1tk-kkv9gr


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https://wolfram.com/xid/0tp1gh65gqu1tk-ca0wen


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https://wolfram.com/xid/0tp1gh65gqu1tk-cnfe6k

https://wolfram.com/xid/0tp1gh65gqu1tk-pqgfdc


https://wolfram.com/xid/0tp1gh65gqu1tk-nylmyx


https://wolfram.com/xid/0tp1gh65gqu1tk-dvwij4


https://wolfram.com/xid/0tp1gh65gqu1tk-l4zx6v

https://wolfram.com/xid/0tp1gh65gqu1tk-5fx0vo


https://wolfram.com/xid/0tp1gh65gqu1tk-fz9nz1

https://wolfram.com/xid/0tp1gh65gqu1tk-qvme8b

分布函数 (6)
绘制某分布的 PDF:

https://wolfram.com/xid/0tp1gh65gqu1tk-81fcz8

https://wolfram.com/xid/0tp1gh65gqu1tk-v7omgq


https://wolfram.com/xid/0tp1gh65gqu1tk-gm668q

https://wolfram.com/xid/0tp1gh65gqu1tk-fg91iz

绘制某分布的 CDF:

https://wolfram.com/xid/0tp1gh65gqu1tk-nxzhru

https://wolfram.com/xid/0tp1gh65gqu1tk-yt2zy


https://wolfram.com/xid/0tp1gh65gqu1tk-edamg1

https://wolfram.com/xid/0tp1gh65gqu1tk-qx27e1


https://wolfram.com/xid/0tp1gh65gqu1tk-cexal0

https://wolfram.com/xid/0tp1gh65gqu1tk-n33x61

找出 MultinormalDistribution 的 Correlation 参数,其中 ρab 是 a 和 b 之间的相关系数:

https://wolfram.com/xid/0tp1gh65gqu1tk-ebuscf

https://wolfram.com/xid/0tp1gh65gqu1tk-cjos6v

https://wolfram.com/xid/0tp1gh65gqu1tk-ddnesr


https://wolfram.com/xid/0tp1gh65gqu1tk-c1wejj

https://wolfram.com/xid/0tp1gh65gqu1tk-cime7c


https://wolfram.com/xid/0tp1gh65gqu1tk-f3rc7e

https://wolfram.com/xid/0tp1gh65gqu1tk-eqsrfd

可视化一个 ProductDistribution 的 PDF:

https://wolfram.com/xid/0tp1gh65gqu1tk-kiukzo


https://wolfram.com/xid/0tp1gh65gqu1tk-5jjcws


https://wolfram.com/xid/0tp1gh65gqu1tk-d59pdt


https://wolfram.com/xid/0tp1gh65gqu1tk-occsfc


https://wolfram.com/xid/0tp1gh65gqu1tk-grjaas


https://wolfram.com/xid/0tp1gh65gqu1tk-cffc9p

绘制 CopulaDistribution 的概率密度函数(pdf):

https://wolfram.com/xid/0tp1gh65gqu1tk-jkj62p


https://wolfram.com/xid/0tp1gh65gqu1tk-e6pr6h

可视化某三元分布数据核密度估计的 PDF:

https://wolfram.com/xid/0tp1gh65gqu1tk-bw70il

https://wolfram.com/xid/0tp1gh65gqu1tk-czjlu4

势函数和波函数 (4)

https://wolfram.com/xid/0tp1gh65gqu1tk-etkey6

https://wolfram.com/xid/0tp1gh65gqu1tk-3d0i0n


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https://wolfram.com/xid/0tp1gh65gqu1tk-csopkl

https://wolfram.com/xid/0tp1gh65gqu1tk-mfxobq


https://wolfram.com/xid/0tp1gh65gqu1tk-mqewd6


https://wolfram.com/xid/0tp1gh65gqu1tk-uu22nj

https://wolfram.com/xid/0tp1gh65gqu1tk-bcu9xj


https://wolfram.com/xid/0tp1gh65gqu1tk-gyax69


https://wolfram.com/xid/0tp1gh65gqu1tk-kr4jq4


https://wolfram.com/xid/0tp1gh65gqu1tk-jsa59j

偏微分方程 (3)
使用周期性边界条件(periodic boundary conditions)在两个空间维度中可视化一个非线性的 sine-Gordon 方程,z 轴表示时间:

https://wolfram.com/xid/0tp1gh65gqu1tk-3imqic


https://wolfram.com/xid/0tp1gh65gqu1tk-o5fvxw

在两个空间维度中可视化 Wolfram 的非线性波动方程,z 轴表示时间:

https://wolfram.com/xid/0tp1gh65gqu1tk-fkj


https://wolfram.com/xid/0tp1gh65gqu1tk-s7i4od

可视化三维偏微分方程的解. 在此例中,为一个 Ball 上的泊松方程(Poisson equation)和狄利克雷边界条件(Dirichlet boundary conditions):

https://wolfram.com/xid/0tp1gh65gqu1tk-yfl4db


https://wolfram.com/xid/0tp1gh65gqu1tk-4pd8oc

属性和关系 (5)函数的属性及与其他函数的关联
用 SliceDensityPlot3D 在曲面上绘制连续密度图:

https://wolfram.com/xid/0tp1gh65gqu1tk-y3eawx

用 ContourPlot3D 来绘制数值为常数的曲面:

https://wolfram.com/xid/0tp1gh65gqu1tk-4gfzgs

用 DensityPlot3D 来呈现数值的整体可视化:

https://wolfram.com/xid/0tp1gh65gqu1tk-4kw5kb

对数据使用 ListSliceContourPlot3D:

https://wolfram.com/xid/0tp1gh65gqu1tk-ywzg95

https://wolfram.com/xid/0tp1gh65gqu1tk-3v60u6

用 ContourPlot 得到二维等高线图:

https://wolfram.com/xid/0tp1gh65gqu1tk-z3puov

Wolfram Research (2015),SliceContourPlot3D,Wolfram 语言函数,https://reference.wolfram.com/language/ref/SliceContourPlot3D.html (更新于 2022 年).
文本
Wolfram Research (2015),SliceContourPlot3D,Wolfram 语言函数,https://reference.wolfram.com/language/ref/SliceContourPlot3D.html (更新于 2022 年).
Wolfram Research (2015),SliceContourPlot3D,Wolfram 语言函数,https://reference.wolfram.com/language/ref/SliceContourPlot3D.html (更新于 2022 年).
CMS
Wolfram 语言. 2015. "SliceContourPlot3D." Wolfram 语言与系统参考资料中心. Wolfram Research. 最新版本 2022. https://reference.wolfram.com/language/ref/SliceContourPlot3D.html.
Wolfram 语言. 2015. "SliceContourPlot3D." Wolfram 语言与系统参考资料中心. Wolfram Research. 最新版本 2022. https://reference.wolfram.com/language/ref/SliceContourPlot3D.html.
APA
Wolfram 语言. (2015). SliceContourPlot3D. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/SliceContourPlot3D.html 年
Wolfram 语言. (2015). SliceContourPlot3D. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/SliceContourPlot3D.html 年
BibTeX
@misc{reference.wolfram_2025_slicecontourplot3d, author="Wolfram Research", title="{SliceContourPlot3D}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/SliceContourPlot3D.html}", note=[Accessed: 01-April-2025
]}
BibLaTeX
@online{reference.wolfram_2025_slicecontourplot3d, organization={Wolfram Research}, title={SliceContourPlot3D}, year={2022}, url={https://reference.wolfram.com/language/ref/SliceContourPlot3D.html}, note=[Accessed: 01-April-2025
]}