ComplexVectorPlot
更多信息和选项




- ComplexVectorPlot 亦称为场图或方向图.
- ComplexVectorPlot 通过绘制箭头来显示向量场. 默认情况下,向量的方向由箭头的方向表示,幅值由颜色表示.
- ComplexVectorPlot 在对 f 的值进行计算后,在结果不是复数的位置处不显示箭头.
- ComplexVectorPlot[f,{z,n}] 等价于 ComplexVectorPlot[f,{z,-n-n I,n+n I}].
- ComplexVectorPlot 将变量 z 视为局部变量,相当于使用 Block.
- ComplexVectorPlot 具有属性 HoldAll,只在对 z 赋值后才计算 f. 某些情况下,先用 Evaluate 对 f 进行符号式计算效率更高.
- ComplexVectorPlot 和 Graphics 有相同的选项,不同之处和更多选项如下所示: [所有选项的列表]
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AspectRatio 1 高宽比 ClippingStyle Automatic 怎样显示向量范围之外的箭头 EvaluationMonitor None 每次运行函数时要计算的表达式 Frame True 是否为图形绘制边框 FrameTicks Automatic 边框刻度标记 Method Automatic 使用何种方法绘图 PerformanceGoal $PerformanceGoal 优化的目标 PlotLegends None 要包含的图例 PlotRange {Full,Full} 包括的 x、y 值的范围 PlotRangePadding Automatic 对数值范围进行多少填充 PlotTheme $PlotTheme 绘图的整体外观主题 RegionFunction (True&) 确定要包含的区域 RegionBoundaryStyle Automatic 怎样设置绘图区域边界的样式 RegionFillingStyle Automatic 怎样设置绘图区域内部的样式 VectorAspectRatio Automatic 箭头的宽度与长度的比 VectorColorFunction Automatic 如何为箭头着色 VectorColorFunctionScaling True 是否缩放传递给 VectorColorFunction 的函数 VectorMarkers Automatic 箭头的形状 VectorPoints Automatic 箭头的数量或放置方式 VectorRange Automatic 显示出来的向量的长度范围 VectorScaling None 怎样缩放箭头的大小 VectorSizes Automatic 显示出来的箭头的大小 VectorStyle Automatic 怎样设置箭头的样式 WorkingPrecision MachinePrecision 内部计算使用的精度 - 按比例缩放各个箭头以适应每个点周围的边界圆.
- VectorPoints{c1,c2,…} 在复数点 c1、c2、… 处绘制箭头.
- VectorScaling 将向量的幅值缩放到 VectorSizes 给定的箭头大小范围:smin 到 smax.
- VectorScaling->Automatic 将根据向量幅值缩放箭头的长度:
- 由 VectorMarkers 给定的箭头符号被绘制在一个方框内,方框的宽度和长度的比例为由 VectorAspectRatio 指定的
.
- 常见的标记有:
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"Segment" 与场方向一致的线段 "PinDart" 沿场方向的销镖形 "Dart" 镖形标记 "Drop" 水滴形标记 - VectorColorFunction->None 将按 VectorStyle 指定的样式绘制箭头.
- 提供给 RegionFunction 和 VectorColorFunction 中的函数的参数为 z 和 f.



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 (3)常见实例总结
范围 (19)标准用法实例范围调查
采样 (7)

https://wolfram.com/xid/0n4i0sam2ea-bnkdo9


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在赋值前用 Evaluate 符号式计算向量场:

https://wolfram.com/xid/0n4i0sam2ea-dzznsr

演示 (12)

https://wolfram.com/xid/0n4i0sam2ea-bs9khg


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选项 (65)各选项的常用值和功能
ClippingStyle (4)

https://wolfram.com/xid/0n4i0sam2ea-dxfsnw

用 ClippingStyleNone 移除极短和极长的向量:

https://wolfram.com/xid/0n4i0sam2ea-f7s8c3


https://wolfram.com/xid/0n4i0sam2ea-edm9pg


https://wolfram.com/xid/0n4i0sam2ea-b6iwnl

EvaluationMonitor (2)
PlotLegends (5)

https://wolfram.com/xid/0n4i0sam2ea-js95u9


https://wolfram.com/xid/0n4i0sam2ea-ba8k3h


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PlotRange (5)

https://wolfram.com/xid/0n4i0sam2ea-g6xoyw


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https://wolfram.com/xid/0n4i0sam2ea-f1lr1g

PlotTheme (2)
RegionBoundaryStyle (5)

https://wolfram.com/xid/0n4i0sam2ea-d6s6um


https://wolfram.com/xid/0n4i0sam2ea-7wf5ba

使用 None 不显示边界:

https://wolfram.com/xid/0n4i0sam2ea-d87zny


https://wolfram.com/xid/0n4i0sam2ea-gr12m6


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RegionFillingStyle (5)

https://wolfram.com/xid/0n4i0sam2ea-b1r4jl


https://wolfram.com/xid/0n4i0sam2ea-cxnsd5

使用 None 不显示内部填充:

https://wolfram.com/xid/0n4i0sam2ea-clzxe7


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RegionFunction (2)
VectorAspectRatio (2)
VectorColorFunction (5)

https://wolfram.com/xid/0n4i0sam2ea-b7adpr


https://wolfram.com/xid/0n4i0sam2ea-cdiw5o

使用来自 ColorData 的已命名的颜色梯度:

https://wolfram.com/xid/0n4i0sam2ea-dsi8pl


https://wolfram.com/xid/0n4i0sam2ea-bw7lma


https://wolfram.com/xid/0n4i0sam2ea-lf15n

VectorColorFunctionScaling (2)

https://wolfram.com/xid/0n4i0sam2ea-c7h4ae

用 VectorColorFunctionScalingFalse 获取未经缩放的值:

https://wolfram.com/xid/0n4i0sam2ea-drzoi2

VectorMarkers (4)

https://wolfram.com/xid/0n4i0sam2ea-d31ee2


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VectorPoints (5)

https://wolfram.com/xid/0n4i0sam2ea-bkxnrk


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VectorRange (6)

https://wolfram.com/xid/0n4i0sam2ea-fdojbp


https://wolfram.com/xid/0n4i0sam2ea-m4l3r

对箭头的长度进行缩放,绘制幅值在 0.2 到 2 之间的向量:

https://wolfram.com/xid/0n4i0sam2ea-gthzzm


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VectorScaling (2)
默认情况下,VectorScaling 被设为 None:

https://wolfram.com/xid/0n4i0sam2ea-ml02wa


https://wolfram.com/xid/0n4i0sam2ea-84w8x5

VectorSizes (2)
VectorStyle (6)

https://wolfram.com/xid/0n4i0sam2ea-hnrejz


https://wolfram.com/xid/0n4i0sam2ea-fqpqa1

用 Arrowheads 明确指定箭头的样式:

https://wolfram.com/xid/0n4i0sam2ea-bjd7u


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对于没有 Arrowheads 的图像指令,按向量的 scale 进行缩放:

https://wolfram.com/xid/0n4i0sam2ea-dmphsg

用 VectorScaling 选项改变缩放方式:

https://wolfram.com/xid/0n4i0sam2ea-i0vjuu

应用 (7)用该函数可以解决的问题范例

https://wolfram.com/xid/0n4i0sam2ea-de7yae

向量的长度随 Abs[f] 的增大而增大,方向则由 Arg[f] 决定:

https://wolfram.com/xid/0n4i0sam2ea-c2tmq2


https://wolfram.com/xid/0n4i0sam2ea-lm37cf


https://wolfram.com/xid/0n4i0sam2ea-bftb2b

场向量沿单位圆环绕函数 在原点处的零点两次,这意味着
在原点具有双重零点:

https://wolfram.com/xid/0n4i0sam2ea-gqfooa


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属性和关系 (15)函数的属性及与其他函数的关联
ComplexVectorPlot 是 VectorPlot 的特例:

https://wolfram.com/xid/0n4i0sam2ea-cb87oq

ComplexStreamPlot 将复数绘制为流线:

https://wolfram.com/xid/0n4i0sam2ea-7studa

ComplexStreamPlot 是 StreamPlot 的特殊情况:

https://wolfram.com/xid/0n4i0sam2ea-c53rr6

使用 VectorDisplacementPlot 可视化指定区域内复函数的效果:

https://wolfram.com/xid/0n4i0sam2ea-kx8huh

用 VectorPlot3D 和 StreamPlot3D 可视化三维向量场:

https://wolfram.com/xid/0n4i0sam2ea-h3ykri

ComplexContourPlot 绘制复平面上的曲线:

https://wolfram.com/xid/0n4i0sam2ea-pesif0

ComplexRegionPlot 绘制复平面上的区域:

https://wolfram.com/xid/0n4i0sam2ea-ko83ut

ComplexPlot 用颜色显示函数的辐角和幅值:

https://wolfram.com/xid/0n4i0sam2ea-e28611

通过 ComplexPlot3D 用 轴显示幅值:

https://wolfram.com/xid/0n4i0sam2ea-vgce1e

用 ComplexArrayPlot 绘制复数数组:

https://wolfram.com/xid/0n4i0sam2ea-p6xumo

用 ReImPlot 和 AbsArgPlot 在实平面上绘制复数:

https://wolfram.com/xid/0n4i0sam2ea-0vi62l


https://wolfram.com/xid/0n4i0sam2ea-mqa938

用 ComplexListPlot 显示复数在平面上的位置:

https://wolfram.com/xid/0n4i0sam2ea-wyd4bn

使用 ListVectorPlot 进行数据绘制:

https://wolfram.com/xid/0n4i0sam2ea-czc8d0

https://wolfram.com/xid/0n4i0sam2ea-bzenb8

使用 ListStreamPlot 绘制流线图而非向量:

https://wolfram.com/xid/0n4i0sam2ea-efbl3z

使用 VectorDensityPlot 添加标量场的密度图:

https://wolfram.com/xid/0n4i0sam2ea-gljrl7

函数 StreamDensityPlot 可用于流线图而非向量:

https://wolfram.com/xid/0n4i0sam2ea-kxyms1

使用 ListVectorDensityPlot 生成基于数据的标量场的密度图:

https://wolfram.com/xid/0n4i0sam2ea-2fsjy

https://wolfram.com/xid/0n4i0sam2ea-b5me24

使用 ListStreamDensityPlot 绘制流线图而非向量:

https://wolfram.com/xid/0n4i0sam2ea-eootc

使用 LineIntegralConvolutionPlot 绘制向量场的线积分卷积:

https://wolfram.com/xid/0n4i0sam2ea-c9d537

Wolfram Research (2020),ComplexVectorPlot,Wolfram 语言函数,https://reference.wolfram.com/language/ref/ComplexVectorPlot.html.
文本
Wolfram Research (2020),ComplexVectorPlot,Wolfram 语言函数,https://reference.wolfram.com/language/ref/ComplexVectorPlot.html.
Wolfram Research (2020),ComplexVectorPlot,Wolfram 语言函数,https://reference.wolfram.com/language/ref/ComplexVectorPlot.html.
CMS
Wolfram 语言. 2020. "ComplexVectorPlot." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/ComplexVectorPlot.html.
Wolfram 语言. 2020. "ComplexVectorPlot." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/ComplexVectorPlot.html.
APA
Wolfram 语言. (2020). ComplexVectorPlot. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/ComplexVectorPlot.html 年
Wolfram 语言. (2020). ComplexVectorPlot. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/ComplexVectorPlot.html 年
BibTeX
@misc{reference.wolfram_2025_complexvectorplot, author="Wolfram Research", title="{ComplexVectorPlot}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/ComplexVectorPlot.html}", note=[Accessed: 07-June-2025
]}
BibLaTeX
@online{reference.wolfram_2025_complexvectorplot, organization={Wolfram Research}, title={ComplexVectorPlot}, year={2020}, url={https://reference.wolfram.com/language/ref/ComplexVectorPlot.html}, note=[Accessed: 07-June-2025
]}