RegionHausdorffDistance
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RegionHausdorffDistance
更多信息和选项

- RegionHausdorffDistance 亦称为 Hausdorff 度量和 Pompeiu–Hausdorff 距离.
- Hausdorff 距离量度两个区域之间的差别有多大.
- RegionHausdorffDistance 是从一个区域中的点到另一个区域中最近点的所有距离中的最大值.
- 点 p 和 q 之间的距离为 Norm[p-q].
- 实际上 RegionHausdorffDistance 由 MaxValue[MinValue[Norm[p-q],q∈reg2],p∈reg1] 和 MaxValue[MinValue[Norm[p-q],q∈reg1],p∈reg2] 的最大值给出.
- 除非区域是闭合的,否则 Hausdorff 距离可能不是通过区域中的点而是通过区域的闭包获得的.
- 如果 reg1⊆RegionDilation[reg2,ϵ] 和 reg2⊆RegionDilation[reg1,ϵ],则两个区域 reg1 和 reg2 之间的 Hausdorff 距离为 ϵ.

范例
打开所有单元关闭所有单元基本范例 (4)常见实例总结
In[20]:=20

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-cws0re
Out[20]=20

In[21]:=21

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-tikzl5
Out[21]=21

In[1]:=1

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-gjir76
Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-1czcc9
Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-r89lnj
Out[3]=3

In[1]:=1

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-7eyj5s
Out[1]=1

求 MeshRegion 与其凸包之间的 Hausdorff 距离:
In[1]:=1

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-8xo4vo
In[2]:=2

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-797pmr
Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-5oncx0
Out[3]=3

范围 (9)标准用法实例范围调查
特殊区域 (8)
In[1]:=1

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-6o0jua
Out[1]=1

RegionHausdorffDistance 接受坐标列表:
In[2]:=2

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-0ws9nd
Out[2]=2

In[1]:=1

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-7mi415
Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-jz43r0
Out[2]=2

In[1]:=1

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-00041e
Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-jdusf5
Out[2]=2

In[1]:=1

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-esyw4l
Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-0vnjs9
Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-flk5m8
Out[3]=3

In[1]:=1

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-xmflef
Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-0e5fc5
Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-37qor7
Out[3]=3

In[1]:=1

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-igxar6
Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-cfib7z
Out[2]=2

In[1]:=1

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-1kaba8
Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-jnsvsc
Out[2]=2

In[1]:=1

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-5kmar3
Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-42668q
Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-etilu9
Out[3]=3

In[4]:=4

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-bfevl7
Out[4]=4

网格区域 (1)
In[20]:=20

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-xgplru
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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-73wvv8
Out[10]=10

In[190]:=190

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-868gxk
In[192]:=192

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-cqafsq
Out[192]=192

In[193]:=193

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-vsr1m2
Out[193]=193

In[195]:=195

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-zzum8l
In[207]:=207

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-sjlvdn
Out[207]=207

In[147]:=147

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-qtc04f
Out[147]=147

选项 (2)各选项的常用值和功能
WorkingPrecision (2)
RegionHausdorffDistance 将尝试使用与输入相同的精度来计算距离:
In[1]:=1

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-c9oegt
Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-cuwkuv
Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-c62f2s
Out[3]=3

用 30 位精度求 RegionHausdorffDistance:
In[1]:=1

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-tbnvx3
Out[1]=1

应用 (1)用该函数可以解决的问题范例
属性和关系 (4)函数的属性及与其他函数的关联
两点之间的 Hausdorff 距离等价于 EuclideanDistance:
In[3]:=3

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-r36bz3
Out[3]=3

In[2]:=2

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-bjlsyt
Out[2]=2

两个点集之间的 Hausdorff 距离是任意点到另一点集的最大 EuclideanDistance:
In[1]:=1

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-pkhc76
In[2]:=2

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-6ymd5k
Out[2]=2

区域与一个点之间的 Hausdorff 距离是该点到该区域中任意点的最远距离:
In[1]:=1

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-uq0mk1
Out[1]=1

RegionDistance 可用于求点到区域的最近距离:
In[1]:=1

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-2f75l8
In[2]:=2

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https://wolfram.com/xid/0e2yzb16oninfyi0ac5e-u671gz
Out[2]=2

Wolfram Research (2023),RegionHausdorffDistance,Wolfram 语言函数,https://reference.wolfram.com/language/ref/RegionHausdorffDistance.html.
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Wolfram Research (2023),RegionHausdorffDistance,Wolfram 语言函数,https://reference.wolfram.com/language/ref/RegionHausdorffDistance.html.
文本
Wolfram Research (2023),RegionHausdorffDistance,Wolfram 语言函数,https://reference.wolfram.com/language/ref/RegionHausdorffDistance.html.
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Wolfram Research (2023),RegionHausdorffDistance,Wolfram 语言函数,https://reference.wolfram.com/language/ref/RegionHausdorffDistance.html.
CMS
Wolfram 语言. 2023. "RegionHausdorffDistance." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/RegionHausdorffDistance.html.
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Wolfram 语言. 2023. "RegionHausdorffDistance." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/RegionHausdorffDistance.html.
APA
Wolfram 语言. (2023). RegionHausdorffDistance. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/RegionHausdorffDistance.html 年
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Wolfram 语言. (2023). RegionHausdorffDistance. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/RegionHausdorffDistance.html 年
BibTeX
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@misc{reference.wolfram_2025_regionhausdorffdistance, author="Wolfram Research", title="{RegionHausdorffDistance}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/RegionHausdorffDistance.html}", note=[Accessed: 02-April-2025
]}
BibLaTeX
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@online{reference.wolfram_2025_regionhausdorffdistance, organization={Wolfram Research}, title={RegionHausdorffDistance}, year={2023}, url={https://reference.wolfram.com/language/ref/RegionHausdorffDistance.html}, note=[Accessed: 02-April-2025
]}