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CoordinateBounds
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CoordinateBounds

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gives a list {{xmin,xmax},{ymin,ymax},…} of the bounds in each dimension of the region defined by coords.

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CoordinateBounds[coords,δ]

pads the ranges of coordinates by ±δ in each dimension.

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pads by the scaled amount s in each dimension.

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CoordinateBounds[coords,{p1,p2,…}]

pads by p1, p2, … in successive dimensions.

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CoordinateBounds[coords,{{p1min,p1max},{p2min,p2max},…}]

gives {{xmin-p1min,xmax+p1max},{ymin-p2min,ymax+p2max},…}

Details

Examples

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Basic Examples  (1)Summary of the most common use cases

Find bounds for coordinates in 2 dimensions:

In[1]:=1
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https://wolfram.com/xid/0pus8svbcm-hitwzc
Out[1]=1

Pad by 1 in each direction:

In[2]:=2
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https://wolfram.com/xid/0pus8svbcm-cwy92l
Out[2]=2

Pad by 1/4 of the span in each dimension:

In[3]:=3
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https://wolfram.com/xid/0pus8svbcm-cy684v
Out[3]=3

Scope  (1)Survey of the scope of standard use cases

Coordinates in 3D of different types at various levels in a list:

In[1]:=1
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https://wolfram.com/xid/0pus8svbcm-crp46q
Out[1]=1

Find the bounding box:

In[2]:=2
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https://wolfram.com/xid/0pus8svbcm-e6b4rx
Out[2]=2

Pad by 1 in each dimension:

In[3]:=3
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https://wolfram.com/xid/0pus8svbcm-hf89ki
Out[3]=3

Pad by a fraction of the difference in each dimension:

In[4]:=4
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https://wolfram.com/xid/0pus8svbcm-md4lqb
Out[4]=4

Pad by different amounts for different dimensions:

In[5]:=5
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https://wolfram.com/xid/0pus8svbcm-nhvo85
Out[5]=5

Pad the minima and maxima differently:

In[6]:=6
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https://wolfram.com/xid/0pus8svbcm-hiq93
Out[6]=6

Generalizations & Extensions  (1)Generalized and extended use cases

When there are coordinates that are not numerical, the result is typically expressed in terms of Min and Max:

In[1]:=1
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https://wolfram.com/xid/0pus8svbcm-dipljh
Out[1]=1

Properties & Relations  (2)Properties of the function, and connections to other functions

Generally, CoordinateBounds[coords] is the transpose of CoordinateBoundingBox[coords]:

In[4]:=4
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https://wolfram.com/xid/0pus8svbcm-bw5sm2
In[5]:=5
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https://wolfram.com/xid/0pus8svbcm-bfh3p2
Out[5]=5
In[6]:=6
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https://wolfram.com/xid/0pus8svbcm-cf0io4
Out[6]=6

For coordinates given in a matrix, CoordinateBounds[coords] is equivalent to Map[MinMax, Transpose[coords]]:

In[1]:=1
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https://wolfram.com/xid/0pus8svbcm-e3ij7g
In[2]:=2
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https://wolfram.com/xid/0pus8svbcm-jws0xh
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0pus8svbcm-iehnx4
Out[3]=3
Wolfram Research (2015), CoordinateBounds, Wolfram Language function, https://reference.wolfram.com/language/ref/CoordinateBounds.html.
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Wolfram Research (2015), CoordinateBounds, Wolfram Language function, https://reference.wolfram.com/language/ref/CoordinateBounds.html.

Text

Wolfram Research (2015), CoordinateBounds, Wolfram Language function, https://reference.wolfram.com/language/ref/CoordinateBounds.html.

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Wolfram Research (2015), CoordinateBounds, Wolfram Language function, https://reference.wolfram.com/language/ref/CoordinateBounds.html.

CMS

Wolfram Language. 2015. "CoordinateBounds." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CoordinateBounds.html.

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Wolfram Language. 2015. "CoordinateBounds." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CoordinateBounds.html.

APA

Wolfram Language. (2015). CoordinateBounds. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CoordinateBounds.html

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Wolfram Language. (2015). CoordinateBounds. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CoordinateBounds.html

BibTeX

@misc{reference.wolfram_2025_coordinatebounds, author="Wolfram Research", title="{CoordinateBounds}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/CoordinateBounds.html}", note=[Accessed: 25-April-2025 ]}

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@misc{reference.wolfram_2025_coordinatebounds, author="Wolfram Research", title="{CoordinateBounds}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/CoordinateBounds.html}", note=[Accessed: 25-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_coordinatebounds, organization={Wolfram Research}, title={CoordinateBounds}, year={2015}, url={https://reference.wolfram.com/language/ref/CoordinateBounds.html}, note=[Accessed: 25-April-2025 ]}

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@online{reference.wolfram_2025_coordinatebounds, organization={Wolfram Research}, title={CoordinateBounds}, year={2015}, url={https://reference.wolfram.com/language/ref/CoordinateBounds.html}, note=[Accessed: 25-April-2025 ]}