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ViewPoint

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is an option for Graphics3D and related functions which gives the point in space from which three‐dimensional objects are to be viewed.

Details

  • ViewPoint->{x,y,z} gives the position of the view point relative to the center of the three‐dimensional box that contains the objects.
  • The view point is given in a special scaled coordinate system in which the longest side of the bounding box has length 1. The center of the bounding box is taken to have coordinates {0,0,0}.
  • Common settings for ViewPoint are:
  • {1.3,-2.4,2}default setting
    {0,-2,0}directly in front
    {0,-2,2}in front and up
    {0,-2,-2}in front and down
    {-2,-2,0}left‐hand corner
    {2,-2,0}right‐hand corner
    {0,0,2}directly above
  • The following symbolic forms can also be used: »
  • Aboveabove, along the positive z direction
    Belowbelow, along the negative z direction
    Frontin front, along the negative y direction
    Backat back, along the positive y direction
    Leftleft, along the negative x direction
    Rightright, along the positive x direction
    {Left,Top}, etc.corners
  • Choosing a ViewPoint farther away from the object reduces the distortion associated with perspective.
  • Infinite coordinates can be used to specify orthographic views: »
  • {0,0,Infinity}view from above (plan view)
    {0,0,-Infinity}view from below
    {0,-Infinity,0}view from the front (front elevation)
    {0,Infinity,0}view from the back
    {-Infinity,0,0}view from the left
    {Infinity,0,0}view from the right
  • The coordinates of the corners of the bounding box in the special coordinate system used for ViewPoint are determined by the setting for the BoxRatios option.
  • In a notebook front end, dragging with the mouse rotates a 3D object, by changing the azimuthal components of ViewPoint, as well as the setting for ViewVertical.
  • Dragging with the mouse while pressing , , or zooms in or out, changing the value of ViewAngle, but keeping ViewPoint fixed.
  • Explicit settings for ViewVector or ViewMatrix override settings for ViewPoint.

Examples

open allclose all

Basic Examples  (3)Summary of the most common use cases

Specify the view point using special scaled coordinates:

In[1]:=1
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https://wolfram.com/xid/0bdp9fxpu-busg2j
Out[1]=1

Use symbolic view points:

In[1]:=1
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https://wolfram.com/xid/0bdp9fxpu-ibt4hf
Out[1]=1

Specify orthographic views:

In[1]:=1
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https://wolfram.com/xid/0bdp9fxpu-dmmnhe
Out[1]=1

Scope  (5)Survey of the scope of standard use cases

The view point coordinates are scaled to the longest side of the bounding box:

In[1]:=1
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https://wolfram.com/xid/0bdp9fxpu-bbtp1r
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdp9fxpu-cr89cp
Out[2]=2

Default view point:

In[1]:=1
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https://wolfram.com/xid/0bdp9fxpu-dtx5mp
Out[1]=1

Use symbolic view points:

In[1]:=1
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https://wolfram.com/xid/0bdp9fxpu-baibjf
Out[1]=1

Use orthographic views:

In[1]:=1
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https://wolfram.com/xid/0bdp9fxpu-d7e72w
Out[1]=1

The camera is located at ViewPoint, and aimed toward ViewCenter:

In[1]:=1
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https://wolfram.com/xid/0bdp9fxpu-eneu5d
Out[1]=1

Same ViewPoint, but ViewCenter is the red point:

In[2]:=2
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https://wolfram.com/xid/0bdp9fxpu-dqj872
Out[2]=2

Applications  (1)Sample problems that can be solved with this function

Illustrate the relation between ViewPoint and the simulated camera view:

In[1]:=1
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https://wolfram.com/xid/0bdp9fxpu-my8vn9
Out[1]=1

Properties & Relations  (6)Properties of the function, and connections to other functions

ViewVector uses the ordinary coordinates system:

In[1]:=1
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https://wolfram.com/xid/0bdp9fxpu-bjv477
Out[1]=1

In this case, the longest edge has length 2 and the center of the box is {0,0,0}:

In[1]:=1
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https://wolfram.com/xid/0bdp9fxpu-buxou8
Out[1]=1

Convert ViewPoint to ViewVector by multiplying the length and pointing the center:

In[2]:=2
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https://wolfram.com/xid/0bdp9fxpu-hlr8si
Out[2]=2

ViewAngle controls the opening angle of a simulated camera:

In[1]:=1
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https://wolfram.com/xid/0bdp9fxpu-gm0z5b
Out[1]=1

Transforming ViewPoint is equivalent to applying the inverse transformation to objects:

In[1]:=1
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https://wolfram.com/xid/0bdp9fxpu-izgbje
In[2]:=2
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https://wolfram.com/xid/0bdp9fxpu-bu7odt
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0bdp9fxpu-fpes7p
Out[3]=3

After a dynamic view change using a mouse, apply Options to get current camera parameters:

In[1]:=1
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https://wolfram.com/xid/0bdp9fxpu-e6kole
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdp9fxpu-mqdg99
Out[2]=2

An orthographic view of Plot3D can be used to simulate DensityPlot:

In[1]:=1
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https://wolfram.com/xid/0bdp9fxpu-bfxsti
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdp9fxpu-btzafy
Out[2]=2

Neat Examples  (1)Surprising or curious use cases

Random camera views of a molecular model:

In[1]:=1
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https://wolfram.com/xid/0bdp9fxpu-gq36ew
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdp9fxpu-wsbqs6
Out[2]=2
Wolfram Research (1988), ViewPoint, Wolfram Language function, https://reference.wolfram.com/language/ref/ViewPoint.html (updated 2008).
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Wolfram Research (1988), ViewPoint, Wolfram Language function, https://reference.wolfram.com/language/ref/ViewPoint.html (updated 2008).

Text

Wolfram Research (1988), ViewPoint, Wolfram Language function, https://reference.wolfram.com/language/ref/ViewPoint.html (updated 2008).

✖
Wolfram Research (1988), ViewPoint, Wolfram Language function, https://reference.wolfram.com/language/ref/ViewPoint.html (updated 2008).

CMS

Wolfram Language. 1988. "ViewPoint." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2008. https://reference.wolfram.com/language/ref/ViewPoint.html.

✖
Wolfram Language. 1988. "ViewPoint." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2008. https://reference.wolfram.com/language/ref/ViewPoint.html.

APA

Wolfram Language. (1988). ViewPoint. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ViewPoint.html

✖
Wolfram Language. (1988). ViewPoint. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ViewPoint.html

BibTeX

@misc{reference.wolfram_2025_viewpoint, author="Wolfram Research", title="{ViewPoint}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/ViewPoint.html}", note=[Accessed: 19-April-2025 ]}

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@misc{reference.wolfram_2025_viewpoint, author="Wolfram Research", title="{ViewPoint}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/ViewPoint.html}", note=[Accessed: 19-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_viewpoint, organization={Wolfram Research}, title={ViewPoint}, year={2008}, url={https://reference.wolfram.com/language/ref/ViewPoint.html}, note=[Accessed: 19-April-2025 ]}

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@online{reference.wolfram_2025_viewpoint, organization={Wolfram Research}, title={ViewPoint}, year={2008}, url={https://reference.wolfram.com/language/ref/ViewPoint.html}, note=[Accessed: 19-April-2025 ]}