ViewPoint

ViewPoint

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

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Basic Examples  (3)

Specify the view point using special scaled coordinates:

Use symbolic view points:

Specify orthographic views:

Scope  (5)

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

Default view point:

Use symbolic view points:

Use orthographic views:

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

Same ViewPoint, but ViewCenter is the red point:

Applications  (1)

Illustrate the relation between ViewPoint and the simulated camera view:

Properties & Relations  (6)

ViewVector uses the ordinary coordinates system:

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

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

ViewAngle controls the opening angle of a simulated camera:

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

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

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

Neat Examples  (1)

Random camera views of a molecular model:

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).

CMS

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

BibTeX

@misc{reference.wolfram_2024_viewpoint, author="Wolfram Research", title="{ViewPoint}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/ViewPoint.html}", note=[Accessed: 21-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_viewpoint, organization={Wolfram Research}, title={ViewPoint}, year={2008}, url={https://reference.wolfram.com/language/ref/ViewPoint.html}, note=[Accessed: 21-December-2024 ]}