Editing Viewing frustum

{{Short description|Region of space in the modeled world that may appear on the screen}}{{more citations needed|date=August 2014}}
{{3D computer graphics}}
[[File:ViewFrustum.svg|thumb|right|A view frustum]]
[[File:Pyramid of vision.svg|thumb|right|The appearance of an object in a pyramid of vision]]
[[File:Orthographic view frustum.png|thumb|right|When creating a [[parallel projection]], the viewing frustum is shaped like a box as opposed to a pyramid.]]

In [[3D computer graphics]], a '''viewing frustum'''<ref name="SungShirley2008">{{cite book|author1=Kelvin Sung|author2=Peter Shirley|author2-link=Peter Shirley|author3= Steven Baer|title=Essentials of Interactive Computer Graphics: Concepts and Implementation|url= https://books.google.com/books?id=PqT3RRVo4isC&pg=PA390|date=6 November 2008|publisher=CRC Press|isbn=978-1-56881-257-1|page=390}}</ref> or '''view frustum'''<ref name=ms/> is the region of space in the modeled world that may appear on the screen; it is the [[field of view in video games|field of view]] of a [[Perspective (graphical)|perspective]] [[virtual camera system]].<ref name=ms>{{cite web |url=https://docs.microsoft.com/en-us/previous-versions/windows/xna/ff634570(v=xnagamestudio.42) |title=What Is a View Frustum? |date=15 August 2012 |publisher=Microsoft |access-date=1 January 2022}}</ref>

The view frustum is typically obtained by taking a geometrical [[frustum]]—that is a truncation with parallel planes—of the '''pyramid of vision''', which is the adaptation of (idealized) ''[[cone of vision]]'' that a camera or eye would have to the rectangular [[viewport]]s typically used in computer graphics.<ref name="Parekh2013">{{cite book|author=Ranjan Parekh|title=Principles of Multimedia|url=https://books.google.com/books?id=jacQAgAAQBAJ&pg=PA413|year=2013|publisher=Tata McGraw-Hill Education|isbn=978-1-259-00650-0|page=413|edition=2nd}}</ref><ref name="Goulekas2001">{{cite book|author=Karen Goulekas|title=Visual Effects in A Digital World: A Comprehensive Glossary of over 7000 Visual Effects Terms|url=https://books.google.com/books?id=vGgymugduCsC&pg=PA409|year=2001|publisher=Morgan Kaufmann|isbn=978-0-08-052071-1|page=409}}</ref> Some authors use ''pyramid of vision'' as a synonym for view frustum itself, i.e. consider it [[Truncation (geometry)|truncated]].<ref name="Kerlow2004">{{cite book|author=Isaac V. Kerlow|title=The Art of 3D: Computer Animation and Effects|url=https://books.google.com/books?id=5G-5iyasSk8C&pg=PA185|year=2004|publisher=John Wiley & Sons|isbn=978-0-471-43036-0|page=185}}</ref>

The exact shape of this region varies depending on what kind of camera lens is being simulated, but typically it is a frustum of a rectangular pyramid (hence the name). The planes that cut the frustum perpendicular to the viewing direction are called the ''near plane'' and the ''far plane''. Objects closer to the camera than the near plane or beyond the far plane are not drawn. Sometimes, the far plane is placed infinitely far away from the camera so all objects within the frustum are drawn regardless of their distance from the camera.

[[Hidden-surface determination#Viewing-frustum culling| Viewing-frustum culling]] is the process of removing from the [[rendering (computer graphics)|rendering]] process those objects that lie completely outside the viewing frustum.<ref>{{cite web |url=http://www.lighthouse3d.com/tutorials/view-frustum-culling/ |title=View Frustum Culling |date=15 April 2011 |publisher= lighthouse3d.com |access-date= 11 June 2014}}</ref> Rendering these objects would be a waste of resources since they are not directly visible. To make culling fast, it is usually done using [[bounding volume]]s surrounding the objects rather than the objects themselves.

==Definitions==
;VPN: the view-plane normal – a [[Surface normal|normal]] to the view plane.

;VUV: the view-up vector – the vector on the view plane that indicates the upward direction.

;VRP: the viewing reference point – a point located on the view plane, and the origin of the VRC.

;PRP: the projection reference point – the point where the image is projected from, for parallel projection, the PRP is at infinity.

;VRC: the viewing-reference coordinate system.

The geometry is defined by a [[field of view]] angle (in the 'y' direction), as well as an [[Aspect ratio (image)|aspect ratio]].  Further, a set of z-planes define the '''near and far bounds''' of the frustum. Together this information can be used to calculate a [[Projection matrix (computer graphics)|projection matrix]] for rendering [[Transformation matrix|transformation]] in a [[graphics pipeline]].

==References==
{{Reflist}}

[[Category:3D computer graphics]]


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