3D computer graphics 3D computer graphics, or “3D graphics,” sometimes called CGI, 3D-CGI or three-dimensional computer graphics are graphics that use a three-dimensional representation of geometric data (often Cartesian) that is stored in the computer for th ...

, the view frustum (also called viewing

frustum In geometry, a (from the Latin for "morsel"; plural: ''frusta'' or ''frustums'') is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting this solid. In the case of a pyramid, the base faces are ...

) is the region of space in the modeled world that may appear on the screen; it is the

field of view The field of view (FoV) is the extent of the observable world that is seen at any given moment. In the case of optical instruments or sensors it is a solid angle through which a detector is sensitive to electromagnetic radiation. Humans a ...

of a perspective

virtual camera system In 3D video games, a virtual camera system aims at controlling a camera or a set of cameras to display a view of a 3D virtual world. Camera systems are used in video games where their purpose is to show the action at the best possible angle; m ...

. The view frustum is typically obtained by taking a

—that is a truncation with parallel planes—of the pyramid of vision, which is the adaptation of (idealized)

cone of vision The angle of view is the decisive variable for the visual perception of the size or projection of the size of an object. Angle of view and perception of size The perceived size of an object depends on the size of the image projected onto the ...

that a camera or eye would have to the rectangular

viewport A viewport is a polygon viewing region in computer graphics. In computer graphics theory, there are two region-like notions of relevance when rendering some objects to an image. In textbook terminology, the '' world coordinate window'' is the area ...

s typically used in computer graphics. Some authors use ''pyramid of vision'' as a synonym for view frustum itself, i.e. consider it truncated. The exact shape of this region varies depending on what kind of camera lens is being simulated, but typically it is a

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. Viewing-frustum culling is the process of removing from the rendering process those objects that lie completely outside the viewing frustum. 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 In computer graphics and computational geometry, a bounding volume for a set of objects is a closed volume that completely contains the union of the objects in the set. Bounding volumes are used to improve the efficiency of geometrical operatio ...

s surrounding the objects rather than the objects themselves.

Definitions

;VPN: the view-plane normal – a

normal Normal(s) or The Normal(s) may refer to: Film and television * ''Normal'' (2003 film), starring Jessica Lange and Tom Wilkinson * ''Normal'' (2007 film), starring Carrie-Anne Moss, Kevin Zegers, Callum Keith Rennie, and Andrew Airlie * ''Norma ...

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

angle (in the 'y' direction), as well as an 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 In statistics, the projection matrix (\mathbf), sometimes also called the influence matrix or hat matrix (\mathbf), maps the vector of response values (dependent variable values) to the vector of fitted values (or predicted values). It describes t ...

for rendering

transformation Transformation may refer to: Science and mathematics In biology and medicine * Metamorphosis, the biological process of changing physical form after birth or hatching * Malignant transformation, the process of cells becoming cancerous * Trans ...

in a

graphics pipeline In computer graphics, a computer graphics pipeline, rendering pipeline or simply graphics pipeline, is a conceptual model that describes what steps a graphics system needs to perform to Rendering (computer graphics), render a ...

References

3D computer graphics {{Compu-graphics-stub