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Topic: Frustum

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	XEngine: Frustum Class Reference
		This class represents a pyramidal frustum which is defined as the volume created by 6 planes where always 3 planes intersect each other to form the 8 corner points of the frustum.
		Internally, the Frustum class stores the 6 planes and not the 8 corner vertices, although it is possible to create a frustum specifying only the corner vertices.
		The volume of the frustum therefore is: V = (h / 3) * (B + sqrt(B * A) + A) where h is the distance from the front to the back plane, A is the area of the quadrilateral on the front plane and B is the area of the quadrilateral on the back plane.
	xengine.sourceforge.net /docs/classXEngine_1_1Math_1_1Frustum.html (1171 words)

	Frustum - Wikipedia, the free encyclopedia
		A frustum is the portion of a solid ;– normally a cone or pyramid ;– which lies between two parallel planes cutting the solid.
		An example of a pyramidal frustum may be seen on the reverse of the Great Seal of the United States, as on the back of the U.S. one-dollar bill.
		Certain ancient Native American mounds also form the frustum of a pyramid.
	en.wikipedia.org /wiki/Frustum (258 words)

	Frustum - DmWiki
		The top of the pyramid is usually the location of the camera; you can extract the frustum from the view matrix, or calculate it directly from the camera location, direction, and field of view.
		Each side of the frustum is a plane in 3D space.
		If the frustum planes are defined with outward-facing normals, than an object is within the frustum, and thus visible, if its bounding volume is inside (at least partially inside) all the planes.
	www.devmaster.net /wiki/Frustum (246 words)

	Viewing frustum - Wikipedia, the free encyclopedia
		In 3D computer graphics, the viewing frustum or view frustum is the region of space in the modeled world that may appear on the screen; it is the field of view of the notional camera.
		Viewing frustum culling or view frustum culling is the process of removing objects that lie completely outside the viewing frustum from the rendering process.
		In ray tracing, viewing frustum culling cannot be performed because objects outside the viewing frustum may be visible when reflected off an object inside the frustum.
	en.wikipedia.org /wiki/Viewing_frustum (242 words)

	OpenVRML: openvrml::frustum Class Reference
		A frustum is more or less a truncated pyramid.
		This class represents frustums with their wide end facing down the -z axis, and their (theoretical) tip at the origin.
		A frustum is a convenient representation of the volume of virtual space visible through the on-screen window when using a perspective projection.
	www.openvrml.org /doc/classopenvrml_1_1frustum.html (165 words)

	flipcode - Frustum Culling
		Without a hierarchal method, frustum culling still has a good advantage over not doing it at all but it also means that it scales linearly with the number of objects in our world.
		This means that we want to be able to construct the 6 planes of the frustum from our view/projection matrices as well as check whether a sphere is outside the frustum and whether a bounding box is outside the frustum.
		What we want with the sphere is to have it situated in the middle of the frustum with a radius that extends from the center of the sphere to a far corner of the frustum.
	www.flipcode.com /articles/article_frustumculling.shtml (4216 words)

	Projecting a Ray from 2D Screen Coordinates
		The viewing frustum has an origin (0,0) at the center of the screen, while screen coordinates have an origin at the upper left of the screen.
		Since we defined the frustum, we know the angle at which the sides of the frustum meet - this is the field of view we used to create the projection matrix in the first place.
		The distance to the center of the frustum to the sides of the frustum (1 or -1) at a given depth is
	www.mvps.org /directx/articles/rayproj.htm (1487 words)

	[No title]
		The shape of the frustum is a pyramid with the nearest peak truncated at what is deemed the ‘near’ clipping plane (see Figure 1).
		Frustum culling is simply the process of determining whether or not objects are visible in this area.
		If we choose the cone angle to be the same as the field of view of the frustum, then we create a cone that cuts off the corners of the frustum.
	www.flipcode.com /articles/article_frustumculling-pf.shtml (4276 words)

	Performer Perfly
		It interacts with the cull process and the viewing frustum to determine which nodes should be displayed.
		The isec process determines what objects are outside the viewing frustum and passes this information on to the cull process.
		Because the bounding volume may be larger than the object it surrounds, it is possible for it to be partially in the viewing frustum and yet have none of its geometry displayed to the user.
	www.eg.bucknell.edu /~lwittie/reu/perfly.html (1359 words)

	The Continuous World of Dungeon Siege
		The world frustum dimensions are set by default for the map but can also be adjusted on the fly as needed to meet performance demands for a particular area.
		The solution was to invent a “glomming” technology that lets frustums merge and separate, with a dominant frustum being the owner of the intersection of nodes among the glommed frustums.
		Each world frustum has an ID assigned from a bit field (so there may be up to 32 frustums total) and node and Go membership is the OR’d result of the ID’s of the frustums that it intersects.
	www.drizzle.com /~scottb/gdc/continuous-world.htm (9134 words)

	Frustum culling (Site not responding. Last check: 2007-10-13)
		In some packages this is calculated from the vertical aperture, some on the horizontal, whichever is chosen the other is fixed given the ratio of the window width and height.
		In order to determine whether part of a primitive is inside the frustum it is necessary to check that every vertex in the primitive is outside the volume.
		When the shape intersects the view frustum one can choose whether to further test the individual primitives or simple pass the whole shape to the rendering engine.
	astronomy.swin.edu.au /~pbourke/projection/frustum (344 words)

	markmorley.com \| frustum culling in opengl
		The view frustum is the volume of space that includes everything that is currently visible from a given viewpoint.
		A point can't be bigger than the frustum, and the sphere test works even when the sphere totally encloses the frustum, but a box is a bit more complicated.
		If it's totally inside the frustum then so are all of the things inside it, so you can jump straight to the objects and render them all without further testing.
	www.artlum.com /pub/frustumculling.html (2936 words)

	GameDev.net -- Super Frustums
		Adaptability to what we really need to be loaded (the view frustum): the better the loaded terrain zone adapts to the view frustum the less memory resources will be needed and the less data will have to be loaded from disk to memory.
		The limits of the matrix are determined by the points (xmin,ymin) and (xmax,ymax), which are calculated from the cells containing the projections of the frustum's 3 points (although it has 8 points, it can be approximated with 3).
		A Super Frustum can be 2D (defined by a triangle that contains the frustum's 2d projection) or 3D (defined by a pyramid similar to the frustum that contains the 8-point defined view frustum).
	www.gamedev.net /reference/programming/features/superfrustum (718 words)

	Chad's Homepage > Tutorials > Managed DirectX (Site not responding. Last check: 2007-10-13)
		To store the frustum information, we'll use 6 Plane structures, which will represent the left, right, top, bottom, near, and far planes of the view frustum.
		Each Plane structue represents the a, b, c, and d of the general plane equation: ax + by + cz + dw = 0, where a, b, and c form the normal of the plane and d is the distance from the origin.
		The SphereInFrustum method of the Camera class uses the camera's view frustum to determine whether the mesh's bounding sphere is inside the view frustum.
	www.c-unit.com /tutorials/mdirectx/?t=45 (730 words)

	Frustum Clipping for PovRay (Site not responding. Last check: 2007-10-13)
		In order to compute which polygons are outside the frustum one needs to be able to define the 4 planes making up the view frustum against which each vertex of the polygons will be tested.
		Where vp is the view position vector, vd is the unit view direction vector, vu is the unit up vector, and right is the unit vector to the right (the cross product between vd and vu).
		The 4 frustum planes are (vp,p0,p1), (vp,p1,p2), (vp,p2,p3), (vp,p3,p0) from which the normal of each plane can be computed.
	local.wasp.uwa.edu.au /~pbourke/rendering/clipping (450 words)

	Volume of a Frustum of a Cone (Site not responding. Last check: 2007-10-13)
		A frustum may be formed from a cone with a circular base by cutting off the tip of the cone with a cut perpendicular to the height, forming a lower base and an upper base that are circular and parallel.
		Let h be the height, R the radius of the lower base, and r the radius of the upper base.
		What is the volume of a frustum formed from square based pyramid of height h, lower base having a side length of S, and an upper base of side length s?
	jwilson.coe.uga.edu /emt725/Frustum/Frustum.cone.html (176 words)

	A9Frustum (AgentFX 2.4 API Specification)
		A view frustum is a set of planes defining the viewing volume.
		The view frustum can be created at any node level by passing in the absolute projection and transform matrix.
		The matrices can be retrived from the renderer passed in to the node in the render(A9Renderer r, Object o) render pass.
	www.agency9.se /developers/apispec/com/agency9/render/A9Frustum.html (1104 words)

	OGRE: Ogre::Frustum Class Reference - OGRE Documentation
		A frustum represents a pyramid, capped at the near and far end which is used to represent either a visible area or a projection area.
		Links the frustum to a custom near clip plane, which can be used to clip geometry in a custom manner without using user clip planes.
		This does change the shape of the frustum, leading to some depth buffer loss of precision, but for many of the uses of this technique that is not an issue.
	ogre.sourceforge.net /docs/api/html/classOgre_1_1Frustum.html (2473 words)

	UDN - Two - LevelOptimization
		The frustum is the volume of space that encompasses everything in the field of view of the player’s camera.
		The frustum extends from the player’s view to form a four-sided pyramid extended from the eye of the player outward.
		Other attributes of the frustum include the near and far clipping planes which determine how far away or how close an object must be located to be drawn.
	udn.epicgames.com /pub/Content/LevelOptimization (1448 words)

	OpenGL @ Lighthouse 3D - View Frustum Culling Tutorial
		The view frustum is the volume that contains everything that is potentially (there may be occlusions) visible on the screen.
		The apex of the pyramid is the camera position and the base of the pyramid is the far plane.
		The goal of view frustum culling is therefore to be able to identify what is inside the frustum (totally or partially), and cull everything that is not inside.
	www.lighthouse3d.com /opengl/viewfrustum (419 words)

	The SGADE Documentation
		Identifies the frustum to which you want to know the distance.
		If the vertex cannot be projected because it is outside of the frustum a negative value is loaded in the X component.
		This safeproject marks any vertex that couldn't be projected because it was outside of the frustum.
	www.suddenpresence.com /sgade/documentation/SoCamera_8c.html (1022 words)

	Culling your scene to the View Frustum.
		Everything that's completely inside the 'view frustum' needs to be drawn - everything that's completely outside can certainly be thrown away - anything that crosses the frustum is...erm...
		Well, think of the frustum as four intersecting infinite planes (actually, it's six because near and far are also clipping planes - if you are using the custom clip planes that OpenGL supports, you might want to toss those in too).
		If you have a relatively 'normal' symmetrical view frustum, there are some simplifications that save a lot of CPU time in calculating those six distances.
	www.sjbaker.org /steve/omniv/frustcull.html (964 words)

	Trouble with frustum culling - GameDev.Net Discussion Forums
		might the points of the bounding box miss the frustum if, for example, you are looking at a side of the box.
		All points are outside of the frustum, but the box is totally visible.
		The problem with the frustum seeming to be pushed to the left and towards the user, remains.
	www.gamedev.net /community/forums/viewreply.asp?ID=2063152 (1112 words)

	Hint: Volume of a Frustum (Site not responding. Last check: 2007-10-13)
		The cone formed by the "tip" cut off to make the frustum.
		The cone formed by the frustum AND the tip.
		The volume of the frustum could be derived by subtracting the volume of the first cone from the volume of the second.
	jwilson.coe.uga.edu /EMT725/Frustum/Hint.Frustum.html (43 words)

	Webpage of Computer Graphics Notes---Twenty Eight
		If we know the angle θ, the ratio of w/h, and the position of the small rectangle and the distance between the front and back rectangles, then the frustum is well and uniquely defined.
		It takes four parameters: the angle θ, the ratio w/h, the distance from the center of projection to the front rectangle and the stance from the center of projection to the back rectangle.
		When using orthographic view, the frustum is cuboid.
	asuweb.asurams.edu /whu/ComputerGraphics/cg-web28.html (146 words)

	Conical Frustum -- from Wolfram MathWorld (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-10-13)
		A conical frustum is a frustum created by slicing the top off a cone (with the cut made parallel to the base).
		The volume of the frustum is given by
		be the base areas of the top and bottom of the frustum.
	mathworld.wolfram.com.cob-web.org:8888 /ConicalFrustum.html (157 words)

	Faster 3D Game Graphics by Not Drawing What Is Not Seen
		This explains why we call this a conservative visibility algorithm: polygons that are sent to the graphics subsystem may still be invisible to the viewer since they could be behind other polygons (for example, another room or the rest of a building behind a wall).
		Nevertheless, this still does nothing for all of the polygons in the viewing frustum that we cannot see; these are sent to the graphics pipeline only to get covered up by those occluding polygons.
		All of the polygons making up the sphere are clearly in the viewing frustum so they would not be culled with the previous method alone; however, all of the polygons completely in the hemisphere facing away from the viewer are effectively invisible and can be culled.
	www.acm.org /crossroads/xrds3-4/faster3d.html (2431 words)

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