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In geometry, a frustum (plural: frusta or frustums) is the portion of a solid (normally a cone or pyramid) which lies between two parallel planes cutting it. The term is commonly used in computer graphics to describe the three-dimensional region which is visible on the screen (which is formed by a clipped pyramid); in particular, frustum culling is a method of hidden surface determination. In the aerospace industry, frustum is the common term for the fairing between two stages of a multistage rocket (such as the Saturn V), which is shaped like a truncated cone. Elements, special cases, and related conceptsEach plane section is a floor or base of the frustum. Its axis if any, is that of the original cone or pyramid. A frustum is circular if it has circular bases; it is right if the axis is perpendicular to both bases, and oblique otherwise. The height of a frustum is the perpendicular distance between the planes of the two bases. Cones and pyramids can be viewed as degenerate cases of frusta, where one of the cutting planes passes through the apex (so that the corresponding base reduces to a point). The pyramidal frusta are a subclass of the prismatoids. Two frusta joined at their bases make a bifrustum. FormulaeFrom Wikipedia under the
GNU Free Documentation License Help with calculus problem. Find the volume of a frustum of a cone of height H and radii of base r1 and r2? Q. I initially tried using the disk method and this problem got very messy. I still think the disk method might be the way to go on this, though I could be wrong. Please help. Asked by Wonder - Mon Oct 20 10:29:58 2008 - - 1 Answers - 0 Comments Prove that volume of frustum cone is equal to V=1/3 h(R2+r2+Rr) where h is a height of the frustum cone, .....? Q. Prove that volume of frustum cone is equal to V=1/3 h(R2+r2+Rr) where h is a height of the frustum cone, R and r is the radii of the frustum bases. Asked by MIchael - Sun Jun 7 10:54:25 2009 - - 1 Answers - 0 Comments A. Consider the difference of the two cones: If h is the height of the frustum, then by similar triangles the height of the clipped section is rh/(R-r). V = 1/3 R h (1 + r/(R-r)) - 1/3 r rh/(R-r) = 1/3 h [ R (1 + r/(R-r)) - r /(R-r) ] = 1/3 h [ (R - r ) / (R - r) ] = 1/3 h [ (R - r) (R + Rr + r ) / (R - r) ] = 1/3 h (R + Rr + r ) Answer: see above Answered by intc_escapee - Thu Jun 11 04:01:33 2009 Derive a formula for the surface area of a conical frustum?
Q. I want to derive the formula for the surface area of a frustum with slant height h, and radii r and R (r being the smaller radius and R the bigger), which is A = pi(R+r)h. If I unfold the surface such that I get a remainder of a sector with radius H (H being the slant height of a cone, extended from the frustum), with a smaller sector removed, which has radius H-h. I want to find the area this remaing part; that is, find the area of the sector with radius H and substract the area of the sector with radius H-h. Let t be the central angle in radians. I get t*H = 2piR and t*(H-h) = 2pi r. So the area of the sector with radius H is piH^2 *(t/2pi), and t = 2piR/H, so the area of sector with radius H is R/H * piH^2 = piRH; the… [cont.] Asked by never mind - Sun Jan 13 21:18:23 2008 - - 1 Answers - 0 Comments A. thus A=(t*H)*H/2 -(t*(H-h))*(H-h)/2; 2A=t*(H^2 (H-h)^2) = t*(2H-h)*h; meanwhile t*H=2pi*R, t*(H-h)=2pi*r; or subtracting we get -t*h =2pi*r 2pi*R, hence t=2pi(R-r)/h; t*H=2pi*R, hence t=2pi*R/H; t=t; thus 2pi(R-r)/h =2pi*R/H, hence H=h(R/(R-r)); 2A= t*(2H-h)*h =2pi*R/H *(2H-h)*h = = 2pi*R*(2-h/H)*h = 2pi*R*(2-h/[h(R/(R-r))])* h = = 2pi*R*(2 - (R-r)/R)*h =2pi*(R+r)*h; A= pi*(R+r)*h; QED; Answered by ( )kaksi_guy - Sun Jan 13 23:15:03 2008 From Yahoo Answer Search: "Frustum"  news.google.com Java World For example, if not touched earlier by any user defined event handler, then when the render pass occurs and view frustum culling is performed, ... news.google.com TMC Net Stack one is made up of eight individual pieces: interstages 1 and 2, the frustum , the forward skirt extension, the forward skirt and the aft, ... and more » From Google News Search: "Frustum"  programovanie.host.sk 310px x 400px | 39.40kB [source page] je frustum culling efektivny urobime si jednoduchy program Budeme vykreslova 2000 gu po et pod a rychlosti po ita a mo eme zmeni s frustum cullingom a bez neho Pri zapnutom frustum cullingu je na za iatku ke je vidie v etky gule FPS asi 20 av ak ako gule miznu z monitora FPS plynule stupa a k hodnote akoby sme iadne gule  flashsandy.org 250px x 450px | 16.20kB [source page] to the viewing direction This defines a cut pyramid or frustum called the view frustum To save computational power objects outside this volume are not computed or rendered When we create the Sandy camera the frustum planes are calculated from the default view angle of 45 degrees the aspect ratio and the position of the near and far planes The aspect From Yahoo Image Search: "Frustum"  floridatoday.com Todd Halvorson 2009-01-30 15:44:00 The test Thursday demonstrated the ignition of the linear-shaped charge, which cleanly severed an Ares 1X . frustum. from its forward skirt extension. Sensors on the test article measured the shock created by the ignition. . ...  playtechs.blogspot.com James McNeill 2007-03-12 15:00:00 The algorithm clips the left edge of the . frustum. by taking the rightmost of (1, 1) and (-1, -1). But these lie on a parallel line, so neither is rightmost. The same is true for the right edges of the . frustum. and portal. . ...  forums.xna.com Byron Nelson 2009-04-21 16:23:27 a direction from the light to the geometry along the plane that is most nearly parallel to the camera near . frustum. . It uses that direction as a texture coordinate in a noise volume (plus some variation over time). . ... From Google Blog Search: "Frustum" |
