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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 polygonal, the side faces are trapezoidal. A right frustum is a right pyramid or a right cone truncated perpendicularly to its axis; otherwise it is an oblique frustum. If all its edges are forced to become of the same length, then a frustum becomes a prism (possibly oblique or/and with irregular bases). In computer graphics, the viewing frustum is the three-dimensional region which is visible on the screen. It is formed by a clipped pyramid; in particular, ''frustum culling'' is a method of hidden surface determination. In the aerospace industry, a frustum is 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 concepts A frustu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
En:frustum
In geometry, a frustum (from the Latin for 'morsel'; plural: ''frusta'' or ''frustums'') is the portion of a Polyhedron, solid (normally a Pyramid (geometry), pyramid or a Cone (geometry), cone) that lies between two parallel planes cutting this solid. In the case of a pyramid, the base faces are polygonal, the side faces are trapezoidal. A right frustum is a right pyramid or a right cone Truncation (geometry), truncated perpendicularly to its axis; otherwise it is an oblique frustum. If all its edges are forced to become of the same length, then a frustum becomes a Prism (geometry), prism (possibly oblique or/and with irregular bases). In computer graphics, the viewing frustum is the three-dimensional region which is visible on the screen. It is formed by a Clipping (computer graphics), clipped pyramid; in particular, ''frustum culling'' is a method of hidden surface determination. In the aerospace industry, a frustum is the Payload fairing, fairing between two stages of a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Viewing Frustum
In 3D computer graphics, the view frustum (also called viewing frustum) is the region of space in the modeled world that may appear on the screen; it is the field of view of a perspective virtual camera system. The view frustum is typically obtained by taking a 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 viewports 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 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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hidden Surface Determination
In 3D computer graphics, hidden-surface determination (also known as shown-surface determination, hidden-surface removal (HSR), occlusion culling (OC) or visible-surface determination (VSD)) is the process of identifying what surfaces and parts of surfaces can be seen from a particular viewing angle. A hidden-surface determination algorithm is a solution to the visibility problem, which was one of the first major problems in the field of 3D computer graphics . The process of hidden-surface determination is sometimes called hiding, and such an algorithm is sometimes called a hider. When referring to line rendering it is known as hidden-line removal. Hidden-surface determination is necessary to render a scene correctly, so that one may not view features hidden behind the model itself, allowing only the naturally viewable portion of the graphic to be visible. Background Hidden-surface determination is a process by which surfaces that should not be visible to the user (for example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clipping (computer Graphics)
Clipping, in the context of computer graphics, is a method to selectively enable or disable rendering operations within a defined region of interest. Mathematically, clipping can be described using the terminology of constructive geometry. A rendering algorithm only draws pixels in the intersection between the clip region and the scene model. Lines and surfaces outside the view volume (aka. frustum) are removed. Clip regions are commonly specified to improve render performance. A well-chosen clip allows the renderer to save time and energy by skipping calculations related to pixels that the user cannot see. Pixels that will be drawn are said to be within the clip region. Pixels that will not be drawn are outside the clip region. More informally, pixels that will not be drawn are said to be "clipped." Clipping in 2D graphics In two-dimensional graphics, a clip region may be defined so that pixels are only drawn within the boundaries of a window or frame. Clip regions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frustum Culling
In 3D computer graphics, hidden-surface determination (also known as shown-surface determination, hidden-surface removal (HSR), occlusion culling (OC) or visible-surface determination (VSD)) is the process of identifying what surfaces and parts of surfaces can be seen from a particular viewing angle. A hidden-surface determination algorithm is a solution to the visibility problem, which was one of the first major problems in the field of 3D computer graphics . The process of hidden-surface determination is sometimes called hiding, and such an algorithm is sometimes called a hider. When referring to line rendering it is known as hidden-line removal. Hidden-surface determination is necessary to render a scene correctly, so that one may not view features hidden behind the model itself, allowing only the naturally viewable portion of the graphic to be visible. Background Hidden-surface determination is a process by which surfaces that should not be visible to the user (for example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prism (geometry)
In geometry, a prism is a polyhedron comprising an polygon Base (geometry), base, a second base which is a Translation (geometry), translated copy (rigidly moved without rotation) of the first, and other Face (geometry), faces, necessarily all parallelograms, joining corresponding sides of the two bases. All Cross section (geometry), cross-sections parallel to the bases are translations of the bases. Prisms are named after their bases, e.g. a prism with a pentagonal base is called a pentagonal prism. Prisms are a subclass of prismatoids. Like many basic geometric terms, the word ''prism'' () was first used in Euclid's Elements. Euclid defined the term in Book XI as “a solid figure contained by two opposite, equal and parallel planes, while the rest are parallelograms”. However, this definition has been criticized for not being specific enough in relation to the nature of the bases, which caused confusion among later geometry writers. Oblique prism An oblique prism is a pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cone (geometry)
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex. Depending on the author, the base may be restricted to be a circle, any one-dimensional quadratic form in the plane, any closed one-dimensional figure, or any of the above plus all the enclosed points. If the enclosed points are included in the base, the cone is a solid object; otherwise it is a two-dimensional object in three-dimensional space. In the case of a solid object, the boundary formed by these lines or partial lines is called the ''lateral surface''; if the lateral surface is unbounded, it is a conical surface. In the case of line segments, the cone does not extend beyond the base, while in the case of half-lin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bipyramid
A (symmetric) -gonal bipyramid or dipyramid is a polyhedron formed by joining an -gonal pyramid and its mirror image base-to-base. An -gonal bipyramid has triangle faces, edges, and vertices. The "-gonal" in the name of a bipyramid does not refer to a face but to the internal polygon base, lying in the mirror plane that connects the two pyramid halves. (If it were a face, then each of its edges would connect three faces instead of two.) "Regular", right bipyramids A ''"regular"'' bipyramid has a ''regular'' polygon base. It is usually implied to be also a ''right'' bipyramid. A ''right'' bipyramid has its two apices ''right'' above and ''right'' below the center or the ''centroid'' of its polygon base. A "regular" right (symmetric) -gonal bipyramid has Schläfli symbol . A right (symmetric) bipyramid has Schläfli symbol , for polygon base . The "regular" right (thus face-transitive) -gonal bipyramid with regular vertices is the dual of the -gonal uniform (thus right) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pentagonal Frustum
In geometry, a pentagon (from the Greek πέντε ''pente'' meaning ''five'' and γωνία ''gonia'' meaning ''angle'') is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°. A pentagon may be simple or self-intersecting. A self-intersecting ''regular pentagon'' (or ''star pentagon'') is called a pentagram. Regular pentagons A '' regular pentagon'' has Schläfli symbol and interior angles of 108°. A '' regular pentagon'' has five lines of reflectional symmetry, and rotational symmetry of order 5 (through 72°, 144°, 216° and 288°). The diagonals of a convex regular pentagon are in the golden ratio to its sides. Given its side length t, its height H (distance from one side to the opposite vertex), width W (distance between two farthest separated points, which equals the diagonal length D) and circumradius R are given by: :\begin H &= \frac~t \approx 1.539~t, \\ W= D &= \frac~t\approx 1.618~t, \\ W &= \sqrt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aerospace Industry
Aerospace is a term used to collectively refer to the atmosphere and outer space. Aerospace activity is very diverse, with a multitude of commercial, industrial and military applications. Aerospace engineering consists of aeronautics and astronautics. Aerospace organizations research, design, manufacture, operate, or maintain both aircraft and spacecraft. The beginning of space and the ending of the air is considered as 100 km (62 mi) above the ground according to the physical explanation that the air pressure is too low for a lifting body to generate meaningful lift force without exceeding orbital velocity. Overview In most industrial countries, the aerospace industry is a cooperation of the public and private sectors. For example, several states have a civilian space program funded by the government, such as National Aeronautics and Space Administration in the United States, European Space Agency in Europe, the Canadian Space Agency in Canada, Indian Space R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Payload Fairing
A payload fairing is a nose cone used to protect a spacecraft payload against the impact of dynamic pressure and aerodynamic heating during launch through an atmosphere. An additional function on some flights is to maintain the cleanroom environment for precision instruments. Once outside the atmosphere the fairing is jettisoned, exposing the payload to outer space. The standard payload fairing is typically a cone-cylinder combination, due to aerodynamic considerations, although other specialized fairings are in use. The type of fairing which separates into two halves upon jettisoning is called a clamshell fairing by way of analogy to the bifurcating shell of a clam. In some cases the fairing may enclose both the payload and the upper stage of the rocket, such as on Atlas V and Proton M. If the payload is attached both to the booster's core structures and to the fairing, the payload may still be affected by the fairing's bending loads, as well as inertia loads due to vibrations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
