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Sphere Mapping
In computer graphics, sphere mapping (or spherical environment mapping) is a type of reflection mapping that approximates reflective surfaces by considering the environment to be an infinitely far-away spherical wall. This environment is stored as a texture depicting what a mirrored sphere would look like if it were placed into the environment, using an orthographic projection (as opposed to one with perspective). This texture contains reflective data for the entire environment, except for the spot directly behind the sphere. (For one example of such an object, see Escher's drawing Hand with Reflecting Sphere.) To use this data, the surface normal of the object, view direction from the object to the camera, and/or reflected direction from the object to the environment is used to calculate a texture coordinate to look up in the aforementioned texture map. The result appears like the environment is reflected in the surface of the object that is being rendered. Usage example I ...
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Computer Graphics
Computer graphics deals with generating images and art with the aid of computers. Computer graphics is a core technology in digital photography, film, video games, digital art, cell phone and computer displays, and many specialized applications. A great deal of specialized hardware and software has been developed, with the displays of most devices being driven by graphics hardware, computer graphics hardware. It is a vast and recently developed area of computer science. The phrase was coined in 1960 by computer graphics researchers Verne Hudson and William Fetter of Boeing. It is often abbreviated as CG, or typically in the context of film as Computer-generated imagery, computer generated imagery (CGI). The non-artistic aspects of computer graphics are the subject of Computer graphics (computer science), computer science research. Some topics in computer graphics include user interface design, Sprite (computer graphics), sprite graphics, raster graphics, Rendering (computer graph ...
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Reflection Mapping
In computer graphics, reflection mapping or environment mapping is an efficient image-based lighting technique for approximating the appearance of a reflective surface by means of a precomputed texture. The texture is used to store the image of the distant environment surrounding the rendered object. Several ways of storing the surrounding environment have been employed. The first technique was sphere mapping, in which a single texture contains the image of the surroundings as reflected on a spherical mirror. It has been almost entirely surpassed by cube mapping, in which the environment is projected onto the six faces of a cube and stored as six square textures or unfolded into six square regions of a single texture. Other projections that have some superior mathematical or computational properties include the paraboloid mapping, the pyramid mapping, the octahedron mapping, and the HEALPix mapping. Reflection mapping is one of several approaches to reflection rendering, ...
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Orthographic Projection
Orthographic projection (also orthogonal projection and analemma) is a means of representing Three-dimensional space, three-dimensional objects in Plane (mathematics), two dimensions. Orthographic projection is a form of parallel projection in which all the projection lines are orthogonal to the projection plane, resulting in every plane of the scene appearing in affine transformation on the viewing surface. The obverse of an orthographic projection is an oblique projection, which is a parallel projection in which the projection lines are ''not'' orthogonal to the projection plane. The term ''orthographic'' sometimes means a technique in multiview projection in which principal axes or the planes of the subject are also parallel with the projection plane to create the ''primary views''. If the principal planes or axes of an object in an orthographic projection are ''not'' parallel with the projection plane, the depiction is called ''axonometric'' or an ''auxiliary views''. (''Ax ...
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Perspective (graphical)
Linear or point-projection perspective () is one of two types of graphical projection perspective in the graphic arts; the other is parallel projection. Linear perspective is an approximate representation, generally on a flat surface, of an image as it is seen by the eye. Perspective drawing is useful for representing a three-dimensional scene in a two-dimensional medium, like paper. It is based on the optical fact that for a person an object looks N times (linearly) smaller if it has been moved N times further from the eye than the original distance was. The most characteristic features of linear perspective are that objects appear smaller as their distance from the observer increases, and that they are subject to , meaning that an object's dimensions parallel to the line of sight appear shorter than its dimensions perpendicular to the line of sight. All objects will recede to points in the distance, usually along the horizon line, but also above and below the horiz ...
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Hand With Reflecting Sphere
''Hand with Reflecting Sphere'', also known as ''Self-Portrait in Spherical Mirror'', is a lithograph by Dutch artist M. C. Escher, first printed in January 1935. The piece depicts a hand holding a reflective sphere. In the reflection, most of the room around Escher can be seen, and the hand holding the sphere is revealed to be Escher's. Self-portraits in reflective, spherical surfaces are common in Escher's work. In much of his self-portraiture of this type, Escher is in the act of drawing the sphere, whereas in this image he is seated and gazing into it. On the walls there are several framed pictures, one of which appears to be of an Indonesian shadow puppet. See also * Alhazen's problem * '' Still Life with Spherical Mirror'' * '' Three Spheres II'' * Lithography Lithography () is a planographic method of printing originally based on the miscibility, immiscibility of oil ...
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Surface Normal
In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the infinite straight line perpendicular to the tangent line to the curve at the point. A normal vector is a vector perpendicular to a given object at a particular point. A normal vector of length one is called a unit normal vector or normal direction. A curvature vector is a normal vector whose length is the curvature of the object. Multiplying a normal vector by results in the opposite vector, which may be used for indicating sides (e.g., interior or exterior). In three-dimensional space, a surface normal, or simply normal, to a surface at point is a vector perpendicular to the tangent plane of the surface at . The vector field of normal directions to a surface is known as '' Gauss map''. The word "normal" is also used as an adjective: a line ''normal'' to a plane, the ''normal'' component of ...
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Skybox (video Games)
A skybox is a method of creating backgrounds to make a video game level appear larger than it really is. When a skybox is used, the level is enclosed in a cuboid. The sky, distant mountains, distant buildings, and other unreachable objects are projected onto the cube's faces (using a technique called cube mapping), thus creating the illusion of distant three-dimensional surroundings. A skydome employs the same concept but uses either a sphere or a hemisphere instead of a cube. Processing of 3D graphics is computationally expensive, especially in real-time games, and poses multiple limits. Levels have to be processed at tremendous speeds, making it difficult to render vast skyscapes in real-time. Additionally, real-time graphics generally have depth buffers with limited bit-depth, which puts a limit on the amount of details that can be rendered at a distance. To avoid these problems, games often employ skyboxes. Traditionally, these are simple cubes with up to six different ...
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HEALPix
HEALPix (sometimes written as Healpix), an acronym for Hierarchical Equal Area isoLatitude Pixelisation of a 2-sphere, is an algorithm for pixelisation of the 2-sphere based on subdivision of a distorted rhombic dodecahedron, and the associated class of map projections. The pixelisation algorithm was devised in 1997 by Krzysztof M. Górski at the Theoretical Astrophysics Center in Copenhagen, Denmark, and first published as a preprint in 1998. Projection and pixelisation The HEALPix projection is a general class of spherical projections, sharing several key properties, which map the 2-sphere to the Euclidean plane. Any of these can be followed by partitioning (pixelising) the resulting region of the 2-plane. In particular, when one of these projections (the H=4, K=3 HEALPix projection) is followed by a pixelisation of the 2-plane, the result is generally known as the HEALPix pixelisation, which is widely used in physical cosmology for maps of the cosmic microwave background. T ...
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