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.)
Computer graphics are pictures and films created using computers. Usually, the term refers to computer-generated image data created with the help of specialized graphical hardware and software. 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, though sometimes erroneously referred to as computer-generated imagery (CGI).
In computer graphics, environment mapping, or reflection mapping, is an efficient image-based lighting technique for approximating the appearance of a reflective surface by means of a precomputed texture image. The texture is used to store the image of the distant environment surrounding the rendered object.
Orthographic projection is a means of representing three-dimensional objects in two dimensions. It 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.
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
In the simplest case for generating texture coordinates, suppose:
The map has been created as above, looking at the sphere along the z-axis.
The texture coordinate of the center of the map is (0,0), and the sphere's image has radius 1.
We are rendering an image in the same exact situation as the sphere, but the sphere has been replaced with a reflective object.
The image being created is orthographic, or the viewer is infinitely far away, so that the view direction does not change as one moves across the image.
At texture coordinate , note that the depicted location on the sphere is (where z is ), and the normal at that location is also . However, we are given the reverse task (a normal for which we need to produce a texture map coordinate). So the texture coordinate corresponding to normal is .
HEALPix, mapping with little distortion, arbitrary precision, and equal-sized fragments
A skybox is a method of creating backgrounds to make a computer and video games level look bigger 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, 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.
HEALPix, an acronym for Hierarchical Equal Area isoLatitude Pixelisation of a 2-sphere, is an algorithm for pixelisation of the 2-sphere, and the associated class of map projections.
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In computer graphics, ray tracing is a rendering technique for generating an image by tracing the path of light as pixels in an image plane and simulating the effects of its encounters with virtual objects. The technique is capable of producing a very high degree of visual realism, usually higher than that of typical scanline rendering methods, but at a greater computational cost. This makes ray tracing best suited for applications where taking a relatively long time to render a frame can be tolerated, such as in still images and film and television visual effects, and more poorly suited for real-time applications such as video games where speed is critical. Ray tracing is capable of simulating a wide variety of optical effects, such as reflection and refraction, scattering, and dispersion phenomena.
A sphere is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball.
In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object. A frequent notation for the symmetry group of an object X is G = Sym(X).
Texture mapping is a method for defining high frequency detail, surface texture, or color information on a computer-generated graphic or 3D model. Its application to 3D graphics was pioneered by Edwin Catmull in 1974.
3D projection is any method of mapping three-dimensional points to a two-dimensional plane. As most current methods for displaying graphical data are based on planar two-dimensional media, the use of this type of projection is widespread, especially in computer graphics, engineering and drafting.
In 3D computer graphics, normal mapping, or Dot3 bump mapping, is a technique used for faking the lighting of bumps and dents – an implementation of bump mapping. It is used to add details without using more polygons. A common use of this technique is to greatly enhance the appearance and details of a low polygon model by generating a normal map from a high polygon model or height map.
In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface. It cannot be embedded in standard three-dimensional space without intersecting itself. It has basic applications to geometry, since the common construction of the real projective plane is as the space of lines in R3 passing through the origin.
Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Mirrors exhibit specular reflection.
In mathematics, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the line integral. Given a surface, one may integrate over its scalar fields, and vector fields.
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 render a 3D scene to a 2D screen. Once a 3D model has been created, for instance in a video game or any other 3D computer animation, the graphics pipeline is the process of turning that 3D model into what the computer displays.
Because the steps required for this operation depend on the software and hardware used and the desired display characteristics, there is no universal graphics pipeline suitable for all cases. However, graphics application programming interfaces (APIs) such as Direct3D and OpenGL were created to unify similar steps and to control the graphics pipeline of a given hardware accelerator. These APIs abstract the underlying hardware and keep the programmer away from writing code to manipulate the graphics hardware accelerators.
The equirectangular projection is a simple map projection attributed to Marinus of Tyre, who Ptolemy claims invented the projection about AD 100. The projection maps meridians to vertical straight lines of constant spacing, and circles of latitude to horizontal straight lines of constant spacing. The projection is neither equal area nor conformal. Because of the distortions introduced by this projection, it has little use in navigation or cadastral mapping and finds its main use in thematic mapping. In particular, the plate carrée has become a standard for global raster datasets, such as Celestia and NASA World Wind, because of the particularly simple relationship between the position of an image pixel on the map and its corresponding geographic location on Earth.
In computer graphics, cube mapping is a method of environment mapping that uses the six faces of a cube as the map shape. The environment is projected onto the sides of a cube and stored as six square textures, or unfolded into six regions of a single texture. The cube map is generated by first rendering the scene six times from a viewpoint, with the views defined by a 90 degree view frustum representing each cube face.
Three-dimensional space is a geometric setting in which three values are required to determine the position of an element. This is the informal meaning of the term dimension.
UV mapping is the 3D modelling process of projecting a 2D image to a 3D model's surface for texture mapping. The letters "U" and "V" denote the axes of the 2D texture because "X", "Y" and "Z" are already used to denote the axes of the 3D object in model space.
The Lambert azimuthal equal-area projection is a particular mapping from a sphere to a disk. It accurately represents area in all regions of the sphere, but it does not accurately represent angles. It is named for the Swiss mathematician Johann Heinrich Lambert, who announced it in 1772. "Zenithal" being synonymous with "azimuthal", the projection is also known as the Lambert zenithal equal-area projection.
In computer vision and computer graphics, 3D reconstruction is the process of capturing the shape and appearance of real objects.
This process can be accomplished either by active or passive methods. If the model is allowed to change its shape in time, this is referred to as non-rigid or spatio-temporal reconstruction.
Conformal geometric algebra (CGA) is the geometric algebra constructed over the resultant space of a map from points in an n-dimensional base space ℝp,q to null vectors in ℝp+1,q+1. This allows operations on the base space, including reflections, rotations and translations to be represented using versors of the geometric algebra; and it is found that points, lines, planes, circles and spheres gain particularly natural and computationally amenable representations.
Axonometry is a graphical procedure belonging to descriptive geometry that generates a planar image of a three-dimensional object. The term "axonometry" means "to measure along axes", and indicates that the dimensions and scaling of the coordinate axes play a crucial role. The result of an axonometric procedure is a uniformly-scaled parallel projection of the object. In general, the resulting parallel projection is oblique ; but in special cases the result is orthographic, which in this context is called an orthogonal axonometry.
