Linear algebra is the branch of mathematics concerning linear equations such as:
In Euclidean geometry, an affine transformation, or an affinity, is a geometric transformation that preserves lines and parallelism.
In linear algebra, the trace of a square matrix A, denoted tr(A), is defined to be the sum of elements on the main diagonal of A. The trace is only defined for a square matrix.
Texture mapping is a method for mapping a texture on a computer-generated graphic. Texture here can be high frequency detail, surface texture, or color.
A 3D projection is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to project a complex object for viewing capability on a simpler plane.
In mathematics, the modular group is the projective special linear group PSL(2, Z) of 2 × 2 matrices with integer coefficients and determinant 1. The matrices A and −A are identified. The modular group acts on the upper-half of the complex plane by fractional linear transformations, and the name "modular group" comes from the relation to moduli spaces and not from modular arithmetic.
This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector spaces and through matrices.
In 3D computer graphics, normal mapping, or Dot3 bump mapping, is a texture mapping 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.
Ray casting is the methodological basis for 3D CAD/CAM solid modeling and image rendering. It is essentially the same as ray tracing for computer graphics where virtual light rays are "cast" or "traced" on their path from the focal point of a camera through each pixel in the camera sensor to determine what is visible along the ray in the 3D scene. The term "Ray Casting" was introduced by Scott Roth while at the General Motors Research Labs from 1978–1980. His paper, "Ray Casting for Modeling Solids", describes modeled solid objects by combining primitive solids, such as blocks and cylinders, using the set operators union (+), intersection (&), and difference (-). The general idea of using these binary operators for solid modeling is largely due to Voelcker and Requicha's geometric modelling group at the University of Rochester. See Solid modeling for a broad overview of solid modeling methods. This figure on the right shows a U-Joint modeled from cylinders and blocks in a binary tree using Roth's ray casting system, circa 1979.
In linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then
In computing, D3DX is a high level API library which is written to supplement Microsoft's Direct3D graphics API. The D3DX library was introduced in Direct3D 7, and subsequently was improved in Direct3D 9. It provides classes for common calculations on vectors, matrices and colors, calculating look-at and projection matrices, spline interpolations, and several more complicated tasks, such as compiling or assembling shaders used for 3D graphic programming, compressed skeletal animation storage and matrix stacks. There are several functions that provide complex operations over 3D meshes like tangent-space computation, mesh simplification, precomputed radiance transfer, optimizing for vertex cache friendliness and strip reordering, and generators for 3D text meshes. 2D features include classes for drawing screen-space lines, text and sprite based particle systems. Spatial functions include various intersection routines, conversion from/to barycentric coordinates and bounding box and sphere generators.
In computer graphics, a shader is a computer program that calculates the appropriate levels of light, darkness, and color during the rendering of a 3D scene - a process known as shading. Shaders have evolved to perform a variety of specialized functions in computer graphics special effects and video post-processing, as well as general-purpose computing on graphics processing units.
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.
Subsurface scattering (SSS), also known as subsurface light transport (SSLT), is a mechanism of light transport in which light that penetrates the surface of a translucent object is scattered by interacting with the material and exits the surface at a different point. The light will generally penetrate the surface and be reflected a number of times at irregular angles inside the material before passing back out of the material at a different angle than it would have had if it had been reflected directly off the surface. Subsurface scattering is important for realistic 3D computer graphics, being necessary for the rendering of materials such as marble, skin, leaves, wax and milk. If subsurface scattering is not implemented, the material may look unnatural, like plastic or metal.
Shadow mapping or shadowing projection is a process by which shadows are added to 3D computer graphics. This concept was introduced by Lance Williams in 1978, in a paper entitled "Casting curved shadows on curved surfaces." Since then, it has been used both in pre-rendered and realtime scenes in many console and PC games.
UV mapping is the 3D modeling 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, while "W" is used in calculating quaternion rotations, a common operation in computer graphics.
Multilinear subspace learning is an approach to dimensionality reduction. Dimensionality reduction can be performed on a data tensor whose observations have been vectorized and organized into a data tensor, or whose observations are matrices that are concatenated into a data tensor. Here are some examples of data tensors whose observations are vectorized or whose observations are matrices concatenated into data tensor images (2D/3D), video sequences (3D/4D), and hyperspectral cubes (3D/4D).
Additive manufacturing file format (AMF) is an open standard for describing objects for additive manufacturing processes such as 3D printing. The official ISO/ASTM 52915:2016 standard is an XML-based format designed to allow any computer-aided design software to describe the shape and composition of any 3D object to be fabricated on any 3D printer via a computer-aided manufacturing software. Unlike its predecessor STL format, AMF has native support for color, materials, lattices, and constellations.
3D reconstruction from multiple images is the creation of three-dimensional models from a set of images. It is the reverse process of obtaining 2D images from 3D scenes.
This is a glossary of terms relating to computer graphics.
