Concepts inA fast multigrid algorithm for mesh deformation
Multigrid method
Multigrid (MG) methods in numerical analysis are a group of algorithms for solving differential equations using a hierarchy of discretizations. They are an example of a class of techniques called multiresolution methods, very useful in (but not limited to) problems exhibiting multiple scales of behavior.
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Polygon mesh
A polygon mesh or unstructured grid is a collection of vertices, edges and faces that defines the shape of a polyhedral object in 3D computer graphics and solid modeling. The faces usually consist of triangles, quadrilaterals or other simple convex polygons, since this simplifies rendering, but may also be composed of more general concave polygons, or polygons with holes. The study of polygon meshes is a large sub-field of computer graphics and geometric modeling.
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Precomputation
In algorithms, precomputation is the act of performing an initial computation before run time to generate a lookup table that can be used by an algorithm to avoid repeated computation each time it is executed. Precomputation is often used in algorithms that depend on the results of expensive computations that don't depend on the input of the algorithm.
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Laplace operator
In mathematics the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space. It is usually denoted by the symbols ¿·¿, ¿ or ¿. The Laplacian ¿¿(p) of a function ¿ at a point p, up to a constant depending on the dimension, is the rate at which the average value of ¿ over spheres centered at p, deviates from ¿(p) as the radius of the sphere grows.
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Least squares
The method of least squares is a standard approach to the approximate solution of overdetermined systems, i.e. , sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in the results of every single equation. The most important application is in data fitting.
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Motion capture
Motion capture, motion tracking, or mocap are terms used to describe the process of recording movement of one or more objects or persons. It is used in military, entertainment, sports, and medical applications, and for validation of computer vision and robotics. In filmmaking, and games, it refers to recording actions of human actors, and using that information to animate digital character models in 2D or 3D computer animation.
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Graph (mathematics)
In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges. Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics.
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