Search results
Results from the WOW.Com Content Network
Unit stride arrays are sometimes more efficient than non-unit stride arrays, but non-unit stride arrays can be more efficient for 2D or multi-dimensional arrays, depending on the effects of caching and the access patterns used. [citation needed] This can be attributed to the principle of locality, specifically spatial locality.
The Z-ordering can be used to efficiently build a quadtree (2D) or octree (3D) for a set of points. [4] [5] The basic idea is to sort the input set according to Z-order.Once sorted, the points can either be stored in a binary search tree and used directly, which is called a linear quadtree, [6] or they can be used to build a pointer based quadtree.
A vector space is finite-dimensional if its dimension is a natural number. Otherwise, it is infinite-dimensional, and its dimension is an infinite cardinal. Finite-dimensional vector spaces occur naturally in geometry and related areas. Infinite-dimensional vector spaces occur in many areas of mathematics.
GraphCalc is an open-source computer program that runs in Microsoft Windows and Linux that provides the functionality of a graphing calculator. GraphCalc includes many of the standard features of graphing calculators, but also includes some higher-end features: High resolution
Chan's algorithm is used for dimensions 2 and 3, and Quickhull is used for computation of the convex hull in higher dimensions. [9] For a finite set of points, the convex hull is a convex polyhedron in three dimensions, or in general a convex polytope for any number of dimensions, whose vertices are some of the points in the input set. Its ...
In a d-dimensional space, Hodge star takes a k-vector to a (d–k)-vector; thus only in d = 3 dimensions is the result an element of dimension one (3–2 = 1), i.e. a vector. For example, in d = 4 dimensions, the cross product of two vectors has dimension 4–2 = 2, giving a bivector. Thus, only in three dimensions does cross product define an ...
O'Rourke's approach uses a 3-dimensional rotating calipers technique, and is based on lemmas characterizing the minimum enclosing box: There must exist two neighbouring faces of the smallest-volume enclosing box which both contain an edge of the convex hull of the point set.
In numerical linear algebra, the Arnoldi iteration is an eigenvalue algorithm and an important example of an iterative method.Arnoldi finds an approximation to the eigenvalues and eigenvectors of general (possibly non-Hermitian) matrices by constructing an orthonormal basis of the Krylov subspace, which makes it particularly useful when dealing with large sparse matrices.