Search results
Results from the WOW.Com Content Network
The failure function for the string is computed as normal, but the string is rotated during the computation so some indices must be computed more than once as they wrap around. Once all indices of the failure function have been successfully computed without the string rotating again, the minimal lexicographical rotation is known to be found and ...
In the theory of three-dimensional rotation, Rodrigues' rotation formula, named after Olinde Rodrigues, is an efficient algorithm for rotating a vector in space, given an axis and angle of rotation. By extension, this can be used to transform all three basis vectors to compute a rotation matrix in SO(3) , the group of all rotation matrices ...
Most rotation matrices fit this description, and for them it can be shown that (Q − I)(Q + I) −1 is a skew-symmetric matrix, A. Thus A T = − A ; and since the diagonal is necessarily zero, and since the upper triangle determines the lower one, A contains 1 / 2 n ( n − 1) independent numbers.
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.
More formally, for any language L and string x over an alphabet Σ, the language edit distance d(L, x) is given by [14] (,) = (,), where (,) is the string edit distance. When the language L is context free , there is a cubic time dynamic programming algorithm proposed by Aho and Peterson in 1972 which computes the language edit distance. [ 15 ]
Curve fitting [1] [2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [3] possibly subject to constraints. [ 4 ] [ 5 ] Curve fitting can involve either interpolation , [ 6 ] [ 7 ] where an exact fit to the data is required, or smoothing , [ 8 ] [ 9 ] in which a "smooth ...
An equivalent version which shuffles the array in the opposite direction (from lowest index to highest) is: -- To shuffle an array a of n elements (indices 0..n-1): for i from 0 to n−2 do j ← random integer such that i ≤ j ≤ n-1 exchange a[i] and a[j]
The mathematical basis for Bézier curves—the Bernstein polynomials—was established in 1912, but the polynomials were not applied to graphics until some 50 years later when mathematician Paul de Casteljau in 1959 developed de Casteljau's algorithm, a numerically stable method for evaluating the curves, and became the first to apply them to computer-aided design at French automaker Citroën ...