翻訳と辞書 Words near each other ・ Sierosławice, Opole Voivodeship ・ Sierosławice, Świętokrzyskie Voivodeship ・ Sierosławiec ・ Sieroty ・ Sierowo ・ Sierpc ・ Sierpc County ・ Sierpe River ・ Sierpienica ・ Sierpin ・ Sierpinski (crater) ・ Sierpinski carpet ・ Sierpinski number ・ Sierpinski triangle ・ Sierpiński arrowhead curve ・ Sierpiński curve ・ Sierpiński set ・ Sierpiński space ・ Sierpiński's constant ・ Sierpnica ・ Sierpowo, Greater Poland Voivodeship ・ Sierpowo, Pomeranian Voivodeship ・ Sierpów ・ Sierpówko ・ Sierra ・ Sierra (Dollhouse) ・ Sierra (film) ・ Sierra (group) ・ Sierra (name) ・ Sierra (TV series) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Sierpiński curve ： ウィキペディア英語版 Sierpiński curve Sierpiński curves are a recursively defined sequence of continuous closed plane fractal curves discovered by Wacław Sierpiński, which in the limit $n\; \backslash rightarrow\; \backslash infty$ completely fill the unit square: thus their limit curve, also called the Sierpiński curve, is an example of a space-filling curve. Because the Sierpiński curve is space-filling, its Hausdorff dimension (in the limit $n\; \backslash rightarrow\; \backslash infty$) is $2$. The Euclidean length of :$S\_n$ is $l\_n\; =\; (1+\backslash sqrt\; 2)\; 2^n\; -\; (2-\backslash sqrt\; 2)$, i.e., it grows ''exponentially'' with $n$ beyond any limit, whereas the limit for $n\; \backslash rightarrow\; \backslash infty$ of the area enclosed by $S\_n$ is $5/12\; \backslash ,$ that of the square (in Euclidean metric). ==Uses of the curve== The Sierpiński curve is useful in several practical applications because it is more symmetrical than other commonly studied space-filling curves. For example, it has been used as a basis for the rapid construction of an approximate solution to the Travelling Salesman Problem (which asks for the shortest sequence of a given set of points): The heuristic is simply to visit the points in the same sequence as they appear on the Sierpiński curve. To do this requires two steps: First compute an inverse image of each point to be visited; then sort the values. This idea has been used to build routing systems for commercial vehicles based only on Rolodex card files. A space-filling curve is a continuous map of the unit interval onto a unit square and so a (pseudo) inverse maps the unit square to the unit interval. One way of constructing a pseudo-inverse is as follows. Let the lower-left corner (0, 0) of the unit square correspond to 0.0 (and 1.0). Then the upper-left corner (0, 1) must correspond to 0.25, the upper-right corner (1, 1) to 0.50, and the lower-right corner (1, 0) to 0.75. The inverse map of interior points are computed by taking advantage of the recursive structure of the curve. Here is a function coded in Java that will compute the relative position of any point on the Sierpiński curve (that is, a pseudo-inverse value). It takes as input the coordinates of the point (x,y) to be inverted, and the corners of an enclosing right isosceles triangle (ax, ay), (bx, by), and (cx, cy). (Note that the unit square is the union of two such triangles.) The remaining parameters specify the level of accuracy to which the inverse should be computed. static long sierp_pt2code( double ax, double ay, double bx, double by, double cx, double cy, int currentLevel, int maxLevel, long code, double x, double y ) } return code; } 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Sierpiński curve」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.