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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Moving least squares ： ウィキペディア英語版 Moving least squares Moving least squares is a method of reconstructing continuous functions from a set of unorganized point samples via the calculation of a weighted least squares measure biased towards the region around the point at which the reconstructed value is requested. In computer graphics, the moving least squares method is useful for reconstructing a surface from a set of points. Often it is used to create a 3D surface from a point cloud through either downsampling or upsampling. ==Definition== Consider a function $f:\; \backslash mathbb^n\; \backslash to\; \backslash mathbb$ and a set of sample points $S\; =\; \backslash$ where $x\_i\; \backslash in\; \backslash mathbb^n$ and the $f\_i$'s are real numbers. Then, the moving least square approximation of degree $m$ at the point $x$ is $\backslash tilde(x)$ where $\backslash tilde$ minimizes the weighted least-square error :$\backslash sum\_\; (p(x\_i)-f\_i)^2\backslash theta(\backslash |x-x\_i\backslash |)$ over all polynomials $p$ of degree $m$ in $\backslash mathbb^n$. $\backslash theta(s)$ is the weight and it tends to zero as $s\backslash to\; \backslash infty$. In the example $\backslash theta(s)\; =\; e^$. The smooth interpolator of "order 3" is a quadratic interpolator. 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「Moving least squares」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.