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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 PDE surface ： ウィキペディア英語版 PDE surface PDE surfaces are used in geometric modelling and computer graphics for creating smooth surfaces conforming to a given boundary configuration. PDE surfaces utilise partial differential equations to generate a surface which usually satisfy a mathematical boundary value problem. PDE surfaces were first introduced into the area of geometric modelling and computer graphics by two British mathematicians, Malcolm Bloor and Michael Wilson. ==Technical details== The PDE method involves generating a surface for some boundary by means of solving an elliptic partial differential equation of the form :$$ \left( \frac} + a^\frac } \right)^ X(u,v) = 0. Here $X(u,v)$ is a function parameterised by the two parameters $u$ and $v$ such that $X(u,v)\; =\; (x(u,v),\; y(u,v),\; z(u,v))$ where $x$, $y$ and $z$ are the usual cartesian coordinate space. The boundary conditions on the function $X(u,v)$ and its normal derivatives $\backslash partial/\backslash partial$ are imposed at the edges of the surface patch. With the above formulation it is notable that the elliptic partial differential operator in the above PDE represents a smoothing process in which the value of the function at any point on the surface is, in some sense, a weighted average of the surrounding values. In this way a surface is obtained as a smooth transition between the chosen set of boundary conditions. The parameter $a$ is a special design parameter which controls the relative smoothing of the surface in the $u$ and $v$ directions. 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「PDE surface」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.