翻訳と辞書 Words near each other ・ Distance and Clime ・ Distance and Time ・ Distance between two straight lines ・ Distance classroom ・ Distance correlation ・ Distance decay ・ Distance Diagnostics Through Digital Imaging ・ Distance education ・ Distance Education Accrediting Commission ・ Distance Education Centre, Victoria ・ Distance Education Council ・ Distance Education Learning Environments Survey ・ Distance education librarian ・ Distance fog ・ Distance from a point to a line ・ Distance from a point to a plane ・ Distance geometry problem ・ Distance Learning and Telemedicine Grant and Loan Program ・ Distance line ・ Distance matrices in phylogeny ・ Distance matrix ・ Distance measures (cosmology) ・ Distance measuring equipment ・ Distance medley relay ・ Distance model ・ Distance modulus ・ Distance of closest approach of ellipses and ellipsoids ・ Distance Only Makes the Heart Grow Fonder ・ Distance oracle ・ Distance sampling 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 Distance from a point to a plane ： ウィキペディア英語版 Distance from a point to a plane In Euclidean space, the point on a plane $ax\; +\; by\; +\; cz\; =\; d$ that is closest to the origin has the Cartesian coordinates $(x,y,z)$, where :$\backslash displaystyle\; x\; =\; \backslash frac\; ,\; \backslash quad\; \backslash quad\; \backslash displaystyle\; y\; =\; \backslash frac\; ,\; \backslash quad\; \backslash quad\; \backslash displaystyle\; z\; =\; \backslash frac\; .$ From this the distance from the origin to the plane can be found. If what is desired is the distance from a point not at the origin to the nearest point on a plane, this can be found by a change of variables that moves the origin to coincide with the given point. ==Converting general problem to distance-from-origin problem== Suppose we wish to find the nearest point on a plane to the point (''X''0, ''Y''0, ''Z''0), where the plane is given by ''aX + bY + cZ = D''. We define ''x = X - X''0, ''y = Y - Y''0, ''z = Z - Z''0, and ''d = D - aX''0 - ''bY''0 - ''cZ''0, to obtain ''ax + by + cz = d'' as the plane expressed in terms of the transformed variables. Now the problem has become one of finding the nearest point on this plane to the origin, and its distance from the origin. The point on the plane in terms of the original coordinates can be found from this point using the above relationships between ''x'' and ''X'', between ''y'' and ''Y'', and between ''z'' and ''Z''; the distance in terms of the original coordinates is the same as the distance in terms of the revised coordinates. 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「Distance from a point to a plane」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.