翻訳と辞書 Words near each other ・ Intersect ENT ・ Intersecting Storage Rings ・ Intersection ・ Intersection (1994 film) ・ Intersection (aeronautics) ・ Intersection (album) ・ Intersection (disambiguation) ・ Intersection (Euclidean geometry) ・ Intersection (novel) ・ Intersection (road) ・ Intersection (sculpture) ・ Intersection (set theory) ・ Intersection algorithm ・ Intersection assistant ・ Intersection capacity utilization ・ Intersection curve ・ Intersection for the Arts ・ Intersection for the Arts Literary Series ・ Intersection form ・ Intersection form (4-manifold) ・ Intersection graph ・ Intersection homology ・ Intersection Mountain ・ Intersection number ・ Intersection number (graph theory) ・ Intersection of a polyhedron with a line ・ Intersection syndrome ・ Intersection theorem ・ Intersection theory ・ Intersection theory (disambiguation) 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 Intersection curve ： ウィキペディア英語版 Intersection curve In geometry, an intersection curve is, in the most simple case, the intersection line of two non-parallel planes in Euclidean 3-space. In general, an intersection curve consists of the common points of two ''transversally'' intersecting surfaces, meaning that at any common point the surface normals are not parallel. This restriction excludes cases where the surfaces are touching or have surface parts in common. The analytic determination of the intersection curve of two surfaces is easy only in simple cases; for example: a) the intersection of two planes, b) plane section of a quadric (sphere, cylinder, cone, etc.), c) intersection of two quadrics in special cases. For the general case, literature provides algorithms, in order to calculate points of the intersection curve of two surfaces.〔(''Geometry and Algorithms for COMPUTER AIDED DESIGN'' ), p. 94〕 == Intersection line of two planes == Given: two planes $\backslash varepsilon\_i:\; \backslash quad\; \backslash vec\; n\_i\backslash cdot\backslash vec\; x=d\_i,\; \backslash quad\; i=1,2,\; \backslash quad$ \vec n_1,\vec n_2 linearly independent, i.e. the planes are not parallel. Wanted: A parametric representation $\backslash vec\; x=\; \backslash vec\; p\; +\; t\backslash vec\; r$ of the intersection line. The direction of the line one gets from the crossproduct of the normal vectors: $\backslash vec\; r=\backslash vec\; n\_1\backslash times\backslash vec\; n\_2$. A point $P:\backslash vec\; p$ of the intersection line can be determined by intersecting the given planes $\backslash varepsilon\_1,\; \backslash varepsilon\_2$ with the plane $\backslash varepsilon\_3:\; \backslash vec\; x\; =\; s\_1\backslash vec\; n\_1\; +\; s\_2\backslash vec\; n\_2$, which is perpendicular to $\backslash varepsilon\_1$ and $\backslash varepsilon\_2$. Inserting the parametric representation of $\backslash varepsilon\_3$ into the equations of $\backslash varepsilon\_1$ und $\backslash varepsilon\_2$ yields the parameters $s\_1$ und $s\_2$. $P:\; \backslash vec\; p=\; \backslash frac$ \vec n_1 + \frac \vec n_2\ . ''Example:'' $\backslash varepsilon\_1:\backslash \; x+2y+z=1,\; \backslash quad\; \backslash varepsilon\_2:\backslash \; 2x-3y+2z=2\; \backslash \; .$ The normal vectors are $\backslash vec\; n\_1=(1,2,1)^\backslash top,\; \backslash \; \backslash vec\; n\_2=(2,-3,2)^\backslash top$ and the direction of the intersection line is $\backslash vec\; r=\backslash vec\; n\_1\backslash times\backslash vec\; n\_2=(7,0,-7)^\backslash top$. For point $P:\backslash vec\; p$, one gets from the formula above $\backslash vec\; p=\backslash tfrac(1,0,1)^\backslash top\; \backslash \; .$ Hence :$\backslash vec\; x=\backslash tfrac(1,0,1)^\backslash top\; +\; t\; (7,0,-7)^\backslash top$ is a parametric representation of the line of intersection. ''Remarks:'' # In special cases, the determination of the intersection line by the Gaussian elimination may be faster. # If one (or both) of the planes is given parametrically by $\backslash vec\; x=\; \backslash vec\; p\; +\; s\backslash vec\; v\; +\; t\; \backslash vec\; w$, one gets $\backslash vec\; n\; =\; \backslash vec\; v\; \backslash times\; \backslash vec\; w$ as normal vector and the equation is: $\backslash vec\; n\backslash cdot\; \backslash vec\; x\; =\; \backslash vec\; n\backslash cdot\; \backslash vec\; p$. 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「Intersection 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.