From 1f50ca6ee29c4b9eefd58c37ec1a6a5951465395 Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Fri, 17 Jul 2009 01:47:10 +0000 Subject: [PATCH] Add to documentation. git-svn-id: https://svn.dealii.org/trunk@19109 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/base/include/base/geometry_info.h | 32 +++++++++++++++++++++++ 1 file changed, 32 insertions(+) diff --git a/deal.II/base/include/base/geometry_info.h b/deal.II/base/include/base/geometry_info.h index b5ed5ba9c1..8cf3f8a00e 100644 --- a/deal.II/base/include/base/geometry_info.h +++ b/deal.II/base/include/base/geometry_info.h @@ -2101,6 +2101,38 @@ struct GeometryInfo * parallel-epipeds, it is the volume of * the cell. * + * Likewise, if we have dim==spacedim-1 + * (e.g. we have a quad in 3d space, or a + * line in 2d), then the alternating + * product denotes the normal vector + * (i.e. a rank-1 tensor, since + * spacedim-dim=1) to the object at each + * vertex, where the normal vector's + * magnitude denotes the area element of + * the transformation from the reference + * object to the object given by the + * vertices. In particular, if again the + * mapping from reference object to the + * object under consideration here is + * linear (not bi- or trilinear), then + * the returned vectors are all + * %parallel, perpendicular to the mapped + * object described by the vertices, and + * have a magnitude equal to the + * area/volume of the mapped object. If + * dim=1, spacedim=2, then the returned + * value is $\mathbf v_1^\perp$, where + * $\mathbf v_1$ is the image of the sole + * unit vector of a line mapped to the + * line in 2d given by the vertices; if + * dim=2, spacedim=3, then the returned + * values are $\mathbf v_1 \wedge \mathbf + * v_2=\mathbf v_1 \times \mathbf v_2$ + * where $\mathbf v_1,\mathbf v_2$ are + * the two three-dimensional vectors that + * are tangential to the quad mapped into + * three-dimensional space. + * * This function is used in order to * determine how distorted a cell is (see * the entry on -- 2.39.5