From: Wolfgang Bangerth <bangerth@math.tamu.edu>
Date: Fri, 17 Jul 2009 01:47:10 +0000 (+0000)
Subject: Add to documentation.
X-Git-Tag: v8.0.0~7453
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=1f50ca6ee29c4b9eefd58c37ec1a6a5951465395;p=dealii.git

Add to documentation.


git-svn-id: https://svn.dealii.org/trunk@19109 0785d39b-7218-0410-832d-ea1e28bc413d
---

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