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 b5ed5ba9c1675979722f18d905c223ea8dd74623..8cf3f8a00eb010cdc9636ac3292dcaf720778650 100644 (file)
--- 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