From febc1d4303b0fe988151d912243c42e3aff43637 Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Sat, 26 Jul 2014 06:11:56 -0500 Subject: [PATCH] Improve documentation. --- include/deal.II/fe/mapping_cartesian.h | 33 +++++++++++++++++++------- 1 file changed, 25 insertions(+), 8 deletions(-) diff --git a/include/deal.II/fe/mapping_cartesian.h b/include/deal.II/fe/mapping_cartesian.h index c7be0546c7..790fd10444 100644 --- a/include/deal.II/fe/mapping_cartesian.h +++ b/include/deal.II/fe/mapping_cartesian.h @@ -29,17 +29,34 @@ DEAL_II_NAMESPACE_OPEN /*@{*/ /** - * Mapping of an axis-parallel cell. + * A class providing a mapping from the reference cell to cells that are axiparallel. * * This class maps the unit cell to a grid cell with surfaces parallel - * to the coordinate lines/planes. The mapping is therefore a scaling - * along the coordinate directions. It is specifically developed for - * cartesian meshes. Apply this mapping to a general mesh to get - * strange results. + * to the coordinate lines/planes. It is specifically developed for + * Cartesian meshes. In other words, the mapping is meant for cells for which the + * mapping from the reference to the real cell is a scaling + * along the coordinate directions: The transformation from reference coordinates + * $\hat {\mathbf x}$ to real coordinates $\mathbf x$ on each cell is of the + * form + * @f{align*} + * {\mathbf x}(\hat {\mathbf x}) + * = + * \begin{pmatrix} h_x & 0 \\ 0 & h_y \end{pmatrix} + * \hat{\mathbf x} + {\mathbf v}_0 + * @f} + * in 2d, and + * @f{align*} + * {\mathbf x}(\hat {\mathbf x}) + * = + * \begin{pmatrix} h_x & 0 & 0 \\ 0 & h_y & 0 \\ 0 & 0 & h_z \end{pmatrix} + * \hat{\mathbf x} + {\mathbf v}_0 + * @f} + * in 3d, where ${\mathbf v}_0$ is the bottom left vertex and $h_x,h_y,h_z$ are + * the extents of the cell along the axes. * - * For more information about the spacedim template parameter - * check the documentation of FiniteElement or the one of - * Triangulation. + * The class is intended for efficiency, and it does not do a whole lot of + * error checking. If you apply this mapping to a cell that does not conform to + * the requirements above, you will get strange results. * * @author Guido Kanschat, 2001; Ralf Hartmann, 2005 */ -- 2.39.5