From: Wolfgang Bangerth Date: Thu, 16 Jul 2009 23:51:01 +0000 (+0000) Subject: Fix a bug in the documentation. X-Git-Tag: v8.0.0~7456 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=95a77597ee062adaa017e58afdd72148835b148b;p=dealii.git Fix a bug in the documentation. git-svn-id: https://svn.dealii.org/trunk@19106 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 c1ad6a5e16..b5ed5ba9c1 100644 --- a/deal.II/base/include/base/geometry_info.h +++ b/deal.II/base/include/base/geometry_info.h @@ -2065,47 +2065,41 @@ struct GeometryInfo * element to the element * described by the vertices. * - * For example, if - * dim==spacedim==2, then the - * alternating form is a scalar - * (because spacedim-dim=0) and - * its value equals $\mathbf - * v_1\wedge \mathbf v_2=\mathbf - * v_1\cdot\mathbf v_2$. If - * dim==spacedim==3, then the - * result is again a scalar with - * value $\mathbf v_1\wedge - * \mathbf v_2 \wedge \mathbf v_3 - * = (\mathbf v_1\times \mathbf - * v_2)\cdot \mathbf v_3$, where - * $\mathbf v_1, \mathbf v_2, - * \mathbf v_3$ are the images of - * the unit vectors at a vertex - * of the unit dim-dimensional - * cell under transformation to - * the dim-dimensional cell in - * spacedim-dimensional space. In - * both cases, i.e. for dim==2 or - * 3, the result happens to equal - * the determinant of the - * Jacobian of the mapping from - * reference cell to cell in real - * space. Note that it is the - * actual determinant, not its - * absolute value as often used - * in transforming integrals from - * one coordinate system to - * another. In particular, if the - * object specified by the - * vertices is a parallelogram - * (i.e. a linear transformation - * of the reference cell) then - * the computed values are the - * same at all vertices and equal - * the (signed) area of the cell; - * similarly, for - * parallel-epipeds, it is the - * volume of the cell. + * For example, if dim==spacedim==2, then + * the alternating form is a scalar + * (because spacedim-dim=0) and its value + * equals $\mathbf v_1\wedge \mathbf + * v_2=\mathbf v_1^\perp \cdot\mathbf + * v_2$, where $\mathbf v_1^\perp$ is a + * vector that is rotated to the right by + * 90 degrees from $\mathbf v_1$. If + * dim==spacedim==3, then the result is + * again a scalar with value $\mathbf + * v_1\wedge \mathbf v_2 \wedge \mathbf + * v_3 = (\mathbf v_1\times \mathbf + * v_2)\cdot \mathbf v_3$, where $\mathbf + * v_1, \mathbf v_2, \mathbf v_3$ are the + * images of the unit vectors at a vertex + * of the unit dim-dimensional cell under + * transformation to the dim-dimensional + * cell in spacedim-dimensional space. In + * both cases, i.e. for dim==2 or 3, the + * result happens to equal the + * determinant of the Jacobian of the + * mapping from reference cell to cell in + * real space. Note that it is the actual + * determinant, not its absolute value as + * often used in transforming integrals + * from one coordinate system to + * another. In particular, if the object + * specified by the vertices is a + * parallelogram (i.e. a linear + * transformation of the reference cell) + * then the computed values are the same + * at all vertices and equal the (signed) + * area of the cell; similarly, for + * parallel-epipeds, it is the volume of + * the cell. * * This function is used in order to * determine how distorted a cell is (see