From: Martin Kronbichler Date: Thu, 1 Jun 2017 19:21:08 +0000 (+0200) Subject: Fix one more typo in documentation. X-Git-Tag: v9.0.0-rc1~1545^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=01bfc31f9de78eae222e9dd0289f3fe4edcb05a9;p=dealii.git Fix one more typo in documentation. --- diff --git a/include/deal.II/grid/manifold_lib.h b/include/deal.II/grid/manifold_lib.h index 1d84896d12..b92941bf5c 100644 --- a/include/deal.II/grid/manifold_lib.h +++ b/include/deal.II/grid/manifold_lib.h @@ -512,14 +512,14 @@ private: * The mechanism to extend the boundary information is a so-called transfinite * interpolation. * - * The formula for extending such a description in 2D is inspired by + * The formula for extending such a description in 2D is, for example, + * described on * - * Wikipedia - * Given a point $(u,v)$ on the chart, the image of this point in real space - * is given by + * Wikipedia. Given a point $(u,v)$ on the chart, the image of this point + * in real space is given by * @f{align*}{ - * \bf S(u,v) &= (1-v)\bf c_0(u)+v \bf c_1(u) + (1-u)\bf c_2(v) + u \bf c_3(v) \\ - * &\quad - \left[(1-u)(1-v) \bf x_0 + u(1-v) \bf x_1 + (1-u)v \bf x_2 + uv \bf x_3 \right] + * \mathbf S(u,v) &= (1-v)\mathbf c_0(u)+v \mathbf c_1(u) + (1-u)\mathbf c_2(v) + u \mathbf c_3(v) \\ + * &\quad - \left[(1-u)(1-v) \mathbf x_0 + u(1-v) \mathbf x_1 + (1-u)v \mathbf x_2 + uv \mathbf x_3 \right] * @f} * where $\bf x_0, \bf x_1, \bf x_2, \bf x_3$ denote the four bounding vertices * bounding the image space and $\bf c_0, \bf c_1, \bf c_2, \bf c_3$ are the @@ -532,8 +532,8 @@ private: * * This manifold is usually attached to a coarse mesh and then places new * points as a combination of the descriptions on the boundaries, weighted - * appropriately according to the position of the point on the original chart - * point $(u,v)$. Whenever possible, this manifold should be preferred over + * appropriately according to the position of the point in the original chart + * coordinates $(u,v)$. Whenever possible, this manifold should be preferred over * setting only a curved manifold on the boundary of a mesh, since the latter * will need to switch from a curved description to a straight description in a * single layer of elements, which causes an error order on cells close to the @@ -593,10 +593,10 @@ private: * the case for PolarManifold but not for Spherical manifold, so be careful * when using the latter. In case the quality of the manifold is not good * enough, upon mesh refinement it may happen that the transformation to a - * chart inside the get_new_point() or add_new_point() methods produces points - * that are outside the unit cells, then this class throws an exception of - * type Manifold@::ExcTransformationFailed. If that happens, - * the mesh should be refined before applying this class, as done in the + * chart inside the get_new_point() or add_new_points() methods produces points + * that are outside the unit cell. Then this class throws an exception of + * type Manifold@::ExcTransformationFailed. In that case, + * the mesh should be refined before attaching this class, as done in the * following example: * * @code @@ -625,11 +625,12 @@ private: * performance, the identification of the correct coarse cell in the * get_new_point() method needs to pass all coarse cells, so expect a linear * complexity in the number of coarse cells for each single mapping operation, - * i.e., at least quadratic in the number of coarse mesh cells. Thus, the - * current implementation is only economical when there are not more than a - * few hundreds of coarse cells. To make performance better for larger numbers - * of cells, one could extend the current implementation by a - * pre-identification of relevant cells with axis-aligned bounding boxes. + * i.e., at least quadratic in the number of coarse mesh cells for any global + * operation on the whole mesh. Thus, the current implementation is only + * economical when there are not more than a few hundreds of coarse cells. To + * make performance better for larger numbers of cells, one could extend the + * current implementation by a pre-identification of relevant cells with + * axis-aligned bounding boxes. * * @ingroup manifold *