From f215848bc3546ad0dd6dc44f3c34965b806571f3 Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Tue, 6 Jul 2021 14:10:45 -0600 Subject: [PATCH] Minor doc update to BoundingBox. --- include/deal.II/base/bounding_box.h | 20 +++++++++++++++----- 1 file changed, 15 insertions(+), 5 deletions(-) diff --git a/include/deal.II/base/bounding_box.h b/include/deal.II/base/bounding_box.h index 2b77526b2f..045a2a0f21 100644 --- a/include/deal.II/base/bounding_box.h +++ b/include/deal.II/base/bounding_box.h @@ -66,14 +66,14 @@ enum class NeighborType /** * A class that represents a box of arbitrary dimension spacedim and * with sides parallel to the coordinate axes, that is, a region - * * @f[ * [x_0^L, x_0^U] \times ... \times [x_{spacedim-1}^L, x_{spacedim-1}^U], * @f] - * - * where $(x_0^L , ..., x_{spacedim-1}^L) and $(x_0^U , ..., x_{spacedim-1}^U) + * where $(x_0^L , ..., x_{spacedim-1}^L)$ and $(x_0^U , ..., x_{spacedim-1}^U)$ * denote the two vertices (bottom left and top right) which are used to - * represent the box. + * represent the box. The quantities $x_k^L$ and $x_k^U$ denote the "lower" + * and "upper" bounds of values that are within the box for each coordinate + * direction $k$. * * Geometrically, a bounding box is thus: * - 1D: a segment (represented by its vertices in the proper order) @@ -96,7 +96,17 @@ enum class NeighborType * @endcode * * Bounding boxes are, for example, useful in parallel distributed meshes to - * give a general description of the owners of each portion of the mesh. + * give a general description of the owners of each portion of the mesh. More + * generally, bounding boxes are often used to roughly describe a region of + * space in which an object is contained; if a candidate point is not within + * the bounding box (a test that is cheap to execute), then it is not necessary + * to perform an expensive test whether the candidate point is in fact inside + * the object itself. Bounding boxes are therefore often used as a first, + * cheap rejection test before more detailed checks. As such, bounding boxes + * serve many of the same purposes as the + * [convex hull](https://en.wikipedia.org/wiki/Convex_hull), for which it is + * also relatively straightforward to compute whether a point is inside or + * outside, though not quite as cheap as for the bounding box. * * Taking the cross section of a BoundingBox orthogonal to a given * direction gives a box in one dimension lower: BoundingBox. -- 2.39.5