From: Wolfgang Bangerth <bangerth@colostate.edu>
Date: Wed, 19 Apr 2017 19:38:02 +0000 (-0600)
Subject: Update documentation of TriaAccessor::barycenter.
X-Git-Tag: v9.0.0-rc1~1663^2
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=859a39b8c0fc4bd08cd3e039c66cea0730e4ce55;p=dealii.git

Update documentation of TriaAccessor::barycenter.
---

diff --git a/include/deal.II/grid/tria_accessor.h b/include/deal.II/grid/tria_accessor.h
index 37798404f6..22ac5d147b 100644
--- a/include/deal.II/grid/tria_accessor.h
+++ b/include/deal.II/grid/tria_accessor.h
@@ -1290,7 +1290,21 @@ public:
                           const bool use_laplace_transformation=false) const;
 
   /**
-   * Barycenter of the object.
+   * Return the barycenter (also called centroid)
+   * of the object. The barycenter for an object $K$
+   * of dimension $d$ in $D$ space dimensions is given by the $D$-dimensional
+   * vector $\mathbf x_K$ defined by
+   * @f{
+   *   \mathbf x_K = \frac{1}{|K|} \int_K \mathbf x \; \textrm{d}x
+   * @f}
+   * where the measure of the object is given by
+   * @f{
+   *   |K| = \int_K \mathbf 1 \; \textrm{d}x.
+   * @f}
+   * This function assumes that $K$ is mapped by a $d$-linear function from
+   * the reference $d$-dimensional cell. Then the integrals above can be
+   * pulled back to the reference cell and evaluated exactly (if through
+   * lengthy and, compared to the center() function, expensive computations).
    */
   Point<spacedim> barycenter () const;
 
diff --git a/source/grid/tria_accessor.cc b/source/grid/tria_accessor.cc
index a043d573f5..73a767f36c 100644
--- a/source/grid/tria_accessor.cc
+++ b/source/grid/tria_accessor.cc
@@ -141,7 +141,7 @@ namespace
     /*
       Get the computation of the barycenter by this little Maple script. We
       use the bilinear mapping of the unit quad to the real quad. However,
-      every transformation mapping the unit faces to strait lines should
+      every transformation mapping the unit faces to straight lines should
       do.
 
       Remember that the area of the quad is given by