]> https://gitweb.dealii.org/ - dealii.git/commitdiff
Update documentation of TriaAccessor::barycenter. 4290/head
authorWolfgang Bangerth <bangerth@colostate.edu>
Wed, 19 Apr 2017 19:38:02 +0000 (13:38 -0600)
committerWolfgang Bangerth <bangerth@colostate.edu>
Thu, 20 Apr 2017 13:58:29 +0000 (07:58 -0600)
include/deal.II/grid/tria_accessor.h
source/grid/tria_accessor.cc

index 37798404f699d1d0151704f1791929c4c128ee24..22ac5d147b3d4cff03e91cb876715373a43359da 100644 (file)
@@ -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;
 
index a043d573f55d0c29ed6b4b2ddaa324fb5cb0d024..73a767f36c7692d7b4a237c97625f2b94819527f 100644 (file)
@@ -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

In the beginning the Universe was created. This has made a lot of people very angry and has been widely regarded as a bad move.

Douglas Adams


Typeset in Trocchi and Trocchi Bold Sans Serif.