fix some typos [ci skip]

diff --git a/include/deal.II/grid/manifold.h b/include/deal.II/grid/manifold.h
index e664042ed556b584cc45ab512d808d0789b2b87c..6018d0a039d84d3285b42224c7a7c223ba08f642 100644 (file)
--- a/include/deal.II/grid/manifold.h
+++ b/include/deal.II/grid/manifold.h
@@ -65,7 +65,7 @@ namespace Manifolds
  * <h3>Common use case: Creating a new vertex</h3>
  *
  * In the most essential use of manifolds, manifold descriptions are used
- * to create a "point between other points. For example, when a triangulation
+ * to create a "point between other points". For example, when a triangulation
  * creates a new vertex on a cell, face, or edge , it determines the new
  * vertex' coordinates through the following function call:
  *   @code
@@ -82,9 +82,9 @@ namespace Manifolds
  * new point. In the simplest case, for example in the FlatManifold class, the
  * function simply computes the arithmetic average (with given weights) of
  * the given points. However, other classes do something differently; for example,
- * the SphericalManifold class used to describe domains that form (part of) the
- * sphere, will ensure that if it is given the two vertices of an edge at
- * the boundary, the new point returned will lie on the grand circle that connects
+ * the SphericalManifold class, which is used to describe domains that form (part of) the
+ * sphere, will ensure that, given the two vertices of an edge at
+ * the boundary, the new returned point will lie on the grand circle that connects
  * the two points, rather than choosing a point that is half-way between the
  * two points in ${\mathbb R}^d$.
  *
@@ -173,7 +173,7 @@ namespace Manifolds
  * uses time, not arc length to denote progress along the geodesic.
  *
  * In this picture, computing a mid-point between points $\mathbf x_1$
- * and $\mathbf x_2$ with weights $w_1$ and $w_2=1-w_1$ then simply
+ * and $\mathbf x_2$, with weights $w_1$ and $w_2=1-w_1$, simply
  * requires computing the point $\mathbf s(w_1)$. Computing a new
  * point as a weighted average of more than two points can be done
  * by considering pairwise geodetics, finding suitable points on
@@ -267,7 +267,7 @@ public:
    * Manifolds::get_default_quadrature() function, and then calls the
    * Manifold<dim,spacedim>::get_new_point() function. User derived classes
    * can overload Manifold<dim,spacedim>::get_new_point() or
-   * Manifold<dim,spacedim>::project_to_surface(), which is called by the
+   * Manifold<dim,spacedim>::project_to_manifold(), which is called by the
    * default implementation of Manifold<dim,spacedim>::get_new_point().
    */
   virtual
@@ -288,7 +288,7 @@ public:
    * Manifolds::get_default_quadrature() function, and then calls the
    * Manifold<dim,spacedim>::get_new_point() function. User derived classes
    * can overload Manifold<dim,spacedim>::get_new_point() or
-   * Manifold<dim,spacedim>::project_to_surface(), which is called by the
+   * Manifold<dim,spacedim>::project_to_manifold(), which is called by the
    * default implementation of Manifold<dim,spacedim>::get_new_point().
    */
   virtual
@@ -310,7 +310,7 @@ public:
    * Manifolds::get_default_quadrature() function, and then calls the
    * Manifold<dim,spacedim>::get_new_point() function. User derived classes
    * can overload Manifold<dim,spacedim>::get_new_point() or
-   * Manifold<dim,spacedim>::project_to_surface(), which is called by the
+   * Manifold<dim,spacedim>::project_to_manifold(), which is called by the
    * default implementation of Manifold<dim,spacedim>::get_new_point().
    */
   virtual
@@ -371,7 +371,7 @@ public:
    * $\mathbf s'(0) \approx \frac{$\mathbf s(\epsilon)-\mathbf x_1}{\epsilon}$
    * for a small value of $\epsilon$, and the evaluation of $\mathbf s(\epsilon)$
    * is done by calling get_new_point(). If possible, derived classes should
-   * override this function by an implement of the exact derivative.
+   * override this function by an implemention of the exact derivative.
    *
    * @param x1 The first point that describes the geodesic, and the one
    *   at which the "direction" is to be evaluated.