de-math

Interpolation/doc/Interpolation/CGAL/interpolation_functions.h

@@ -63,8 +63,8 @@ std::pair< Data_type, bool> operator()(const Key_type& p);
 
 generates the interpolated function value computed by Farin's interpolant.
 
-\pre `norm` \f$ \neq0\f$. `function_value(p).second == true` for all points `p` of the point/coordinate pairs in the range \f$ \left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$.
-\pre The range \f$ \left[\right.\f$ `first`, `beyond`\f$ \left.\right)\f$ contains either one or more than three element
+\pre `norm` \f$ \neq0\f$. `function_value(p).second == true` for all points `p` of the point/coordinate pairs in the range `[first, beyond).
+\pre The range `[first, beyond)` contains either one or more than three element
 The function `farin_c1_interpolation()` interpolates the function values and the 
 gradients that are provided by functors using the method described in \cite f-sodt-90. 
 
@@ -89,7 +89,6 @@ to provide the square root operation.
 \sa `PkgInterpolationRegularNeighborCoordinates2`
 \sa PkgInterpolationSurfaceNeighborCoordinates3
 
-s. 
 */
 template < class RandomAccessIterator, class Functor,
 class GradFunctor, class Traits> typename Functor::result_type
@@ -115,8 +114,8 @@ function value and a Boolean. The Boolean indicates whether the
 function value could be retrieved correctly. This function generates
 the interpolated function value as the weighted sum of the values
 corresponding to each point of the point/coordinate pairs in the
-range \f$ \left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$.
-\pre `norm` \f$ \neq0\f$. `function_value(p).second == true` for all points `p` of the point/coordinate pairs in the range \f$ \left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$.
+range `[first, beyond)`.
+\pre `norm` \f$ \neq0\f$. `function_value(p).second == true` for all points `p` of the point/coordinate pairs in the range `[first, beyond)`.
 
 \cgalHeading{Requirements}
 
@@ -155,20 +154,22 @@ norm, Functor function_values);
 /*!
 \ingroup PkgInterpolation2Interpolation
 
-The function `quadratic_interpolation` interpolates the function values and first degree 
+The function `quadratic_interpolation()` interpolates the function values and first degree 
 functions defined from the function gradients. Both, function values and 
 gradients, must be provided by functors. 
 
 This function generates the
 interpolated function value as the weighted sum of the values plus a
 linear term in the gradient for each point of the point/coordinate
-pairs in the range \f$ \left[\right.\f$ `first`,
-`beyond`\f$ \left.\right)\f$. See also
-`sibson_c1_interpolation`. \pre `norm` \f$ \neq0\f$ `function_value(p).second == true` for all points `p` of the point/coordinate pairs in the range \f$ \left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$.
+pairs in the range `[first, beyond)`. See also
+`sibson_c1_interpolation()`. 
+
+\pre `norm` \f$ \neq0\f$ `function_value(p).second == true` for all
+points `p` of the point/coordinate pairs in the range `[first, beyond)`.
 
 \cgalHeading{Parameters}
 
-See `sibson_c1_interpolation`. 
+See `sibson_c1_interpolation()`. 
 
 \cgalHeading{Requirements}
 
@@ -200,7 +201,7 @@ function_gradient,const Traits& traits);
 /*!
 \ingroup PkgInterpolation2Interpolation
 
-The function `sibson_c1_interpolation` interpolates the function values and the 
+The function `sibson_c1_interpolation()` interpolates the function values and the 
 gradients that are provided by functors 
 following the method described in \cite s-bdnni-81. 
 
@@ -210,9 +211,10 @@ This function generates the interpolated function value at the point
 If the functor `function_gradient` cannot supply the gradient of a
 point, the function returns a pair where the Boolean is set to
 `false`. If the interpolation was successful, the pair contains the
-interpolated function value as first and `true` as second value. \pre
-`norm` \f$ \neq0\f$. `function_value(p).second == true` for all points
-`p` of the point/coordinate pairs in the range \f$\left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$.
+interpolated function value as first and `true` as second value. 
+
+\pre `norm` \f$ \neq0\f$. `function_value(p).second == true` for all points
+`p` of the point/coordinate pairs in the range `[first, beyond)`.
 
 
 \cgalHeading{Parameters}
@@ -221,8 +223,7 @@ The template parameter `Traits` is to be
 instantiated with a model of `InterpolationTraits`. 
 The value type of `ForwardIterator` is a pair associating a point to a 
 (non-normalized) barycentric coordinate. `norm` is the 
-normalization factor. The range \f$ \left[\right.\f$ 
-`first`,`beyond`\f$ \left.\right)\f$ contains the barycentric 
+normalization factor. The range `[first, beyond)` contains the barycentric 
 coordinates for the query point `p`. The functor 
 `function_value` allows to access the value of the interpolated 
 function given a point. `function_gradient` allows to access the 

Interpolation/doc/Interpolation/CGAL/sibson_gradient_fitting.h

@@ -50,8 +50,7 @@ estimation method based on natural neighbor coordinates
 /*!
 estimates the
 gradient of a function at the point `p` given natural neighbor
-coordinates of `p` in the range \f$ \left[\right.\f$ `first`,
-`beyond`\f$ \left.\right)\f$ and the function values of the neighbors
+coordinates of `p` in the range `[first, beyond)` and the function values of the neighbors
 provided by the functor `f`. `norm` is the normalization
 factor of the barycentric coordinates.
 */

Interpolation/doc/Interpolation/CGAL/surface_neighbors_3.h

@@ -19,9 +19,8 @@ The functions \c surface_neighbors_certified_3 also return, in
 addition, a Boolean value that certifies whether or not, the Voronoi
 cell of `p` can be affected by points that lie outside the input
 range, i.e. outside the ball centered on `p` passing through the
-furthest sample point from `p` in the range \f$
-\left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$. If the sample
-points are collected by a \f$ k\f$-nearest neighbor or a range search
+furthest sample point from `p` in the range `[first, beyond)`. If the sample
+points are collected by a k-nearest neighbor or a range search
 query, this permits to verify that a large enough neighborhood has
 been considered.
 
@@ -51,7 +50,7 @@ of the cell of `p` in this diagram.
 
 /*!
 The sample points \f$ \mathcal{P}\f$ are provided in the range 
-\f$\left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$.
+`[first, beyond)`.
 `InputIterator::value_type` is the point type `Kernel::Point_3`. The
 tangent plane is defined by the point `p` and the vector `normal`. The
 parameter `K` determines the kernel type that will instantiate the
@@ -59,7 +58,7 @@ template parameter of `Voronoi_intersection_2_traits_3<K>`.
 
 The surface neighbors of `p` are computed which are the
 neighbors of `p` in the regular triangulation that is dual to
-the intersection of the \f$ 3D\f$ Voronoi diagram of \f$ \mathcal{P}\f$ with
+the intersection of the 3D Voronoi diagram of \f$ \mathcal{P}\f$ with
 the tangent plane. The point sequence that is computed by the
 function is placed starting at `out`. The function returns an
 iterator that is placed past-the-end of the resulting point
@@ -85,7 +84,7 @@ const ITraits& traits);
 /*!
 Similar to the first function. The additional third return
 value is `true` if the furthest point in the range
-\f$ \left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$ is further
+`[first, beyond)` is further
 away from `p` than twice the distance from `p` to the
 furthest vertex of the intersection of the Voronoi cell of `p`
 with the tangent plane defined be `(p,normal)`. It is
@@ -101,8 +100,7 @@ K);
 /*!
 The same as above except that this function
 takes the maximal distance from `p` to the points in the range
-\f$ \left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$ as additional
-parameter.
+`[first, beyond)` as additional parameter.
 */
 template <class OutputIterator, class InputIterator, class
 Kernel> std::pair< OutputIterator, bool >