diff --git a/Interpolation/doc/Interpolation/CGAL/interpolation_functions.h b/Interpolation/doc/Interpolation/CGAL/interpolation_functions.h index e11bb97f049..ccb931586cb 100644 --- a/Interpolation/doc/Interpolation/CGAL/interpolation_functions.h +++ b/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 diff --git a/Interpolation/doc/Interpolation/CGAL/sibson_gradient_fitting.h b/Interpolation/doc/Interpolation/CGAL/sibson_gradient_fitting.h index 417166b199a..8a83d3df5fc 100644 --- a/Interpolation/doc/Interpolation/CGAL/sibson_gradient_fitting.h +++ b/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. */ diff --git a/Interpolation/doc/Interpolation/CGAL/surface_neighbors_3.h b/Interpolation/doc/Interpolation/CGAL/surface_neighbors_3.h index a5205bccdfb..9332f60daee 100644 --- a/Interpolation/doc/Interpolation/CGAL/surface_neighbors_3.h +++ b/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$. +`[first, beyond)`. `InputIterator::value_type` is the point type `Kernel::Point_3`. The tangent plane is defined by the point `p` and the vector `normal`. The parameter `K` determines the kernel type that will instantiate the @@ -59,7 +58,7 @@ template parameter of `Voronoi_intersection_2_traits_3`. The surface neighbors of `p` are computed which are the neighbors of `p` in the regular triangulation that is dual to -the intersection of the \f$ 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 std::pair< OutputIterator, bool >