diff --git a/Interpolation/doc/Interpolation/CGAL/Interpolation_traits_2.h b/Interpolation/doc/Interpolation/CGAL/Interpolation_traits_2.h index e9fc03b1af6..4773952e00e 100644 --- a/Interpolation/doc/Interpolation/CGAL/Interpolation_traits_2.h +++ b/Interpolation/doc/Interpolation/CGAL/Interpolation_traits_2.h @@ -14,7 +14,7 @@ is templated by a kernel class `K`. \sa `InterpolationTraits` \sa `GradientFittingTraits` -\sa CGAL::Interpolation_gradient_fitting_traits_2 +\sa `CGAL::Interpolation_gradient_fitting_traits_2` */ template< typename K > diff --git a/Interpolation/doc/Interpolation/CGAL/Voronoi_intersection_2_traits_3.h b/Interpolation/doc/Interpolation/CGAL/Voronoi_intersection_2_traits_3.h index 9ff5a6ea3e8..fdceb675739 100644 --- a/Interpolation/doc/Interpolation/CGAL/Voronoi_intersection_2_traits_3.h +++ b/Interpolation/doc/Interpolation/CGAL/Voronoi_intersection_2_traits_3.h @@ -9,7 +9,7 @@ namespace CGAL { `InterpolationTraits`. It can be used to instantiate the geometric traits class of a two-dimensional regular triangulation. A three-dimensional plane is defined by a point and a vector that -are members of the traits class. The triangulation is defined on \f$ 3D\f$ +are members of the traits class. The triangulation is defined on `3D` points. It is the regular triangulation of the input points projected onto the plane and each weighted with the negative squared distance of the input point to the plane. It can be shown that it is @@ -24,9 +24,9 @@ templated by a kernel class `K`. \models ::RegularTriangulationTraits_2 \sa `RegularTriangulationTraits_2` -\sa CGAL::Regular_triangulation_2 -\sa CGAL::regular_neighbor_coordinates_2 -\sa CGAL::surface_neighbor_coordinates_3 +\sa `CGAL::Regular_triangulation_2` +\sa `CGAL::regular_neighbor_coordinates_2()` +\sa `CGAL::surface_neighbor_coordinates_3()` */ template< typename K > diff --git a/Interpolation/doc/Interpolation/CGAL/interpolation_functions.h b/Interpolation/doc/Interpolation/CGAL/interpolation_functions.h index c4cd3baa09c..bc5a9b4a316 100644 --- a/Interpolation/doc/Interpolation/CGAL/interpolation_functions.h +++ b/Interpolation/doc/Interpolation/CGAL/interpolation_functions.h @@ -61,33 +61,33 @@ std::pair< Data_type, bool> operator()(const Key_type& p); /*! \ingroup PkgInterpolation2Interpolation -generates the interpolated function value -computed by Farin's interpolant \cite f-sodt-90. +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 -The function `farin_c1_interpolation` interpolates the function values and the +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. ### Parameters ### -`RandomAccessIterator::value_type` is a pair +The value type of `RandomAccessIterator` is a pair associating a point to a (non-normalized) barycentric coordinate. See -`CGALL::sibson_c1_interpolation` for the other parameters. +`sibson_c1_interpolation()` for the other parameters. ### Requirements ### -Same requirements as for `sibson_c1_interpolation` only the +Same requirements as for `sibson_c1_interpolation()` only the iterator must provide random access and `Traits::FT` does not need to provide the square root operation. \sa `CGAL::Data_access` -\sa CGAL::linear_interpolation -\sa CGAL::sibson_c1_interpolation -\sa CGAL::sibson_gradient_fitting +\sa `CGAL::linear_interpolation()` +\sa `CGAL::sibson_c1_interpolation()` +\sa `CGAL::sibson_gradient_fitting()` \sa `CGAL::Interpolation_traits_2` -\sa CGAL::natural_neighbor_coordinates_2 -\sa CGAL::regular_neighbor_coordinates_2 -\sa CGAL::surface_neighbor_coordinates_3 +\sa `CGAL::natural_neighbor_coordinates_2()` +\sa `CGAL::regular_neighbor_coordinates_2()` +\sa `CGAL::surface_neighbor_coordinates_3()` s. */ @@ -105,10 +105,10 @@ Traits& traits); /*! \ingroup PkgInterpolation2Interpolation -The function `linear_interpolation` computes the weighted sum of the function +The function `linear_interpolation()` computes the weighted sum of the function values which must be provided via a functor. -`ForwardIterator::value_type` is a pair associating a point to a (non-normalized) barycentric +The value type of `ForwardIterator` is a pair associating a point to a (non-normalized) barycentric coordinate. `norm` is the normalization factor. Given a point, the functor `function_values` allows to access a pair of a function value and a Boolean. The Boolean indicates whether the @@ -121,28 +121,28 @@ range \f$ \left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$. ### Requirements ###
    -
  1. `ForwardIterator::value_type` is a pair of +
  2. The value type of `ForwardIterator` is a pair of point/coordinate value, thus -`ForwardIterator::value_type::first_type` is equivalent to a -point and `ForwardIterator::value_type::second_type` is a +`std::iterator_traits::value_type::first_type` is equivalent to a +point and `std::iterator_traits::value_type::second_type` is a field number type.
  3. `Functor::argument_type` must be equivalent to -`ForwardIterator::value_type::first_type` and +`std::iterator_traits::value_type::first_type` and `Functor::result_type` is a pair of the function value type and a Boolean value. The function value type must provide a multiplication and addition operation with the field number type -`ForwardIterator::value_type::second_type` and a constructor +`std::iterator_traits::value_type::second_type` and a constructor with argument \f$ 0\f$. A model of the functor is provided by the struct `Data_access`. It must be instantiated accordingly with -an associative container (e.g. \stl `std::map`) having the +an associative container (e.g. `std::map`) having the point type as `key_type` and the function value type as `mapped_type`.
\sa `CGAL::Data_access` -\sa CGAL::natural_neighbor_coordinates_2 -\sa CGAL::regular_neighbor_coordinates_2 -\sa CGAL::surface_neighbor_coordinates_3 +\sa `CGAL::natural_neighbor_coordinates_2()` +\sa `CGAL::regular_neighbor_coordinates_2()` +\sa `CGAL::surface_neighbor_coordinates_3()` */ template < class ForwardIterator, class Functor> typename @@ -173,19 +173,19 @@ See `sibson_c1_interpolation`. ### Requirements ### Same requirements as for -`sibson_c1_interpolation` only that `Traits::FT` does not need +`sibson_c1_interpolation()` only that `Traits::FT` does not need to provide the square root operation. \sa `InterpolationTraits` \sa `GradientFittingTraits` \sa `CGAL::Data_access` -\sa CGAL::sibson_gradient_fitting -\sa CGAL::linear_interpolation +\sa `CGAL::sibson_gradient_fitting()` +\sa `CGAL::linear_interpolation()` \sa `CGAL::Interpolation_traits_2` \sa `CGAL::Interpolation_gradient_fitting_traits_2` -\sa CGAL::natural_neighbor_coordinates_2 -\sa CGAL::regular_neighbor_coordinates_2 -\sa CGAL::surface_neighbor_coordinates_3 +\sa `CGAL::natural_neighbor_coordinates_2()` +\sa `CGAL::regular_neighbor_coordinates_2()` +\sa `CGAL::surface_neighbor_coordinates_3()` */ template < class ForwardIterator, class Functor, class GradFunctor, class Traits> typename Functor::result_type @@ -219,7 +219,7 @@ interpolated function value as first and `true` as second value. \pre The template parameter `Traits` is to be instantiated with a model of `InterpolationTraits`. -`ForwardIterator::value_type` is a pair associating a point to a +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 @@ -233,10 +233,10 @@ function gradient given a point.
  1. `Traits` is a model of the concept `InterpolationTraits`. -
  2. `ForwardIterator::value_type` is a point/coordinate pair. -Precisely `ForwardIterator::value_type::first_type` is +
  3. The value type of `ForwardIterator` is a point/coordinate pair. +Precisely `std::iterator_traits::value_type::first_type` is equivalent to `Traits::Point_d` and -`ForwardIterator::value_type::second_type` is equivalent to +`std::iterator_traits::value_type::second_type` is equivalent to `Traits::FT`.
  4. `Functor::argument_type` must be equivalent to `Traits::Point_d` and `Functor::result_type` is a pair of @@ -261,13 +261,13 @@ the square root operation `sqrt()`. \sa `InterpolationTraits` \sa `GradientFittingTraits` \sa `CGAL::Data_access` -\sa CGAL::sibson_gradient_fitting -\sa CGAL::linear_interpolation +\sa `CGAL::sibson_gradient_fitting()` +\sa `CGAL::linear_interpolation()` \sa `CGAL::Interpolation_traits_2` \sa `CGAL::Interpolation_gradient_fitting_traits_2` -\sa CGAL::natural_neighbor_coordinates_2 -\sa CGAL::regular_neighbor_coordinates_2 -\sa CGAL::surface_neighbor_coordinates_3 +\sa `CGAL::natural_neighbor_coordinates_2()` +\sa `CGAL::regular_neighbor_coordinates_2()` +\sa `CGAL::surface_neighbor_coordinates_3()` */ template < class ForwardIterator, class Functor, class GradFunctor, class Traits> std::pair< typename Functor::result_type, @@ -282,7 +282,7 @@ traits); /*! \ingroup PkgInterpolation2Interpolation -The same as `CGAL::sibson_interpolation` except that no square root +The same as `sibson_interpolation()` except that no square root operation is needed for FT. */ template < class ForwardIterator, class Functor, class diff --git a/Interpolation/doc/Interpolation/CGAL/natural_neighbor_coordinates_2.h b/Interpolation/doc/Interpolation/CGAL/natural_neighbor_coordinates_2.h index 1f68bcc89f7..5c309f01397 100644 --- a/Interpolation/doc/Interpolation/CGAL/natural_neighbor_coordinates_2.h +++ b/Interpolation/doc/Interpolation/CGAL/natural_neighbor_coordinates_2.h @@ -5,7 +5,7 @@ namespace CGAL { \ingroup PkgInterpolation2NatNeighbor The function `natural_neighbor_coordinates_2` computes natural neighbor coordinates, also -called Sibson's coordinates, for \f$ 2D\f$ points provided a two-dimensional +called Sibson's coordinates, for `2D` points provided a two-dimensional triangulation and a query point in the convex hull of the vertices of the triangulation. @@ -40,10 +40,10 @@ convex hull, the coordinate values cannot be computed and the third value of the result triple is set to `false`. -\sa CGAL::linear_interpolation -\sa CGAL::sibson_c1_interpolation -\sa CGAL::surface_neighbor_coordinates_3 -\sa CGAL::regular_neighbor_coordinates_2 +\sa `CGAL::linear_interpolation()` +\sa `CGAL::sibson_c1_interpolation()` +\sa `CGAL::surface_neighbor_coordinates_3()` +\sa `CGAL::regular_neighbor_coordinates_2()` */ /// @{ @@ -71,8 +71,8 @@ natural_neighbor_coordinates_2( The same as above. `hole_begin` and `hole_end` determines the iterator range over the boundary edges of the conflict zone of `p` in the triangulation. It is the result of the function -`T.get_boundary_of_conflicts(p,std::back_inserter(hole), start)`, see -`Delaunay_triangulation_2`. +\link Delaunay_triangulation_2::get_boundary_of_conflicts() +`dt.get_boundary_of_conflicts(p,std::back_inserter(hole), start)`\endlink. */ template CGAL::Triple< OutputIterator, typename Dt::Geom_traits::FT, diff --git a/Interpolation/doc/Interpolation/CGAL/natural_neighbor_coordinates_3.h b/Interpolation/doc/Interpolation/CGAL/natural_neighbor_coordinates_3.h index 956a318aa32..f65df73f3d8 100755 --- a/Interpolation/doc/Interpolation/CGAL/natural_neighbor_coordinates_3.h +++ b/Interpolation/doc/Interpolation/CGAL/natural_neighbor_coordinates_3.h @@ -7,7 +7,7 @@ namespace CGAL { Given a 3D point `p` and a 3D Delaunay triangulation `dt`, this function calculates the natural neighbors and coordinates of `p` with regard of `dt`. -\tparam `OutputIterator` must have value type +\tparam OutputIterator must have value type `std::pair` Result : diff --git a/Interpolation/doc/Interpolation/CGAL/regular_neighbor_coordinates_2.h b/Interpolation/doc/Interpolation/CGAL/regular_neighbor_coordinates_2.h index 3fadce12a5f..b85898ecd47 100644 --- a/Interpolation/doc/Interpolation/CGAL/regular_neighbor_coordinates_2.h +++ b/Interpolation/doc/Interpolation/CGAL/regular_neighbor_coordinates_2.h @@ -5,7 +5,7 @@ namespace CGAL { \ingroup PkgInterpolation2NatNeighbor The function `regular_neighbor_coordinates_2` computes natural neighbor coordinates, also -called Sibson's coordinates, for weighted \f$ 2D\f$ points provided a +called Sibson's coordinates, for weighted `2D` points provided a two-dimensional regular triangulation and a (weighted) query point inside the convex hull of the vertices of the triangulation. We call these coordinates regular neighbor coordinates. @@ -21,7 +21,7 @@ type `FT` which is a model for `FieldNumberType` and it must meet the requirements for the traits class of the `polygon_area_2` function. A model of this traits class is `Regular_triangulation_euclidean_traits_2`. -
  5. `OutputIterator::value_type` is equivalent to +
  6. The value type of `OutputIterator` is equivalent to `std::pair`, i.e. a pair associating a point and its regular neighbor coordinate.
@@ -35,7 +35,7 @@ returned by the function. If `p` lies outside the convex hull, the coordinate values cannot be computed and the third value of the result triple is set to `false`. -\sa CGAL::natural_neighbor_coordinates_2 +\sa `CGAL::natural_neighbor_coordinates_2()` */ /// @{ @@ -64,12 +64,12 @@ Rt::Face_handle start = typename Rt::Face_handle()); /*! The same as above. `hole_begin` and `hole_end` determines the iterator range over the boundary edges of the conflict zone of `p` in the -triangulation `rt`. `hidden_vertices_begin` and `hidden_vertices_end` +triangulation `rt`. +\link Regular_triangulation_2::hidden_vertices_begin() `rt.hidden_vertices_begin()`\endlink and +\link Regular_triangulation_2::hidden_vertices_end() `rt.hidden_vertices_end()`\endlink determines the iterator range over the hidden vertices of the conflict zone of `p` in`rt`. It is the result of the function -`T.get_boundary_of_conflicts(p,std::back_inserter(hole), -std::back_inserter(hidden_vertices), start)`, see -`Regular_triangulation_2`. +\link Regular_triangulation_2::get_boundary_of_conflicts() `rt.get_boundary_of_conflicts(p,std::back_inserter(hole), std::back_inserter(hidden_vertices), start)`\endlink. */ template CGAL::Triple< diff --git a/Interpolation/doc/Interpolation/CGAL/sibson_gradient_fitting.h b/Interpolation/doc/Interpolation/CGAL/sibson_gradient_fitting.h index 8ed401cf168..1ac8c73a485 100644 --- a/Interpolation/doc/Interpolation/CGAL/sibson_gradient_fitting.h +++ b/Interpolation/doc/Interpolation/CGAL/sibson_gradient_fitting.h @@ -4,7 +4,7 @@ namespace CGAL { \defgroup sibson_gradient_fitting sibson_gradient_fitting \ingroup PkgInterpolation2Interpolation -The function `sibson_gradient_fitting` approximates the gradient of a +The function `sibson_gradient_fitting()` approximates the gradient of a function at a point `p` given natural neighbor coordinates for `p` and its neighbors' function values. The approximation method is described in \cite s-bdnni-81. Further functions are provided to fit the @@ -15,28 +15,28 @@ coordinates. ### Requirements ###
    -
  1. `ForwardIterator::value_type` is a pair of point/coordinate -value, thus `ForwardIterator::value_type::first_type` is +
  2. The value type of `ForwardIterator` is a pair of point/coordinate +value, thus `std::iterator_traits::value_type::first_type` is equivalent to a point and -`ForwardIterator::value_type::second_type` is a +`std::iterator_traits::value_type::second_type` is a number type.
  3. `Functor::argument_type` must be equivalent to -`ForwardIterator::value_type::first_type` and +`std::iterator_traits::value_type::first_type` and `Functor::result_type` is the function value type. It must provide a multiplication and addition operation with the type -`ForwardIterator::value_type::second_type`. +`std::iterator_traits::value_type::second_type`.
  4. `Traits` is a model of the concept `GradientFittingTraits`.
-\sa CGAL::linear_interpolation -\sa CGAL::sibson_c1_interpolation -\sa CGAL::farin_c1_interpolation -\sa CGAL::quadratic_interpolation +\sa `CGAL::linear_interpolation()` +\sa `CGAL::sibson_c1_interpolation()` +\sa `CGAL::farin_c1_interpolation()` +\sa `CGAL::quadratic_interpolation()` \sa `CGAL::Interpolation_gradient_fitting_traits_2` -\sa CGAL::natural_neighbor_coordinates_2 -\sa CGAL::regular_neighbor_coordinates_2 -\sa CGAL::surface_neighbor_coordinates_3 +\sa `CGAL::natural_neighbor_coordinates_2()` +\sa `CGAL::regular_neighbor_coordinates_2()` +\sa `CGAL::surface_neighbor_coordinates_3()` ### Implementation ### @@ -67,8 +67,8 @@ Functor f, const Traits& traits); /*! estimates the function gradients at all vertices of `dt` that lie inside the convex hull using the coordinates computed by the -function `CGAL::natural_neighbor_coordinates_2`. -`OutputIterator::value_type` is a pair associating a point to a +function `natural_neighbor_coordinates_2()`. +The value type of `OutputIterator` is a pair associating a point to a vector. The sequence of point/gradient pairs computed by this function is placed starting at `out`. The function returns an iterator that is placed past-the-end of the resulting sequence. The @@ -82,8 +82,8 @@ dt, OutputIterator out, Functor f, const Traits& traits); /*! estimates the function gradients at all vertices of `rt` that lie inside the convex hull using the coordinates computed by the -function `CGAL::regular_neighbor_coordinates_2`. -`OutputIterator::value_type` is a pair associating a point to a +function `regular_neighbor_coordinates_2()`. +The value type of `OutputIterator` is a pair associating a point to a vector. The sequence of point/gradient pairs computed by this function is placed starting at `out`. The function returns an iterator that is placed past-the-end of the resulting sequence. The diff --git a/Interpolation/doc/Interpolation/CGAL/surface_neighbor_coordinates_3.h b/Interpolation/doc/Interpolation/CGAL/surface_neighbor_coordinates_3.h index bceef663df6..d7ff094fce6 100644 --- a/Interpolation/doc/Interpolation/CGAL/surface_neighbor_coordinates_3.h +++ b/Interpolation/doc/Interpolation/CGAL/surface_neighbor_coordinates_3.h @@ -4,7 +4,7 @@ namespace CGAL { \defgroup surface_neighbor_coordinates_3 surface_neighbor_coordinates_3 \ingroup PkgInterpolation2SurfaceNeighbor -The function `surface_neighbor_coordinates_3` computes natural neighbor coordinates for +The function `surface_neighbor_coordinates_3()` computes natural neighbor coordinates for surface points associated to a finite set of sample points issued from the surface. The coordinates are computed from the intersection of the Voronoi cell of the query point `p` with the tangent plane to the @@ -14,14 +14,13 @@ and in \cite bf-lcss-02,\cite cgal:f-csapc-03. The query point `p` needs to lie inside the convex hull of the projection of the sample points onto the tangent plane at `p`. -The functions `surface_neighbor_coordinates_certified_3` return, in +The functions `surface_neighbor_coordinates_certified_3()` return, in addition, a second Boolean value (the fourth value of the quadruple) 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$-nearest neighbor or a range search query, this permits to check +the range `[first, beyond)`. If the sample points are collected by a +`k`-nearest neighbor or a range search query, this permits to check whether the neighborhood which has been considered is large enough. ### Requirements ### @@ -29,24 +28,24 @@ whether the neighborhood which has been considered is large enough.
  1. `Dt` is equivalent to the class `Delaunay_triangulation_3`. -
  2. `OutputIterator::value_type` is equivalent to +
  3. The value type of `OutputIterator` is equivalent to `std::pair`, i.e. a pair associating a point and its natural neighbor coordinate.
  4. `ITraits` is equivalent to the class `Voronoi_intersection_2_traits_3`.
-\sa CGAL::linear_interpolation -\sa CGAL::sibson_c1_interpolation -\sa CGAL::farin_c1_interpolation -\sa CGAL::Voronoi_intersection_2_traits_3 -\sa CGAL::surface_neighbors_3 +\sa `CGAL::linear_interpolation()` +\sa `CGAL::sibson_c1_interpolation()` +\sa `CGAL::farin_c1_interpolation()` +\sa `CGAL::Voronoi_intersection_2_traits_3` +\sa `CGAL::surface_neighbors_3()` ### Implementation ### This functions construct the regular triangulation of the input points instantiated with `Voronoi_intersection_2_traits_3` or `ITraits` if provided. They return the result of the function call -`CGAL::regular_neighbor_coordinates_2` +`regular_neighbor_coordinates_2()` with the regular triangulation and `p` as arguments. */ @@ -54,15 +53,15 @@ with the regular triangulation and `p` as arguments. /*! The sample points \f$ \mathcal{P}\f$ are provided in the range -\f$ \left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$. -`InputIterator::value_type` is the point type +`[first`, beyond)`. +The value type of `InputIterator` is the point type `Kernel::Point_3`. The tangent plane is defined by the point `p` and the vector `normal`. The parameter `K` determines the kernel type that will instantiate the template parameter of `Voronoi_intersection_2_traits_3`. The natural neighbor coordinates for `p` are computed in the -power diagram that results from the intersection of the \f$ 3D\f$ Voronoi +power diagram that results from the intersection of the `3D` Voronoi diagram of \f$ \mathcal{P}\f$ with the tangent plane. The sequence of point/coordinate pairs that is computed by the function is placed starting at `out`. The function returns a triple with an @@ -93,7 +92,7 @@ ITraits& traits); /*! Similar to the first function. The additional fourth 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 by `(p,normal)`. It is @@ -109,8 +108,7 @@ 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 CGAL::Quadruple< OutputIterator, @@ -166,7 +164,7 @@ Dt::Geom_traits::Vector_3& normal, OutputIterator out, typename Dt::Cell_handle start = typename Dt::Cell_handle()); /*! -The same as above only that the parameter `traits` instantiates +The same as above only that the parameter traits instantiates the geometric traits class. Its type `ITraits` must be equivalent to `Voronoi_intersection_2_traits_3`. */ diff --git a/Interpolation/doc/Interpolation/Concepts/GradientFittingTraits.h b/Interpolation/doc/Interpolation/Concepts/GradientFittingTraits.h index 8d5631015c9..8691a0f7b70 100644 --- a/Interpolation/doc/Interpolation/Concepts/GradientFittingTraits.h +++ b/Interpolation/doc/Interpolation/Concepts/GradientFittingTraits.h @@ -3,7 +3,7 @@ \ingroup PkgInterpolation2Concepts \cgalconcept -The function `sibson_gradient_fitting` is parameterized by a +The function `sibson_gradient_fitting()` is parameterized by a traits class that defines the primitives used by the algorithm. The concept `GradientFittingTraits` defines this common set of requirements. @@ -11,10 +11,10 @@ concept `GradientFittingTraits` defines this common set of requirements. \sa `InterpolationTraits` \sa `CGAL::Interpolation_traits_2` -\sa CGAL::sibson_gradient_fitting -\sa CGAL::sibson_c1_interpolation -\sa CGAL::farin_c1_interpolation -\sa CGAL::quadratic_interpolation +\sa CGAL::sibson_gradient_fitting() +\sa CGAL::sibson_c1_interpolation() +\sa CGAL::farin_c1_interpolation() +\sa CGAL::quadratic_interpolation() */ diff --git a/Interpolation/doc/Interpolation/Concepts/InterpolationTraits.h b/Interpolation/doc/Interpolation/Concepts/InterpolationTraits.h index ed14c2bcf92..e47b2bdd5a6 100644 --- a/Interpolation/doc/Interpolation/Concepts/InterpolationTraits.h +++ b/Interpolation/doc/Interpolation/Concepts/InterpolationTraits.h @@ -11,10 +11,10 @@ defines the primitives used in the interpolation algorithms. The concept \hasModel `CGAL::Interpolation_gradient_fitting_traits_2` \sa `GradientFittingTraits` -\sa CGAL::sibson_c1_interpolation -\sa CGAL::sibson_gradient_fitting -\sa CGAL::farin_c1_interpolation -\sa CGAL::quadratic_interpolation +\sa CGAL::sibson_c1_interpolation() +\sa CGAL::sibson_gradient_fitting() +\sa CGAL::farin_c1_interpolation() +\sa CGAL::quadratic_interpolation() */ class InterpolationTraits { diff --git a/Interpolation/doc/Interpolation/Interpolation.txt b/Interpolation/doc/Interpolation/Interpolation.txt index 8deacc5f8a7..e745c3d1846 100644 --- a/Interpolation/doc/Interpolation/Interpolation.txt +++ b/Interpolation/doc/Interpolation/Interpolation.txt @@ -96,14 +96,15 @@ The interpolation package of \cgal provides functions to compute natural neighbor coordinates for \f$ 2D\f$ and \f$ 3D\f$ points with respect to Voronoi diagrams as well as with respect to power diagrams (only \f$ 2D\f$), i.e. for weighted points. Refer to the reference pages -`natural_neighbor_coordinates_2`, -`natural_neighbor_coordinates_3` and -`regular_neighbor_coordinates_2`. +`natural_neighbor_coordinates_2()`, +`sibson_natural_neighbor_coordinates_3()` +`laplace_natural_neighbor_coordinates_3()` and +`regular_neighbor_coordinates_2()`. In addition, the package provides functions to compute natural neighbor coordinates on well sampled point set surfaces. See Section \ref secsurface and the reference page -`CGAL::surface_neighbor_coordinates_3` for further information. +`surface_neighbor_coordinates_3()` for further information. ## Implementation ## @@ -198,7 +199,7 @@ upon the computation of regular neighbor coordinates with respect to the regular triangulation that is dual to \f$ {\rm Vor}(\mathcal{P}) \cap \mathcal{T}_x\f$, the intersection of \f$ \mathcal{T}_x\f$ and the Voronoi diagram of \f$ \mathcal{P}\f$, via the function -`CGAL::regular_neighbor_coordinates_2`. +`regular_neighbor_coordinates_2()`. Of course, we might introduce all data points \f$ \mathcal{P}\f$ into this regular triangulation. However, this is not necessary because we are @@ -333,7 +334,7 @@ of \f$ \mathbf{p_i}\f$ with respect to \f$ \mathbf{p_i}\f$ associated to \cgal provides functions to approximate the gradients of all data points that are inside the convex hull. There is one function for each -type of natural neighbor coordinate (i.e. `CGAL::natural_neighbor_coordinates_2`, `CGAL::regular_neighbor_coordinates_2`). +type of natural neighbor coordinate (i.e. `natural_neighbor_coordinates_2()`, `regular_neighbor_coordinates_2()`). \subsection subsecinterpol_examples Example for Linear Interpolation diff --git a/Interpolation/doc/Interpolation/PackageDescription.txt b/Interpolation/doc/Interpolation/PackageDescription.txt index 7e51111e395..44ecba42945 100644 --- a/Interpolation/doc/Interpolation/PackageDescription.txt +++ b/Interpolation/doc/Interpolation/PackageDescription.txt @@ -3,6 +3,7 @@ /// \defgroup PkgInterpolation2Concepts Concepts /// \ingroup PkgInterpolation2 + /// \defgroup PkgInterpolation2Interpolation Interpolation Functions /// \ingroup PkgInterpolation2 @@ -15,7 +16,6 @@ /*! \addtogroup PkgInterpolation2 -\todo check generated documentation \PkgDescriptionBegin{2D and Surface Function Interpolation,PkgInterpolation2Summary} \PkgPicture{interpolation.png} \PkgAuthor{Julia Flötotto} @@ -37,10 +37,10 @@ function gradients are known, we can exactly interpolate quadratic functions given barycentric coordinates. Any further properties of these interpolation functions depend on the properties of the barycentric coordinates. They are provided in this package under the -name `linear_interpolation` and -`quadratic_interpolation`. +name `CGAL::linear_interpolation()` and +`CGAL::quadratic_interpolation()`. -## Natural neighbor interpolation ## +## Natural Neighbor Interpolation ## Natural neighbor coordinates are defined by Sibson in 1980 and are based on the Voronoi diagram of the data points. Interpolation methods based on natural