diff --git a/Interpolation/doc/Interpolation/CGAL/Interpolation_gradient_fitting_traits_2.h b/Interpolation/doc/Interpolation/CGAL/Interpolation_gradient_fitting_traits_2.h index 6fb18c1e68e..624549c84b3 100644 --- a/Interpolation/doc/Interpolation/CGAL/Interpolation_gradient_fitting_traits_2.h +++ b/Interpolation/doc/Interpolation/CGAL/Interpolation_gradient_fitting_traits_2.h @@ -4,133 +4,133 @@ namespace CGAL { /*! \ingroup PkgInterpolation2Interpolation -`Interpolation_gradient_fitting_traits_2` is a model for the concepts -`InterpolationTraits` and `GradientFittingTraits`. It can be -used to instantiate the geometric traits class of interpolation -functions and of Sibson's gradient fitting function when applied on -a function defined over a two-dimensional domain. The traits class -is templated by a kernel class `K`. +`Interpolation_gradient_fitting_traits_2` is a model for the concepts +`InterpolationTraits` and `GradientFittingTraits`. It can be +used to instantiate the geometric traits class of interpolation +functions and of Sibson's gradient fitting function when applied on +a function defined over a two-dimensional domain. The traits class +is templated by a kernel class `K`. \cgalModels `GradientFittingTraits` \cgalModels `InterpolationTraits` -\sa `InterpolationTraits` -\sa `GradientFittingTraits` -\sa `CGAL::Interpolation_traits_2` +\sa `InterpolationTraits` +\sa `GradientFittingTraits` +\sa `CGAL::Interpolation_traits_2` */ template< typename K > class Interpolation_gradient_fitting_traits_2 { public: -/// \name Types +/// \name Types /// @{ /*! -*/ -typedef K::FT FT; +*/ +typedef K::FT FT; /*! -*/ -typedef K::Point_2 Point_d; +*/ +typedef K::Point_2 Point_d; /*! -*/ -typedef K::Vector_2 Vector_d; +*/ +typedef K::Vector_2 Vector_d; /*! -*/ -typedef K::Aff_transformation_2 Aff_transformation_d; +*/ +typedef K::Aff_transformation_2 Aff_transformation_d; /*! -*/ -typedef K::Construct_vector_2 Construct_vector_d; +*/ +typedef K::Construct_vector_2 Construct_vector_d; /*! -*/ -typedef K::Construct_scaled_vector_2 -Construct_scaled_vector_d; +*/ +typedef K::Construct_scaled_vector_2 +Construct_scaled_vector_d; /*! -*/ -typedef K::Compute_squared_distance_2 -Compute_squared_distance_d; +*/ +typedef K::Compute_squared_distance_2 +Compute_squared_distance_d; /*! -*/ -typedef Construct_null_matrix_2 -Construct_null_matrix_d; +*/ +typedef Construct_null_matrix_2 +Construct_null_matrix_d; /*! -*/ -typedef Construct_scaling_matrix_2 -Construct_scaling_matrix_d; +*/ +typedef Construct_scaling_matrix_2 +Construct_scaling_matrix_d; /*! -*/ -typedef Construct_sum_matrix_2 Construct_sum_matrix_d; +*/ +typedef Construct_sum_matrix_2 Construct_sum_matrix_d; /*! -*/ -typedef Construct_outer_product_2 Construct_outer_product_d; +*/ +typedef Construct_outer_product_2 Construct_outer_product_d; -/// @} +/// @} -/// \name Operations +/// \name Operations /// @{ /*! -*/ -Construct_scaled_vector_d -construct_scaled_vector_d_object() const; +*/ +Construct_scaled_vector_d +construct_scaled_vector_d_object() const; /*! -*/ -Construct_vector_d -construct_vector_d_object()const; +*/ +Construct_vector_d +construct_vector_d_object()const; /*! -*/ -Compute_squared_distance_d -compute_squared_distance_d_object() const; +*/ +Compute_squared_distance_d +compute_squared_distance_d_object() const; /*! -*/ -Construct_null_matrix_d -construct_null_matrix_d_object() const; +*/ +Construct_null_matrix_d +construct_null_matrix_d_object() const; /*! -*/ -Construct_scaling_matrix_d -construct_scaling_matrix_d_object() const; +*/ +Construct_scaling_matrix_d +construct_scaling_matrix_d_object() const; /*! -*/ -Construct_sum_matrix_d -construct_sum_matrix_d_object() const; +*/ +Construct_sum_matrix_d +construct_sum_matrix_d_object() const; /*! -*/ -Construct_outer_product_d -construct_outer_product_d_object() const; +*/ +Construct_outer_product_d +construct_outer_product_d_object() const; /// @} diff --git a/Interpolation/doc/Interpolation/CGAL/Interpolation_traits_2.h b/Interpolation/doc/Interpolation/CGAL/Interpolation_traits_2.h index cbf1bd57e8b..918603b4869 100644 --- a/Interpolation/doc/Interpolation/CGAL/Interpolation_traits_2.h +++ b/Interpolation/doc/Interpolation/CGAL/Interpolation_traits_2.h @@ -4,80 +4,80 @@ namespace CGAL { /*! \ingroup PkgInterpolation2Interpolation -`Interpolation_traits_2` is a model for the concept -`InterpolationTraits` and can be used to instantiate the -geometric traits class of interpolation methods applied on a -bivariate function over a two-dimensional domain. The traits class -is templated by a kernel class `K`. +`Interpolation_traits_2` is a model for the concept +`InterpolationTraits` and can be used to instantiate the +geometric traits class of interpolation methods applied on a +bivariate function over a two-dimensional domain. The traits class +is templated by a kernel class `K`. \cgalModels `InterpolationTraits` -\sa `InterpolationTraits` -\sa `GradientFittingTraits` -\sa `CGAL::Interpolation_gradient_fitting_traits_2` +\sa `InterpolationTraits` +\sa `GradientFittingTraits` +\sa `CGAL::Interpolation_gradient_fitting_traits_2` */ template< typename K > class Interpolation_traits_2 { public: -/// \name Types +/// \name Types /// @{ /*! -*/ -typedef K::FT FT; +*/ +typedef K::FT FT; /*! -*/ -typedef K::Point_2 Point_d; +*/ +typedef K::Point_2 Point_d; /*! -*/ -typedef K::Vector_2 Vector_d; +*/ +typedef K::Vector_2 Vector_d; /*! -*/ -typedef K::Construct_vector_2 Construct_vector_d; +*/ +typedef K::Construct_vector_2 Construct_vector_d; /*! -*/ -typedef K::Construct_scaled_vector_2 -Construct_scaled_vector_d; +*/ +typedef K::Construct_scaled_vector_2 +Construct_scaled_vector_d; /*! -*/ -typedef K::Compute_squared_distance_2 -Compute_squared_distance_d; +*/ +typedef K::Compute_squared_distance_2 +Compute_squared_distance_d; -/// @} +/// @} -/// \name Operations +/// \name Operations /// @{ /*! -*/ -Construct_scaled_vector_d -construct_scaled_vector_d_object() const; +*/ +Construct_scaled_vector_d +construct_scaled_vector_d_object() const; /*! -*/ -Construct_vector_d -construct_vector_d_object()const; +*/ +Construct_vector_d +construct_vector_d_object()const; /*! -*/ -Compute_squared_distance_d -compute_squared_distance_d_object() const; +*/ +Compute_squared_distance_d +compute_squared_distance_d_object() const; /// @} 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 4ba9f144641..55df0e2ebd6 100644 --- a/Interpolation/doc/Interpolation/CGAL/Voronoi_intersection_2_traits_3.h +++ b/Interpolation/doc/Interpolation/CGAL/Voronoi_intersection_2_traits_3.h @@ -4,25 +4,25 @@ namespace CGAL { /*! \ingroup PkgInterpolation2SurfaceNeighbor -`Voronoi_intersection_2_traits_3` is a model for the concept +`Voronoi_intersection_2_traits_3` is a model for the concept `RegularTriangulationTraits_2`. 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 `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 -dual to the power diagram obtained by intersecting the -three-dimensional Voronoi diagram of the input points with the -plane. All predicates and constructions used in the computation of -the regular triangulation are formulated on the three dimensional -points without explicitly constructing the projected points and the -weights. This reduces the arithmetic demands. The traits class is +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 `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 +dual to the power diagram obtained by intersecting the +three-dimensional Voronoi diagram of the input points with the +plane. All predicates and constructions used in the computation of +the regular triangulation are formulated on the three dimensional +points without explicitly constructing the projected points and the +weights. This reduces the arithmetic demands. The traits class is templated by a kernel class `K` and inherits from it. \cgalModels `RegularTriangulationTraits_2` -\sa `CGAL::Regular_triangulation_2` +\sa `CGAL::Regular_triangulation_2` \sa `PkgInterpolationRegularNeighborCoordinates2` \sa PkgInterpolationSurfaceNeighborCoordinates3 @@ -38,8 +38,8 @@ public: /*! -*/ -typedef K::Point_3 Point_2; +*/ +typedef K::Point_3 Point_2; /*! @@ -48,28 +48,28 @@ typedef K::Weighted_point_3 Weighted_point_2; /*! -*/ -typedef K::Segment_3 Segment_2; +*/ +typedef K::Segment_3 Segment_2; /*! -*/ -typedef K::Triangle_3 Triangle_2; +*/ +typedef K::Triangle_3 Triangle_2; /*! -*/ -typedef K::Line_3 Line_2; +*/ +typedef K::Line_3 Line_2; /*! -*/ -typedef K::Ray_3 Ray_2; +*/ +typedef K::Ray_3 Ray_2; /*! -*/ -typedef K::Vector_3 Vector_2; +*/ +typedef K::Vector_3 Vector_2; /*! @@ -103,13 +103,13 @@ typedef K::Construct_ray_3 Construct_ray_2; /*! -*/ -typedef K::Construct_triangle_3 Construct_triangle_2; +*/ +typedef K::Construct_triangle_3 Construct_triangle_2; /*! -*/ -typedef K::Compare_distance_3 Compare_distance_2; +*/ +typedef K::Compare_distance_3 Compare_distance_2; /*! * Necessary for certificated coordinates / neighbors computation @@ -137,29 +137,29 @@ typedef K::Construct_circumcenter_3 Construct_circumcenter_2; /// @{ /*! -An instance of this function object class computes the square -root of the result of `K::Compute_squared_area_3`. -If the number type `FT` does not support the square root -operation, the result is cast to `double` -before computing the square root. -*/ +An instance of this function object class computes the square +root of the result of `K::Compute_squared_area_3`. +If the number type `FT` does not support the square root +operation, the result is cast to `double` +before computing the square root. +*/ typedef Compute_area_3 Compute_area_2; /*! -*/ +*/ typedef Orientation_with_normal_plane_2_3 Orientation_2; /*! -*/ +*/ typedef Side_of_plane_centered_sphere_2_3 Power_side_of_oriented_power_circle_2; /*! -*/ +*/ typedef Construct_plane_centered_circumcenter_3 -Construct_weighted_circumcenter_2; +Construct_weighted_circumcenter_2; /*! @@ -169,12 +169,12 @@ Construct_radical_axis_2; /*! -*/ +*/ typedef Compare_first_projection_3 Compare_x_2; /*! -*/ +*/ typedef Compare_second_projection_3 Compare_y_2; /*! @@ -190,13 +190,13 @@ typedef Compare_to_less Compare_y_2; /// @} -/// \name Creation +/// \name Creation /// @{ /*! The plane associated to the traits class contains `point` and has as normal vector `normal`. The optional kernel parameter `k` is the base class of the traits class. -*/ +*/ Voronoi_intersection_2_traits_3(const typename K::Point_3& point = typename K::Point_3(), const typename K::Vector_3& normal = NULL_VECTOR, const K& k = K()); diff --git a/Interpolation/doc/Interpolation/CGAL/interpolation_functions.h b/Interpolation/doc/Interpolation/CGAL/interpolation_functions.h index 352b7ea890f..b1b2305200f 100644 --- a/Interpolation/doc/Interpolation/CGAL/interpolation_functions.h +++ b/Interpolation/doc/Interpolation/CGAL/interpolation_functions.h @@ -4,56 +4,56 @@ namespace CGAL { /*! \ingroup PkgInterpolation2 -The struct `Data_access` implements a functor that allows to retrieve -data from an associative container. The functor keeps a reference to -the container. Given an instance of the container's key type, it -returns a pair of the container's value type and a Boolean indicating -whether the retrieval was successful. +The struct `Data_access` implements a functor that allows to retrieve +data from an associative container. The functor keeps a reference to +the container. Given an instance of the container's key type, it +returns a pair of the container's value type and a Boolean indicating +whether the retrieval was successful. -This class can be used to provide the values and gradients of the -interpolation functions. +This class can be used to provide the values and gradients of the +interpolation functions. \cgalHeading{Parameters} -The class -`Data_access` has the container type `Map` as template parameter. +The class +`Data_access` has the container type `Map` as template parameter. */ template< typename Map > struct Data_access : public CGAL::unary_function< typename Map::key_type, - std::pair< typename Map::mapped_type, bool> > { + std::pair< typename Map::mapped_type, bool> > { public: -/// \name Types +/// \name Types /// @{ /*! -*/ -typedef Map::mapped_type Data_type; +*/ +typedef Map::mapped_type Data_type; /*! -*/ -typedef Map::key_type Key_type; +*/ +typedef Map::key_type Key_type; -/// @} +/// @} -/// \name Creation +/// \name Creation /// @{ /*! -Introduces a `Data_access` to the container `map`. -*/ -Data_access(const Map& map); +Introduces a `Data_access` to the container `map`. +*/ +Data_access(const Map& map); /*! -If -there is an entry for `p` in the container `map`, then the -pair of `map.find(p)` and `true` is returned. Otherwise, the -Boolean value of the pair is `false`. -*/ -std::pair< Data_type, bool> operator()(const Key_type& p); +If +there is an entry for `p` in the container `map`, then the +pair of `map.find(p)` and `true` is returned. Otherwise, the +Boolean value of the pair is `false`. +*/ +std::pair< Data_type, bool> operator()(const Key_type& p); /// @} @@ -66,24 +66,24 @@ 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 `[first, beyond)`. \pre The range `[first, beyond)` contains either one or more than three elements. -The function `farin_c1_interpolation()` interpolates the function values and the -gradients that are provided by functors using the method described in \cgalCite{f-sodt-90}. +The function `farin_c1_interpolation()` interpolates the function values and the +gradients that are provided by functors using the method described in \cgalCite{f-sodt-90}. \cgalHeading{Parameters} -The value type of `RandomAccessIterator` is a pair -associating a point to a (non-normalized) barycentric coordinate. See -`sibson_c1_interpolation()` for the other parameters. +The value type of `RandomAccessIterator` is a pair +associating a point to a (non-normalized) barycentric coordinate. See +`sibson_c1_interpolation()` for the other parameters. \cgalHeading{Requirements} -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. +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::Data_access` +\sa `CGAL::linear_interpolation()` +\sa `CGAL::sibson_c1_interpolation()` \sa PkgInterpolationSibsonGradientFitting \sa `CGAL::Interpolation_traits_2` \sa `PkgInterpolationNaturalNeighborCoordinates2` @@ -105,26 +105,26 @@ Traits& traits); /*! \ingroup PkgInterpolation2Interpolation -The function `linear_interpolation()` computes the weighted sum of the function -values which must be provided via a functor. +The function `linear_interpolation()` computes the weighted sum of the function +values which must be provided via a functor. -\tparam ForwardIterator must have as value type a pair associating a point to a +\tparam ForwardIterator must have as value type a pair associating a point to a (non-normalized) barycentric coordinate, that is -`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. -\tparam Functor The type `Functor::argument_type` must be equivalent to -`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 -`std::iterator_traits::%value_type::second_type` and a constructor -with argument `0`. +`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. +\tparam Functor The type `Functor::argument_type` must be equivalent to +`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 +`std::iterator_traits::%value_type::second_type` and a constructor +with argument `0`. -A model of the functor is provided by the -struct `Data_access`. It must be instantiated accordingly with -an associative container (e.g. `std::map`) having the -point type as `key_type` and the function value type as +A model of the functor is provided by the +struct `Data_access`. It must be instantiated accordingly with +an associative container (e.g. `std::map`) having the +point type as `key_type` and the function value type as `mapped_type`. \param first,beyond are the iterator range for the weighted input points. @@ -134,11 +134,11 @@ function value and a Boolean for a given point. The Boolean indicates whether th 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 `[first, beyond)`. +range `[first, beyond)`. `function_value(q).second == true` for all points `q` of the point/coordinate pairs in the range `[first, beyond)`. -\sa `CGAL::Data_access` +\sa `CGAL::Data_access` \sa `PkgInterpolationNaturalNeighborCoordinates2` \sa `PkgInterpolationRegularNeighborCoordinates2` \sa PkgInterpolationSurfaceNeighborCoordinates3 @@ -157,20 +157,20 @@ norm, Functor function_values); The function `quadratic_interpolation()` 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 `[first, beyond)`. +pairs in the range `[first, beyond)`. \cgalHeading{Parameters and Template Parameters} -The same as for `sibson_c1_interpolation()` only that `Traits::FT` does not need -to provide the square root operation. +The same as for `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 `InterpolationTraits` +\sa `GradientFittingTraits` +\sa `CGAL::Data_access` \sa PkgInterpolationSibsonGradientFitting \sa `CGAL::linear_interpolation()` -\sa `CGAL::Interpolation_traits_2` -\sa `CGAL::Interpolation_gradient_fitting_traits_2` +\sa `CGAL::Interpolation_traits_2` +\sa `CGAL::Interpolation_gradient_fitting_traits_2` \sa `PkgInterpolationNaturalNeighborCoordinates2` \sa `PkgInterpolationRegularNeighborCoordinates2` \sa PkgInterpolationSurfaceNeighborCoordinates3 @@ -179,7 +179,7 @@ template < class ForwardIterator, class Functor, class GradFunctor, class Traits> typename Functor::result_type quadratic_interpolation(ForwardIterator first, ForwardIterator beyond, const typename std::iterator_traits:: -value_type::second_type& norm, +value_type::second_type& norm, const typename std::iterator_traits::value_type:: first_type& p, Functor function_value, GradFunctor function_gradient,const Traits& traits); @@ -189,62 +189,62 @@ function_gradient,const Traits& traits); \ingroup PkgInterpolation2Interpolation The function `sibson_c1_interpolation()` generates the interpolated -function value at the point `p`, using functors for the function values -and the gradients, by applying Sibson's \f$ Z^1\f$ interpolant. +function value at the point `p`, using functors for the function values +and the gradients, by applying Sibson's \f$ Z^1\f$ interpolant. 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. +interpolated function value as first and `true` as second value. -\tparam Traits must be a model of `InterpolationTraits`. -The number type `FT` provided by `Traits` must support -the square root operation `sqrt()`. -\tparam ForwardIterator must have as value type a pair associating a point to a +\tparam Traits must be a model of `InterpolationTraits`. +The number type `FT` provided by `Traits` must support +the square root operation `sqrt()`. +\tparam ForwardIterator must have as value type a pair associating a point to a (non-normalized) barycentric coordinate. -More precisely, `std::iterator_traits::%value_type::first_type` is -equivalent to `Traits::Point_d` and -`std::iterator_traits::%value_type::second_type` is equivalent to -`Traits::FT`. - -\tparam Functor must be a functor where `Functor::argument_type` must be equivalent to -`Traits::Point_d` and `Functor::result_type` is a pair of -the function value type and a Boolean. The function value type must -provide a multiplication and addition operation with the type +More precisely, `std::iterator_traits::%value_type::first_type` is +equivalent to `Traits::Point_d` and +`std::iterator_traits::%value_type::second_type` is equivalent to +`Traits::FT`. + +\tparam Functor must be a functor where `Functor::argument_type` must be equivalent to +`Traits::Point_d` and `Functor::result_type` is a pair of +the function value type and a Boolean. The function value type must +provide a multiplication and addition operation with the type `Traits::FT` as well as a constructor with argument `0`. -\tparam GradFunctor must be a functor where `GradFunctor::argument_type` must be equivalent to -`Traits::Point_d` and `Functor::result_type` is a pair of -the function's gradient type and a Boolean. The -function gradient type must provide a multiplication operation with -`Traits::Vector_d`. +\tparam GradFunctor must be a functor where `GradFunctor::argument_type` must be equivalent to +`Traits::Point_d` and `Functor::result_type` is a pair of +the function's gradient type and a Boolean. The +function gradient type must provide a multiplication operation with +`Traits::Vector_d`. -A model of the functor types `Functor` (resp. -`GradFunctor`) is provided by the struct `Data_access`. It -must be instantiated accordingly with an associative container -(e.g. `std::map`) having the point type as `key_type` -and the function value type (resp. function gradient type) as -`mapped_type`. +A model of the functor types `Functor` (resp. +`GradFunctor`) is provided by the struct `Data_access`. It +must be instantiated accordingly with an associative container +(e.g. `std::map`) having the point type as `key_type` +and the function value type (resp. function gradient type) as +`mapped_type`. -\param first,beyond is the iterator range of the barycentric -coordinates for the query point `p`. +\param first,beyond is the iterator range of the barycentric +coordinates for the query point `p`. \param norm is the normalization factor. `norm` \f$ \neq0\f$. \param p is the point at which the interpolated function value is generated -\param function_value is a functor that allows to access the value of the interpolated +\param function_value is a functor that allows to access the value of the interpolated function given a point. `function_value(q).second == true` for all points `q` of the point/coordinate pairs in the range `[first, beyond)` -\param function_gradient is a functor that allows to access the -function gradient given a point. +\param function_gradient is a functor that allows to access the +function gradient given a point. \param traits is an instance of the traits class -\sa `InterpolationTraits` -\sa `GradientFittingTraits` -\sa `CGAL::Data_access` +\sa `InterpolationTraits` +\sa `GradientFittingTraits` +\sa `CGAL::Data_access` \sa PkgInterpolationSibsonGradientFitting \sa `CGAL::linear_interpolation()` -\sa `CGAL::Interpolation_traits_2` -\sa `CGAL::Interpolation_gradient_fitting_traits_2` +\sa `CGAL::Interpolation_traits_2` +\sa `CGAL::Interpolation_gradient_fitting_traits_2` \sa `PkgInterpolationNaturalNeighborCoordinates2` \sa `PkgInterpolationRegularNeighborCoordinates2` \sa PkgInterpolationSurfaceNeighborCoordinates3 diff --git a/Interpolation/doc/Interpolation/CGAL/natural_neighbor_coordinates_2.h b/Interpolation/doc/Interpolation/CGAL/natural_neighbor_coordinates_2.h index 9e3cc5561d5..e8054986c35 100644 --- a/Interpolation/doc/Interpolation/CGAL/natural_neighbor_coordinates_2.h +++ b/Interpolation/doc/Interpolation/CGAL/natural_neighbor_coordinates_2.h @@ -4,44 +4,44 @@ namespace CGAL { \defgroup PkgInterpolationNaturalNeighborCoordinates2 CGAL::natural_neighbor_coordinates_2() \ingroup PkgInterpolation2NatNeighbor -The functions `natural_neighbor_coordinates_2()` compute natural neighbor coordinates, also -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. +The functions `natural_neighbor_coordinates_2()` compute natural neighbor coordinates, also +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. \cgalHeading{Requirements} -
    -
  1. `Dt` are equivalent to the class -`Delaunay_triangulation_2`. -
  2. The traits class `Traits` of `Dt` is a model of the -concept `DelaunayTriangulationTraits_2`. -Only the following members of this traits class are used: -
      -
    • `Construct_circumcenter_2` -
    • `FT` -
    • `Point_2` -
    • `construct_circumcenter_2_object` -
    • Additionally, `Traits` must meet the requirements for -the traits class of the `polygon_area_2()` function. -
    -
  3. The value type of `OutputIterator` is equivalent to -`std::pair`, i.e., a pair -associating a point and its natural neighbor coordinate. -
+
    +
  1. `Dt` are equivalent to the class +`Delaunay_triangulation_2`. +
  2. The traits class `Traits` of `Dt` is a model of the +concept `DelaunayTriangulationTraits_2`. +Only the following members of this traits class are used: +
      +
    • `Construct_circumcenter_2` +
    • `FT` +
    • `Point_2` +
    • `construct_circumcenter_2_object` +
    • Additionally, `Traits` must meet the requirements for +the traits class of the `polygon_area_2()` function. +
    +
  3. The value type of `OutputIterator` is equivalent to +`std::pair`, i.e., a pair +associating a point and its natural neighbor coordinate. +
\cgalHeading{Implementation} -This function computes the area of the sub-cells -stolen from the Voronoi cells of the points in `dt` when inserting -`p`. The total area of the Voronoi cell of `p` is also -computed and 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`. +This function computes the area of the sub-cells +stolen from the Voronoi cells of the points in `dt` when inserting +`p`. The total area of the Voronoi cell of `p` is also +computed and 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::linear_interpolation()` -\sa `CGAL::sibson_c1_interpolation()` +\sa `CGAL::sibson_c1_interpolation()` \sa PkgInterpolationSurfaceNeighborCoordinates3 \sa `PkgInterpolationRegularNeighborCoordinates2` @@ -50,9 +50,9 @@ value of the result triple is set to `false`. /*! computes the natural neighbor coordinates for `p` with respect to the -points in the two-dimensional Delaunay triangulation `dt`. +points in the two-dimensional Delaunay triangulation `dt`. -\tparam Dt must be of type `Delaunay_triangulation_2`. +\tparam Dt must be of type `Delaunay_triangulation_2`. \tparam OutputIterator must have the value type `std::pair`. The sequence of point/coordinate pairs @@ -65,7 +65,7 @@ the coordinate computation was successful. template < class Dt, class OutputIterator > CGAL::Triple< OutputIterator, typename Dt::Geom_traits::FT, bool > natural_neighbor_coordinates_2( - const Dt& dt, const typename Dt::Geom_traits::Point_2& p, + const Dt& dt, const typename Dt::Geom_traits::Point_2& p, OutputIterator out, typename Dt::Face_handle start = typename Dt::Face_handle()); /*! @@ -76,9 +76,9 @@ the triangulation. It is the result of the function `dt.get_boundary_of_conflicts(p,std::back_inserter(hole), start)`\endlink. */ template CGAL::Triple< OutputIterator, typename Dt::Geom_traits::FT, +class EdgeIterator > CGAL::Triple< OutputIterator, typename Dt::Geom_traits::FT, bool > natural_neighbor_coordinates_2( - const Dt& dt, const typename Dt::Geom_traits::Point_2& p, + const Dt& dt, const typename Dt::Geom_traits::Point_2& p, OutputIterator out, EdgeIterator hole_begin, EdgeIterator hole_end); /*! @@ -86,8 +86,8 @@ computes the natural neighbor coordinates of the point `vh->point()` with respect to the vertices of `dt` excluding `vh->point()`. The same as above for the remaining parameters. */ -template -CGAL::Triple< OutputIterator, typename Dt::Geom_traits::FT, bool > +template +CGAL::Triple< OutputIterator, typename Dt::Geom_traits::FT, bool > natural_neighbor_coordinates_2(const Dt& dt, typename Dt::Vertex_handle vh, OutputIterator out); /// @} diff --git a/Interpolation/doc/Interpolation/CGAL/regular_neighbor_coordinates_2.h b/Interpolation/doc/Interpolation/CGAL/regular_neighbor_coordinates_2.h index 3a5ca84988a..0fe6620d31b 100644 --- a/Interpolation/doc/Interpolation/CGAL/regular_neighbor_coordinates_2.h +++ b/Interpolation/doc/Interpolation/CGAL/regular_neighbor_coordinates_2.h @@ -4,35 +4,35 @@ namespace CGAL { \defgroup PkgInterpolationRegularNeighborCoordinates2 CGAL::regular_neighbor_coordinates_2() \ingroup PkgInterpolation2NatNeighbor -The functions `regular_neighbor_coordinates_2()` compute natural neighbor coordinates, also -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. +The functions `regular_neighbor_coordinates_2()` compute natural neighbor coordinates, also +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. \cgalHeading{Requirements} -
    -
  1. `Rt` are equivalent to the class -`Regular_triangulation_2`. -
  2. The traits class `Traits` of `Rt` is a model of the -concept `RegularTriangulationTraits_2`. It provides the number -type `FT` which is a model for `FieldNumberType` and it must -meet the requirements for the traits class of the +
      +
    1. `Rt` are equivalent to the class +`Regular_triangulation_2`. +
    2. The traits class `Traits` of `Rt` is a model of the +concept `RegularTriangulationTraits_2`. It provides the number +type `FT` which is a model for `FieldNumberType` and it must +meet the requirements for the traits class of the `polygon_area_2()` function. All CGAL kernels are models of this concept. -
    3. The value type of `OutputIterator` is equivalent to +
    4. The value type of `OutputIterator` is equivalent to `std::pair`, i.e.\ a pair -associating a point and its regular neighbor coordinate. -
    +associating a point and its regular neighbor coordinate. +
\cgalHeading{Implementation} -This function computes the areas stolen from the -Voronoi cells of points in `rt` by the insertion of `p`. The -total area of the Voronoi cell of `p` is also computed and -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`. +This function computes the areas stolen from the +Voronoi cells of points in `rt` by the insertion of `p`. The +total area of the Voronoi cell of `p` is also computed and +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 `PkgInterpolationNaturalNeighborCoordinates2` @@ -42,20 +42,20 @@ triple is set to `false`. /*! computes the regular neighbor coordinates for `p` with respect to the weighted points in the two-dimensional regular triangulation -`rt`. +`rt`. \tparam Rt must be a `Regular_triangulation_2`. \tparam OutputIterator must have the value type `std::pair`. The sequence of point/coordinate pairs that is computed by the function is placed -starting at `out`. +starting at `out`. The function returns a triple with an iterator that is placed past-the-end of the resulting sequence of point/coordinate pairs, the normalization factor of the coordinates and a Boolean value which is set to `true`, iff the coordinate computation was successful, i.e., if `p` lies inside the -convex hull of the points in `rt`. +convex hull of the points in `rt`. */ template < class Rt, class OutputIterator > CGAL::Triple< OutputIterator, typename Rt::Geom_traits::FT, bool > @@ -64,9 +64,9 @@ Rt::Weighted_point& p, OutputIterator out, typename Rt::Face_handle start = typename Rt::Face_handle()); /*! -The same as above. The iterator range `[hole_begin, hole_end)` determines -the boundary edges of the conflict zone of `p` in the triangulation `rt`. -\link Regular_triangulation_2::hidden_vertices_begin() `rt.hidden_vertices_begin()`\endlink and +The same as above. The iterator range `[hole_begin, hole_end)` determines +the boundary edges of the conflict zone of `p` in the 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 diff --git a/Interpolation/doc/Interpolation/CGAL/sibson_gradient_fitting.h b/Interpolation/doc/Interpolation/CGAL/sibson_gradient_fitting.h index 2ac00d622e0..8ecdd6e2d4f 100644 --- a/Interpolation/doc/Interpolation/CGAL/sibson_gradient_fitting.h +++ b/Interpolation/doc/Interpolation/CGAL/sibson_gradient_fitting.h @@ -14,25 +14,25 @@ coordinates. \cgalHeading{Requirements} -
    -
  1. 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 -`std::iterator_traits::%value_type::second_type` is a -number type. -
  2. `Functor::argument_type` must be equivalent to -`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 -`std::iterator_traits::%value_type::second_type`. -
  3. `Traits` is a model of the concept -`GradientFittingTraits`. -
+
    +
  1. 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 +`std::iterator_traits::%value_type::second_type` is a +number type. +
  2. `Functor::argument_type` must be equivalent to +`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 +`std::iterator_traits::%value_type::second_type`. +
  3. `Traits` is a model of the concept +`GradientFittingTraits`. +
\sa `CGAL::linear_interpolation()` -\sa `CGAL::sibson_c1_interpolation()` +\sa `CGAL::sibson_c1_interpolation()` \sa `CGAL::farin_c1_interpolation()` -\sa `CGAL::quadratic_interpolation()` +\sa `CGAL::quadratic_interpolation()` \sa `CGAL::Interpolation_gradient_fitting_traits_2` \sa `PkgInterpolationNaturalNeighborCoordinates2` \sa `PkgInterpolationRegularNeighborCoordinates2` @@ -40,9 +40,9 @@ provide a multiplication and addition operation with the type \cgalHeading{Implementation} -This function implements Sibson's gradient -estimation method based on natural neighbor coordinates -\cgalCite{s-bdnni-81}. +This function implements Sibson's gradient +estimation method based on natural neighbor coordinates +\cgalCite{s-bdnni-81}. */ /// @{ diff --git a/Interpolation/doc/Interpolation/CGAL/surface_neighbor_coordinates_3.h b/Interpolation/doc/Interpolation/CGAL/surface_neighbor_coordinates_3.h index 01af70aca08..e9d102915a2 100644 --- a/Interpolation/doc/Interpolation/CGAL/surface_neighbor_coordinates_3.h +++ b/Interpolation/doc/Interpolation/CGAL/surface_neighbor_coordinates_3.h @@ -4,15 +4,15 @@ namespace CGAL { \defgroup PkgInterpolationSurfaceNeighborCoordinates3 3D Surface Neighbor Coordinates Functions \ingroup PkgInterpolation2SurfaceNeighbor -The functions `surface_neighbor_coordinates_3()` compute 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 -surface at `p`. If the sampling is sufficiently dense, the -coordinate system meets the properties described in the manual pages -and in \cgalCite{bf-lcss-02},\cgalCite{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_3()` compute 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 +surface at `p`. If the sampling is sufficiently dense, the +coordinate system meets the properties described in the manual pages +and in \cgalCite{bf-lcss-02},\cgalCite{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 addition, a second Boolean value (the fourth value of the quadruple) @@ -25,28 +25,28 @@ whether the neighborhood which has been considered is large enough. \cgalHeading{Requirements} -
    -
  1. `Dt` is equivalent to the class -`Delaunay_triangulation_3`. -
  2. The value type of `OutputIterator` is equivalent to -`std::pair`, i.e.\ a pair -associating a point and its natural neighbor coordinate. -
  3. `ITraits` is equivalent to the class `Voronoi_intersection_2_traits_3`. -
+
    +
  1. `Dt` is equivalent to the class +`Delaunay_triangulation_3`. +
  2. The value type of `OutputIterator` is equivalent to +`std::pair`, i.e.\ a pair +associating a point and its natural neighbor coordinate. +
  3. `ITraits` is equivalent to the class `Voronoi_intersection_2_traits_3`. +
\sa `CGAL::linear_interpolation()` -\sa `CGAL::sibson_c1_interpolation()` +\sa `CGAL::sibson_c1_interpolation()` \sa `CGAL::farin_c1_interpolation()` \sa `CGAL::Voronoi_intersection_2_traits_3` \sa PkgInterpolationSurfaceNeighbors3 \cgalHeading{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 +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 `PkgInterpolationRegularNeighborCoordinates2` -with the regular triangulation and `p` as arguments. +with the regular triangulation and `p` as arguments. */ /// @{ @@ -58,7 +58,7 @@ 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 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 `3D` Voronoi @@ -150,11 +150,11 @@ of the conflict zone. It may be the result of the call `dt.locate(p)`. This function instantiates the template parameter `ITraits` to be `Voronoi_intersection_2_traits_3`. -This function allows to filter some potential neighbors of the -query point `p` from \f$ \mathcal{P}\f$ via its three-dimensional -Delaunay triangulation. All surface neighbors of `p` are -necessarily neighbors in the Delaunay triangulation of \f$ \mathcal{P} -\cup \{p\}\f$. +This function allows to filter some potential neighbors of the +query point `p` from \f$ \mathcal{P}\f$ via its three-dimensional +Delaunay triangulation. All surface neighbors of `p` are +necessarily neighbors in the Delaunay triangulation of \f$ \mathcal{P} +\cup \{p\}\f$. */ template < class Dt, class OutputIterator > CGAL::Triple< OutputIterator, typename Dt::Geom_traits::FT, bool > diff --git a/Interpolation/doc/Interpolation/CGAL/surface_neighbors_3.h b/Interpolation/doc/Interpolation/CGAL/surface_neighbors_3.h index 1b57660427d..7893e426862 100644 --- a/Interpolation/doc/Interpolation/CGAL/surface_neighbors_3.h +++ b/Interpolation/doc/Interpolation/CGAL/surface_neighbors_3.h @@ -4,16 +4,16 @@ namespace CGAL { \defgroup PkgInterpolationSurfaceNeighbors3 3D Surface Neighbors Functions \ingroup PkgInterpolation2SurfaceNeighbor -Given a set of sample points issued from a surface and a query point -`p`, the functions `surface_neighbors_3()` compute the neighbors of `p` on -the surface within the sample points. If the sampling is sufficiently -dense, the neighbors are provably close to the point `p` on the -surface (cf. the manual pages and -\cgalCite{bf-lcss-02},\cgalCite{cgal:f-csapc-03}). They are defined to -be the neighbors of `p` in the regular triangulation dual -to the power diagram which is equivalent to the intersection of the -Voronoi cell of the query point `p` with the tangent plane to the -surface at `p`. +Given a set of sample points issued from a surface and a query point +`p`, the functions `surface_neighbors_3()` compute the neighbors of `p` on +the surface within the sample points. If the sampling is sufficiently +dense, the neighbors are provably close to the point `p` on the +surface (cf. the manual pages and +\cgalCite{bf-lcss-02},\cgalCite{cgal:f-csapc-03}). They are defined to +be the neighbors of `p` in the regular triangulation dual +to the power diagram which is equivalent to the intersection of the +Voronoi cell of the query point `p` with the tangent plane to the +surface at `p`. The functions \c surface_neighbors_certified_3() also return, in addition, a Boolean value that certifies whether or not, the Voronoi @@ -26,30 +26,30 @@ been considered. \cgalHeading{Requirements} -
    -
  1. `Dt` is equivalent to the class -`Delaunay_triangulation_3`. -
  2. `OutputIterator::value_type` is equivalent to -`Dt::Point_3`, i.e.\ a point type. -
  3. `ITraits` is equivalent to the class `Voronoi_intersection_2_traits_3`. -
+
    +
  1. `Dt` is equivalent to the class +`Delaunay_triangulation_3`. +
  2. `OutputIterator::value_type` is equivalent to +`Dt::Point_3`, i.e.\ a point type. +
  3. `ITraits` is equivalent to the class `Voronoi_intersection_2_traits_3`. +
\sa `CGAL::Voronoi_intersection_2_traits_3` \sa PkgInterpolationSurfaceNeighborCoordinates3 \cgalHeading{Implementation} -These functions compute the regular triangulation of -the sample points and the point `p` using a traits class -equivalent to `Voronoi_intersection_2_traits_3`. They determine -the neighbors of `p` in this triangulation. The functions which -certify the result need to compute, in addition, the Voronoi vertices -of the cell of `p` in this diagram. +These functions compute the regular triangulation of +the sample points and the point `p` using a traits class +equivalent to `Voronoi_intersection_2_traits_3`. They determine +the neighbors of `p` in this triangulation. The functions which +certify the result need to compute, in addition, the Voronoi vertices +of the cell of `p` in this diagram. */ /// @{ /*! -The sample points \f$ \mathcal{P}\f$ are provided in the range +The sample points \f$ \mathcal{P}\f$ are provided in the range `[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 @@ -78,7 +78,7 @@ the user. `ITraits` must be equivalent to template OutputIterator surface_neighbors_3(InputIterator first, InputIterator beyond, -const typename ITraits::Point_2& p,OutputIterator out, +const typename ITraits::Point_2& p,OutputIterator out, const ITraits& traits); /*! @@ -142,11 +142,11 @@ for the search of the conflict zone. It may be the result of the call `dt.locate(p)`. This function instantiates the template parameter `ITraits` to be `Voronoi_intersection_2_traits_3`. -This function allows to filter some potential neighbors of the -query point `p` from \f$ \mathcal{P}\f$ via its three-dimensional -Delaunay triangulation. All surface neighbors of `p` are -necessarily neighbors in the Delaunay triangulation of \f$ \mathcal{P} -\cup \{p\}\f$. +This function allows to filter some potential neighbors of the +query point `p` from \f$ \mathcal{P}\f$ via its three-dimensional +Delaunay triangulation. All surface neighbors of `p` are +necessarily neighbors in the Delaunay triangulation of \f$ \mathcal{P} +\cup \{p\}\f$. */ template < class Dt, class OutputIterator > OutputIterator @@ -161,7 +161,7 @@ the geometric traits class. Its type `ITraits` must be equivalent to `Voronoi_intersection_2_traits_3`. */ template < class Dt, class OutputIterator, -class ITraits> +class ITraits> OutputIterator surface_neighbors_3(const Dt& dt, const typename ITraits::Point_2& p, OutputIterator out, const ITraits& traits, typename Dt::Cell_handle start = typename diff --git a/Interpolation/doc/Interpolation/Concepts/GradientFittingTraits.h b/Interpolation/doc/Interpolation/Concepts/GradientFittingTraits.h index d629a57376b..418a9d4afd2 100644 --- a/Interpolation/doc/Interpolation/Concepts/GradientFittingTraits.h +++ b/Interpolation/doc/Interpolation/Concepts/GradientFittingTraits.h @@ -3,38 +3,38 @@ \ingroup PkgInterpolation2Concepts \cgalConcept -\ref PkgInterpolationSibsonGradientFitting are parameterized by a -traits class that defines the primitives used by the algorithm. The -concept `GradientFittingTraits` defines this common set of requirements. +\ref PkgInterpolationSibsonGradientFitting are parameterized by a +traits class that defines the primitives used by the algorithm. The +concept `GradientFittingTraits` defines this common set of requirements. -\cgalHasModel `CGAL::Interpolation_gradient_fitting_traits_2` +\cgalHasModel `CGAL::Interpolation_gradient_fitting_traits_2` -\sa `InterpolationTraits` -\sa `CGAL::Interpolation_traits_2` +\sa `InterpolationTraits` +\sa `CGAL::Interpolation_traits_2` \sa \ref PkgInterpolationSibsonGradientFitting \sa `CGAL::sibson_c1_interpolation()` \sa `CGAL::farin_c1_interpolation()` -\sa `CGAL::quadratic_interpolation()` +\sa `CGAL::quadratic_interpolation()` */ class GradientFittingTraits { public: -/// \name Types +/// \name Types /// @{ /*! -The number type must follow the model -`FieldNumberType`. -*/ -typedef unspecified_type FT; +The number type must follow the model +`FieldNumberType`. +*/ +typedef unspecified_type FT; /*! -The point type on -which the function is defined and interpolated. -*/ -typedef unspecified_type Point_d; +The point type on +which the function is defined and interpolated. +*/ +typedef unspecified_type Point_d; /*! The weighted point type. @@ -42,23 +42,23 @@ The weighted point type. typedef unspecified_type Weighted_point_d; /*! -The corresponding vector type. -*/ -typedef unspecified_type Vector_d; +The corresponding vector type. +*/ +typedef unspecified_type Vector_d; /*! -defines a -matrix type. -Must provide the following member functions : +defines a +matrix type. +Must provide the following member functions : -`Aff_transformation tr.inverse ()` which gives the inverse -transformation, and +`Aff_transformation tr.inverse ()` which gives the inverse +transformation, and -`Aff_transformation tr.transform( Vector v)` which returns the -multiplication of `tr` with `v`. +`Aff_transformation tr.transform( Vector v)` which returns the +multiplication of `tr` with `v`. -*/ -typedef unspecified_type Aff_transformation_d; +*/ +typedef unspecified_type Aff_transformation_d; /*! A constructor object for `Point_d`. @@ -71,108 +71,108 @@ Provides : typedef unspecified_type Construct_point_d; /*! -A constructor object for -`Vector_d`. -Provides : +A constructor object for +`Vector_d`. +Provides : -`Vector_d operator() (Point_d a, Point_d b)` which produces the -vector `b - a` and +`Vector_d operator() (Point_d a, Point_d b)` which produces the +vector `b - a` and -`Vector_d operator() (Null_vector NULL_VECTOR)` which introduces -the null vector. -*/ -typedef unspecified_type Construct_vector_d; +`Vector_d operator() (Null_vector NULL_VECTOR)` which introduces +the null vector. +*/ +typedef unspecified_type Construct_vector_d; /*! -Constructor object for -`Vector_d`. -Provides : +Constructor object for +`Vector_d`. +Provides : -`Vector_d operator() (Vector_d v,FT scale)` which produces the -vector `v` scaled by a factor `scale`. -*/ -typedef unspecified_type Construct_scaled_vector_d; +`Vector_d operator() (Vector_d v,FT scale)` which produces the +vector `v` scaled by a factor `scale`. +*/ +typedef unspecified_type Construct_scaled_vector_d; /*! -Constructor object for -`Aff_transformation_d`. Provides : +Constructor object for +`Aff_transformation_d`. Provides : -`Aff_transformation_d operator()()` which introduces an affine -transformation whose matrix has only zero entries. -*/ -typedef unspecified_type Construct_null_matrix_d; +`Aff_transformation_d operator()()` which introduces an affine +transformation whose matrix has only zero entries. +*/ +typedef unspecified_type Construct_null_matrix_d; /*! -Constructor object for -`Aff_transformation_d`. Provides : +Constructor object for +`Aff_transformation_d`. Provides : -`Aff_transformation_d operator()(FT scale)` which introduces a -scaling by a scale factor `scale`. -*/ -typedef unspecified_type Construct_scaling_matrix_d; +`Aff_transformation_d operator()(FT scale)` which introduces a +scaling by a scale factor `scale`. +*/ +typedef unspecified_type Construct_scaling_matrix_d; /*! -Constructor object for -`Aff_transformation_d`. Provides : +Constructor object for +`Aff_transformation_d`. Provides : -`Aff_transformation_d operator()(Aff_transformation_d tr1, Aff_transformation_d tr2)` which returns the sum of the two matrices -representing `tr1` and `tr2`. -*/ -typedef unspecified_type Construct_sum_matrix_d; +`Aff_transformation_d operator()(Aff_transformation_d tr1, Aff_transformation_d tr2)` which returns the sum of the two matrices +representing `tr1` and `tr2`. +*/ +typedef unspecified_type Construct_sum_matrix_d; /*! -Constructor object for -`Aff_transformation_d`. Provides : +Constructor object for +`Aff_transformation_d`. Provides : -`Aff_transformation_d operator()(Vector v)` which returns the -outer product, i.e.\ the quadratic matrix `v`\f$ ^t\f$`v`. -*/ -typedef unspecified_type Construct_outer_product_d; +`Aff_transformation_d operator()(Vector v)` which returns the +outer product, i.e.\ the quadratic matrix `v`\f$ ^t\f$`v`. +*/ +typedef unspecified_type Construct_outer_product_d; -/// @} +/// @} -/// \name Creation +/// \name Creation /// @{ /*! -default constructor. -*/ -GradientFittingTraits(); +default constructor. +*/ +GradientFittingTraits(); -/// @} +/// @} -/// \name Operations +/// \name Operations /// The following functions that create instances of the above /// constructor object types must exist. /// @{ /*! -*/ -Construct_vector_d construct_vector_d_object(); +*/ +Construct_vector_d construct_vector_d_object(); /*! -*/ -Construct_scaled_vector_d -construct_scaled_vector_d_object(); +*/ +Construct_scaled_vector_d +construct_scaled_vector_d_object(); /*! -*/ -Construct_null_matrix_d construct_null_matrix_d_object(); +*/ +Construct_null_matrix_d construct_null_matrix_d_object(); /*! -*/ -Construct_sum_matrix_d -construct_sum_matrix_d_object(); +*/ +Construct_sum_matrix_d +construct_sum_matrix_d_object(); /*! -*/ -Construct_outer_product_d -construct_outer_product_d_object(); +*/ +Construct_outer_product_d +construct_outer_product_d_object(); /// @} diff --git a/Interpolation/doc/Interpolation/Concepts/InterpolationTraits.h b/Interpolation/doc/Interpolation/Concepts/InterpolationTraits.h index 299a3680da3..75ce2164149 100644 --- a/Interpolation/doc/Interpolation/Concepts/InterpolationTraits.h +++ b/Interpolation/doc/Interpolation/Concepts/InterpolationTraits.h @@ -3,14 +3,14 @@ \ingroup PkgInterpolation2Concepts \cgalConcept -Most interpolation functions are parameterized by a traits class that -defines the primitives used in the interpolation algorithms. The concept -`InterpolationTraits` defines this common set of requirements. +Most interpolation functions are parameterized by a traits class that +defines the primitives used in the interpolation algorithms. The concept +`InterpolationTraits` defines this common set of requirements. \cgalHasModel `CGAL::Interpolation_traits_2` \cgalHasModel `CGAL::Interpolation_gradient_fitting_traits_2` -\sa `GradientFittingTraits` +\sa `GradientFittingTraits` \sa `CGAL::sibson_c1_interpolation()` \sa \ref PkgInterpolationSibsonGradientFitting \sa `CGAL::farin_c1_interpolation()` @@ -20,84 +20,84 @@ defines the primitives used in the interpolation algorithms. The concept class InterpolationTraits { public: -/// \name Types +/// \name Types /// @{ /*! -The number type must follow the model -`FieldNumberType`. -*/ -typedef unspecified_type FT; +The number type must follow the model +`FieldNumberType`. +*/ +typedef unspecified_type FT; /*! -The point type on -which the function is defined and interpolated. -*/ -typedef unspecified_type Point_d; +The point type on +which the function is defined and interpolated. +*/ +typedef unspecified_type Point_d; /*! -The corresponding vector type. -*/ -typedef unspecified_type Vector_d; +The corresponding vector type. +*/ +typedef unspecified_type Vector_d; /*! -A constructor object for -`Vector_d`. -Provides : +A constructor object for +`Vector_d`. +Provides : -`Vector_d operator() (Point_d a, Point_d b)` which produces the -vector `b - a` and +`Vector_d operator() (Point_d a, Point_d b)` which produces the +vector `b - a` and -`Vector_d operator() (Null_vector NULL_VECTOR)` which introduces -the null vector. -*/ -typedef unspecified_type Construct_vector_d; +`Vector_d operator() (Null_vector NULL_VECTOR)` which introduces +the null vector. +*/ +typedef unspecified_type Construct_vector_d; /*! -Constructor object for -`Vector_d`. -Provides : +Constructor object for +`Vector_d`. +Provides : -`Vector_d operator() (Vector_d v,FT scale)` which produces the -vector `v` scaled by a factor `scale`. -*/ -typedef unspecified_type Construct_scaled_vector_d; +`Vector_d operator() (Vector_d v,FT scale)` which produces the +vector `v` scaled by a factor `scale`. +*/ +typedef unspecified_type Construct_scaled_vector_d; /*! -Constructor -object for `FT`. Provides the operator: +Constructor +object for `FT`. Provides the operator: -`FT operator() (Point_d a, Point_d b)` returning the squared -distance between `a` and `b`. -*/ -typedef unspecified_type Compute_squared_distance_d; +`FT operator() (Point_d a, Point_d b)` returning the squared +distance between `a` and `b`. +*/ +typedef unspecified_type Compute_squared_distance_d; /*! -default constructor. -*/ -InterpolationTraits(); +default constructor. +*/ +InterpolationTraits(); -/// @} +/// @} -/// \name Construction objects +/// \name Construction objects /// The following functions that create instances of the above /// constructor object types must exist. /// @{ /*! -*/ -Construct_vector_d construct_vector_d_object(); +*/ +Construct_vector_d construct_vector_d_object(); /*! -*/ -Construct_scaled_vector_d construct_scaled_vector_d_object(); +*/ +Construct_scaled_vector_d construct_scaled_vector_d_object(); /*! -*/ -Compute_squared_distance_d compute_squared_distance_d_object(); +*/ +Compute_squared_distance_d compute_squared_distance_d_object(); /// @}