mirror of https://github.com/CGAL/cgal
finished
This commit is contained in:
Andreas Fabri
parent
d0931017d6
commit
5dd82a1b37
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@ -14,7 +14,7 @@ is templated by a kernel class `K`.
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\sa `InterpolationTraits`
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\sa `GradientFittingTraits`
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\sa CGAL::Interpolation_gradient_fitting_traits_2<K>
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\sa `CGAL::Interpolation_gradient_fitting_traits_2<K>`
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*/
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template< typename K >
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@ -9,7 +9,7 @@ namespace CGAL {
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`InterpolationTraits`. It can be used to instantiate the
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geometric traits class of a two-dimensional regular triangulation.
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A three-dimensional plane is defined by a point and a vector that
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are members of the traits class. The triangulation is defined on \f$ 3D\f$
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are members of the traits class. The triangulation is defined on `3D`
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points. It is the regular triangulation of the input points
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projected onto the plane and each weighted with the negative squared
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distance of the input point to the plane. It can be shown that it is
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@ -24,9 +24,9 @@ templated by a kernel class `K`.
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\models ::RegularTriangulationTraits_2
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\sa `RegularTriangulationTraits_2`
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\sa CGAL::Regular_triangulation_2<Gt, Tds>
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\sa CGAL::regular_neighbor_coordinates_2
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\sa CGAL::surface_neighbor_coordinates_3
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\sa `CGAL::Regular_triangulation_2<Gt, Tds>`
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\sa `CGAL::regular_neighbor_coordinates_2()`
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\sa `CGAL::surface_neighbor_coordinates_3()`
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*/
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template< typename K >
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@ -61,33 +61,33 @@ std::pair< Data_type, bool> operator()(const Key_type& p);
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/*!
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\ingroup PkgInterpolation2Interpolation
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generates the interpolated function value
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computed by Farin's interpolant \cite f-sodt-90.
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generates the interpolated function value computed by Farin's interpolant.
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\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$.
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\pre The range \f$ \left[\right.\f$ `first`, `beyond`\f$ \left.\right)\f$ contains either one or more than three element
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The function `farin_c1_interpolation` interpolates the function values and the
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The function `farin_c1_interpolation()` interpolates the function values and the
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gradients that are provided by functors using the method described in \cite f-sodt-90.
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### Parameters ###
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`RandomAccessIterator::value_type` is a pair
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The value type of `RandomAccessIterator` is a pair
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associating a point to a (non-normalized) barycentric coordinate. See
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`CGALL::sibson_c1_interpolation` for the other parameters.
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`sibson_c1_interpolation()` for the other parameters.
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### Requirements ###
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Same requirements as for `sibson_c1_interpolation` only the
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Same requirements as for `sibson_c1_interpolation()` only the
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iterator must provide random access and `Traits::FT` does not need
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to provide the square root operation.
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\sa `CGAL::Data_access<Map>`
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\sa CGAL::linear_interpolation
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\sa CGAL::sibson_c1_interpolation
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\sa CGAL::sibson_gradient_fitting
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\sa `CGAL::linear_interpolation()`
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\sa `CGAL::sibson_c1_interpolation()`
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\sa `CGAL::sibson_gradient_fitting()`
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\sa `CGAL::Interpolation_traits_2<K>`
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\sa CGAL::natural_neighbor_coordinates_2
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\sa CGAL::regular_neighbor_coordinates_2
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\sa CGAL::surface_neighbor_coordinates_3
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\sa `CGAL::natural_neighbor_coordinates_2()`
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\sa `CGAL::regular_neighbor_coordinates_2()`
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\sa `CGAL::surface_neighbor_coordinates_3()`
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s.
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*/
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@ -105,10 +105,10 @@ Traits& traits);
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/*!
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\ingroup PkgInterpolation2Interpolation
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The function `linear_interpolation` computes the weighted sum of the function
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The function `linear_interpolation()` computes the weighted sum of the function
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values which must be provided via a functor.
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`ForwardIterator::value_type` is a pair associating a point to a (non-normalized) barycentric
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The value type of `ForwardIterator` is a pair associating a point to a (non-normalized) barycentric
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coordinate. `norm` is the normalization factor. Given a point,
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the functor `function_values` allows to access a pair of a
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function value and a Boolean. The Boolean indicates whether the
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@ -121,28 +121,28 @@ range \f$ \left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$.
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### Requirements ###
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<OL>
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<LI>`ForwardIterator::value_type` is a pair of
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<LI>The value type of `ForwardIterator` is a pair of
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point/coordinate value, thus
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`ForwardIterator::value_type::first_type` is equivalent to a
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point and `ForwardIterator::value_type::second_type` is a
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`std::iterator_traits<ForwardIterator>::value_type::first_type` is equivalent to a
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point and `std::iterator_traits<ForwardIterator>::value_type::second_type` is a
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field number type.
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<LI>`Functor::argument_type` must be equivalent to
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`ForwardIterator::value_type::first_type` and
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`std::iterator_traits<ForwardIterator>::value_type::first_type` and
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`Functor::result_type` is a pair of the function value type
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and a Boolean value. The function value type must provide a
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multiplication and addition operation with the field number type
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`ForwardIterator::value_type::second_type` and a constructor
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`std::iterator_traits<ForwardIterator>::value_type::second_type` and a constructor
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with argument \f$ 0\f$. A model of the functor is provided by the
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struct `Data_access`. It must be instantiated accordingly with
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an associative container (e.g. \stl `std::map`) having the
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an associative container (e.g. `std::map`) having the
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point type as `key_type` and the function value type as
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`mapped_type`.
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</OL>
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\sa `CGAL::Data_access<Map>`
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\sa CGAL::natural_neighbor_coordinates_2
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\sa CGAL::regular_neighbor_coordinates_2
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\sa CGAL::surface_neighbor_coordinates_3
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\sa `CGAL::natural_neighbor_coordinates_2()`
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\sa `CGAL::regular_neighbor_coordinates_2()`
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\sa `CGAL::surface_neighbor_coordinates_3()`
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*/
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template < class ForwardIterator, class Functor> typename
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@ -173,19 +173,19 @@ See `sibson_c1_interpolation`.
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### Requirements ###
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Same requirements as for
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`sibson_c1_interpolation` only that `Traits::FT` does not need
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`sibson_c1_interpolation()` only that `Traits::FT` does not need
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to provide the square root operation.
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\sa `InterpolationTraits`
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\sa `GradientFittingTraits`
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\sa `CGAL::Data_access<Map>`
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\sa CGAL::sibson_gradient_fitting
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\sa CGAL::linear_interpolation
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\sa `CGAL::sibson_gradient_fitting()`
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\sa `CGAL::linear_interpolation()`
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\sa `CGAL::Interpolation_traits_2<K>`
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\sa `CGAL::Interpolation_gradient_fitting_traits_2<K>`
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\sa CGAL::natural_neighbor_coordinates_2
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\sa CGAL::regular_neighbor_coordinates_2
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\sa CGAL::surface_neighbor_coordinates_3
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\sa `CGAL::natural_neighbor_coordinates_2()`
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\sa `CGAL::regular_neighbor_coordinates_2()`
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\sa `CGAL::surface_neighbor_coordinates_3()`
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*/
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template < class ForwardIterator, class Functor, class
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GradFunctor, class Traits> typename Functor::result_type
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@ -219,7 +219,7 @@ interpolated function value as first and `true` as second value. \pre
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The template parameter `Traits` is to be
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instantiated with a model of `InterpolationTraits`.
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`ForwardIterator::value_type` is a pair associating a point to a
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The value type of `ForwardIterator` is a pair associating a point to a
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(non-normalized) barycentric coordinate. `norm` is the
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normalization factor. The range \f$ \left[\right.\f$
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`first`,`beyond`\f$ \left.\right)\f$ contains the barycentric
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@ -233,10 +233,10 @@ function gradient given a point.
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<OL>
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<LI>`Traits` is a model of the concept
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`InterpolationTraits`.
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<LI>`ForwardIterator::value_type` is a point/coordinate pair.
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Precisely `ForwardIterator::value_type::first_type` is
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<LI>The value type of `ForwardIterator` is a point/coordinate pair.
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Precisely `std::iterator_traits<ForwardIterator>::value_type::first_type` is
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equivalent to `Traits::Point_d` and
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`ForwardIterator::value_type::second_type` is equivalent to
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`std::iterator_traits<ForwardIterator>::value_type::second_type` is equivalent to
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`Traits::FT`.
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<LI>`Functor::argument_type` must be equivalent to
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`Traits::Point_d` and `Functor::result_type` is a pair of
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@ -261,13 +261,13 @@ the square root operation `sqrt()`.
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\sa `InterpolationTraits`
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\sa `GradientFittingTraits`
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\sa `CGAL::Data_access<Map>`
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\sa CGAL::sibson_gradient_fitting
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\sa CGAL::linear_interpolation
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\sa `CGAL::sibson_gradient_fitting()`
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\sa `CGAL::linear_interpolation()`
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\sa `CGAL::Interpolation_traits_2<K>`
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\sa `CGAL::Interpolation_gradient_fitting_traits_2<K>`
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\sa CGAL::natural_neighbor_coordinates_2
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\sa CGAL::regular_neighbor_coordinates_2
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\sa CGAL::surface_neighbor_coordinates_3
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\sa `CGAL::natural_neighbor_coordinates_2()`
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\sa `CGAL::regular_neighbor_coordinates_2()`
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\sa `CGAL::surface_neighbor_coordinates_3()`
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*/
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template < class ForwardIterator, class Functor, class
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GradFunctor, class Traits> std::pair< typename Functor::result_type,
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@ -282,7 +282,7 @@ traits);
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/*!
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\ingroup PkgInterpolation2Interpolation
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The same as `CGAL::sibson_interpolation` except that no square root
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The same as `sibson_interpolation()` except that no square root
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operation is needed for FT.
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*/
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template < class ForwardIterator, class Functor, class
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@ -5,7 +5,7 @@ namespace CGAL {
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\ingroup PkgInterpolation2NatNeighbor
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The function `natural_neighbor_coordinates_2` computes natural neighbor coordinates, also
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called Sibson's coordinates, for \f$ 2D\f$ points provided a two-dimensional
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called Sibson's coordinates, for `2D` points provided a two-dimensional
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triangulation and a query point in the convex hull of the vertices
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of the triangulation.
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@ -40,10 +40,10 @@ convex hull, the coordinate values cannot be computed and the third
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value of the result triple is set to `false`.
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\sa CGAL::linear_interpolation
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\sa CGAL::sibson_c1_interpolation
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\sa CGAL::surface_neighbor_coordinates_3
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\sa CGAL::regular_neighbor_coordinates_2
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\sa `CGAL::linear_interpolation()`
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\sa `CGAL::sibson_c1_interpolation()`
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\sa `CGAL::surface_neighbor_coordinates_3()`
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\sa `CGAL::regular_neighbor_coordinates_2()`
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*/
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/// @{
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@ -71,8 +71,8 @@ natural_neighbor_coordinates_2(
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The same as above. `hole_begin` and `hole_end` determines the
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iterator range over the boundary edges of the conflict zone of `p` in
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the triangulation. It is the result of the function
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`T.get_boundary_of_conflicts(p,std::back_inserter(hole), start)`, see
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`Delaunay_triangulation_2<Traits, Tds>`.
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\link Delaunay_triangulation_2::get_boundary_of_conflicts()
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`dt.get_boundary_of_conflicts(p,std::back_inserter(hole), start)`\endlink.
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*/
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template <class Dt, class OutputIterator,
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class EdgeIterator > CGAL::Triple< OutputIterator, typename Dt::Geom_traits::FT,
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@ -7,7 +7,7 @@ namespace CGAL {
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Given a 3D point `p` and a 3D Delaunay triangulation `dt`,
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this function calculates the natural neighbors and coordinates of `p` with regard of `dt`.
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\tparam `OutputIterator` must have value type
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\tparam OutputIterator must have value type
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`std::pair<Dt::Vertex_handle, Dt::Geom_traits::FT>`
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Result :
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@ -5,7 +5,7 @@ namespace CGAL {
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\ingroup PkgInterpolation2NatNeighbor
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The function `regular_neighbor_coordinates_2` computes natural neighbor coordinates, also
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called Sibson's coordinates, for weighted \f$ 2D\f$ points provided a
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called Sibson's coordinates, for weighted `2D` points provided a
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two-dimensional regular triangulation and a (weighted) query point
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inside the convex hull of the vertices of the triangulation. We call these
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coordinates regular neighbor coordinates.
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@ -21,7 +21,7 @@ type `FT` which is a model for `FieldNumberType` and it must
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meet the requirements for the traits class of the
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`polygon_area_2` function. A model of this traits class is
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`Regular_triangulation_euclidean_traits_2<K, Weight>`.
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<LI>`OutputIterator::value_type` is equivalent to
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<LI>The value type of `OutputIterator` is equivalent to
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`std::pair<Rt::Weighted_point, Rt::Geom_traits::FT>`, i.e. a pair
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associating a point and its regular neighbor coordinate.
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</OL>
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@ -35,7 +35,7 @@ returned by the function. If `p` lies outside the convex hull, the
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coordinate values cannot be computed and the third value of the result
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triple is set to `false`.
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\sa CGAL::natural_neighbor_coordinates_2
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\sa `CGAL::natural_neighbor_coordinates_2()`
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*/
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/// @{
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@ -64,12 +64,12 @@ Rt::Face_handle start = typename Rt::Face_handle());
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/*!
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The same as above. `hole_begin` and `hole_end` determines the iterator
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range over the boundary edges of the conflict zone of `p` in the
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triangulation `rt`. `hidden_vertices_begin` and `hidden_vertices_end`
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triangulation `rt`.
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\link Regular_triangulation_2::hidden_vertices_begin() `rt.hidden_vertices_begin()`\endlink and
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\link Regular_triangulation_2::hidden_vertices_end() `rt.hidden_vertices_end()`\endlink
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determines the iterator range over the hidden vertices of the conflict
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zone of `p` in`rt`. It is the result of the function
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`T.get_boundary_of_conflicts(p,std::back_inserter(hole),
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std::back_inserter(hidden_vertices), start)`, see
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`Regular_triangulation_2<Traits, Tds>`.
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\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.
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*/
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template <class Rt, class OutputIterator,
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class EdgeIterator, class VertexIterator > CGAL::Triple<
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@ -4,7 +4,7 @@ namespace CGAL {
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\defgroup sibson_gradient_fitting sibson_gradient_fitting
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\ingroup PkgInterpolation2Interpolation
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The function `sibson_gradient_fitting` approximates the gradient of a
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The function `sibson_gradient_fitting()` approximates the gradient of a
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function at a point `p` given natural neighbor coordinates for `p` and
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its neighbors' function values. The approximation method is described
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in \cite s-bdnni-81. Further functions are provided to fit the
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@ -15,28 +15,28 @@ coordinates.
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### Requirements ###
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<OL>
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<LI>`ForwardIterator::value_type` is a pair of point/coordinate
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value, thus `ForwardIterator::value_type::first_type` is
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<LI>The value type of `ForwardIterator` is a pair of point/coordinate
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value, thus `std::iterator_traits<ForwardIterator>::value_type::first_type` is
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equivalent to a point and
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`ForwardIterator::value_type::second_type` is a
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`std::iterator_traits<ForwardIterator>::value_type::second_type` is a
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number type.
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<LI>`Functor::argument_type` must be equivalent to
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`ForwardIterator::value_type::first_type` and
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`std::iterator_traits<ForwardIterator>::value_type::first_type` and
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`Functor::result_type` is the function value type. It must
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provide a multiplication and addition operation with the type
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`ForwardIterator::value_type::second_type`.
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`std::iterator_traits<ForwardIterator>::value_type::second_type`.
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<LI>`Traits` is a model of the concept
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`GradientFittingTraits`.
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</OL>
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\sa CGAL::linear_interpolation
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\sa CGAL::sibson_c1_interpolation
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\sa CGAL::farin_c1_interpolation
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\sa CGAL::quadratic_interpolation
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\sa `CGAL::linear_interpolation()`
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\sa `CGAL::sibson_c1_interpolation()`
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\sa `CGAL::farin_c1_interpolation()`
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\sa `CGAL::quadratic_interpolation()`
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\sa `CGAL::Interpolation_gradient_fitting_traits_2<K>`
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\sa CGAL::natural_neighbor_coordinates_2
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\sa CGAL::regular_neighbor_coordinates_2
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\sa CGAL::surface_neighbor_coordinates_3
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\sa `CGAL::natural_neighbor_coordinates_2()`
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\sa `CGAL::regular_neighbor_coordinates_2()`
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\sa `CGAL::surface_neighbor_coordinates_3()`
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### Implementation ###
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@ -67,8 +67,8 @@ Functor f, const Traits& traits);
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/*!
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estimates the function gradients at all vertices of `dt` that lie
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inside the convex hull using the coordinates computed by the
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function `CGAL::natural_neighbor_coordinates_2`.
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`OutputIterator::value_type` is a pair associating a point to a
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function `natural_neighbor_coordinates_2()`.
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The value type of `OutputIterator` is a pair associating a point to a
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vector. The sequence of point/gradient pairs computed by this
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function is placed starting at `out`. The function returns an
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iterator that is placed past-the-end of the resulting sequence. The
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@ -82,8 +82,8 @@ dt, OutputIterator out, Functor f, const Traits& traits);
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/*!
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estimates the function gradients at all vertices of `rt` that lie
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inside the convex hull using the coordinates computed by the
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function `CGAL::regular_neighbor_coordinates_2`.
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`OutputIterator::value_type` is a pair associating a point to a
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function `regular_neighbor_coordinates_2()`.
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The value type of `OutputIterator` is a pair associating a point to a
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vector. The sequence of point/gradient pairs computed by this
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function is placed starting at `out`. The function returns an
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iterator that is placed past-the-end of the resulting sequence. The
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|
|
|||
|
|
@ -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$-nearest neighbor or a range search query, this permits to check
|
||||
the range `[first, beyond)`. If the sample points are collected by a
|
||||
`k`-nearest neighbor or a range search query, this permits to check
|
||||
whether the neighborhood which has been considered is large enough.
|
||||
|
||||
### Requirements ###
|
||||
|
|
@ -29,24 +28,24 @@ whether the neighborhood which has been considered is large enough.
|
|||
<OL>
|
||||
<LI>`Dt` is equivalent to the class
|
||||
`Delaunay_triangulation_3`.
|
||||
<LI>`OutputIterator::value_type` is equivalent to
|
||||
<LI>The value type of `OutputIterator` is equivalent to
|
||||
`std::pair<Dt::Point_3, Dt::Geom_traits::FT>`, i.e. a pair
|
||||
associating a point and its natural neighbor coordinate.
|
||||
<LI>`ITraits` is equivalent to the class `Voronoi_intersection_2_traits_3<K>`.
|
||||
</OL>
|
||||
|
||||
\sa CGAL::linear_interpolation
|
||||
\sa CGAL::sibson_c1_interpolation
|
||||
\sa CGAL::farin_c1_interpolation
|
||||
\sa CGAL::Voronoi_intersection_2_traits_3<K>
|
||||
\sa CGAL::surface_neighbors_3
|
||||
\sa `CGAL::linear_interpolation()`
|
||||
\sa `CGAL::sibson_c1_interpolation()`
|
||||
\sa `CGAL::farin_c1_interpolation()`
|
||||
\sa `CGAL::Voronoi_intersection_2_traits_3<K>`
|
||||
\sa `CGAL::surface_neighbors_3()`
|
||||
|
||||
### Implementation ###
|
||||
|
||||
This functions construct the regular triangulation of the input points
|
||||
instantiated with `Voronoi_intersection_2_traits_3<Kernel>` or `ITraits` if provided.
|
||||
They return the result of the function call
|
||||
`CGAL::regular_neighbor_coordinates_2`
|
||||
`regular_neighbor_coordinates_2()`
|
||||
with the regular triangulation and `p` as arguments.
|
||||
|
||||
*/
|
||||
|
|
@ -54,15 +53,15 @@ with the regular triangulation and `p` as arguments.
|
|||
|
||||
/*!
|
||||
The sample points \f$ \mathcal{P}\f$ are provided in the range
|
||||
\f$ \left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$.
|
||||
`InputIterator::value_type` is the point type
|
||||
`[first`, beyond)`.
|
||||
The value type of `InputIterator` is the point type
|
||||
`Kernel::Point_3`. The tangent plane is defined by the point
|
||||
`p` and the vector `normal`. The parameter `K`
|
||||
determines the kernel type that will instantiate
|
||||
the template parameter of `Voronoi_intersection_2_traits_3<K>`.
|
||||
|
||||
The natural neighbor coordinates for `p` are computed in the
|
||||
power diagram that results from the intersection of the \f$ 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 <class OutputIterator,
|
||||
class InputIterator, class Kernel> 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<K>`.
|
||||
*/
|
||||
|
|
|
|||
|
|
@ -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<K>`
|
||||
\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()
|
||||
|
||||
*/
|
||||
|
||||
|
|
|
|||
|
|
@ -11,10 +11,10 @@ defines the primitives used in the interpolation algorithms. The concept
|
|||
\hasModel `CGAL::Interpolation_gradient_fitting_traits_2<K>`
|
||||
|
||||
\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 {
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
|
|
|||
Loading…
Reference in New Issue