mirror of https://github.com/CGAL/cgal
58 lines
2.3 KiB
TeX
58 lines
2.3 KiB
TeX
% +------------------------------------------------------------------------+
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% | Reference manual page: farin_c1_interpolation.tex
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% +------------------------------------------------------------------------+
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% |
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% | August 2003 Julia Floetotto
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% | Package: Interpolation
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% |
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% |
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% +------------------------------------------------------------------------+
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\begin{ccRefFunction}{farin_c1_interpolation}
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\ccDefinition
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The function \ccRefName\ 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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\ccInclude{CGAL/interpolation_functions.h}
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\ccParameters \ccc{RandomAccessIterator::value_type} is a pair
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associating a point to a (non-normalized) barycentric coordinate. See
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\ccc{sibson_c1_interpolation} for the other parameters.
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\ccFunction{template < class RandomAccessIterator, class Functor,
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class GradFunctor, class Traits> typename Functor::result_type
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farin_c1_interpolation(RandomAccessIterator first,
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RandomAccessIterator beyond, const typename
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std::iterator_traits<RandomAccessIterator>::value_type::second_type&
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norm, Functor function_value, GradFunctor function_gradient, const
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Traits& traits);} {generates the interpolated function value
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computed by Farin's interpolant \cite{f-sodt-90}. See also
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\ccc{sibson_c1_interpolation}. \ccPrecond{\ccc{norm} $\neq 0$.
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\ccc{function_value(p).second == true} for all points \ccc{p} of
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the point/coordinate pairs in the range
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$\left[\right.$\ccc{first}, \ccc{beyond}$\left.\right)$.}
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\ccPrecond{The range $\left[\right.$ \ccc{first},
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\ccc{beyond}$\left.\right)$ contains either one or more than three
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elements. } }
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\ccHeading{Requirements}
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Same requirements as for \ccc{sibson_c1_interpolation} only the
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iterator must provide random access and \ccc{Traits::FT} does not need
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to provide the square root operation.
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\ccSeeAlso
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\ccRefIdfierPage{CGAL::Data_access<Map>}\\
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\ccRefIdfierPage{CGAL::linear_interpolation} \\
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\ccRefIdfierPage{CGAL::sibson_c1_interpolation} \\
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\ccRefIdfierPage{CGAL::sibson_gradient_fitting} \\
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\ccRefIdfierPage{CGAL::Interpolation_traits_2<K>} \\
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\ccRefIdfierPage{CGAL::natural_neighbor_coordinates_2}\\
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\ccRefIdfierPage{CGAL::regular_neighbor_coordinates_2} \\
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\ccRefIdfierPage{CGAL::surface_neighbor_coordinates_3}\\
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%\ccImplementation
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\end{ccRefFunction}
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