mirror of https://github.com/CGAL/cgal
66 lines
2.7 KiB
TeX
66 lines
2.7 KiB
TeX
% +------------------------------------------------------------------------+
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% | Reference manual page: quadratic_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}{quadratic_interpolation}
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\ccDefinition
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The function \ccRefName\ interpolates the function values and first degree
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functions defined from the function gradients. Both, function values and
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gradients, must be provided by functors.
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\ccInclude{CGAL/interpolation_functions.h}
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\ccParameters
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See \ccc{sibson_c1_interpolation}.
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\ccFunction{template < class ForwardIterator, class Functor, class
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GradFunctor, class Traits> typename Functor::result_type
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quadratic_interpolation(ForwardIterator first, ForwardIterator
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beyond, const typename std::iterator_traits<ForwardIterator>::
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value_type::second_type& norm, Functor function_value, GradFunctor
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function_gradient,const Traits& traits);} {
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% \ccc{ForwardIterator::value_type} is a pair associating a point to a
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% (non-normalized) barycentric coordinate. \ccc{norm} is the
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% normalization factor. \ccc{function_value} allows to access a value
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% given a point and \ccc{function_gradient} allows to access a
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% function gradient given a point.
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This function generates the
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interpolated function value as the weighted sum of the values plus a
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linear term in the gradient for each point of the point/coordinate
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pairs in the range $\left[\right.$ \ccc{first},
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\ccc{beyond}$\left.\right)$. 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
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\ccc{p} of the point/coordinate pairs in the range
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$\left[\right.$\ccc{first}, \ccc{beyond}$\left.\right)$.}}
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\ccHeading{Requirements} Same requirements as for
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\ccc{sibson_c1_interpolation} only that \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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\ccRefConceptPage{InterpolationTraits}\\
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\ccRefConceptPage{GradientFittingTraits}\\
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\ccRefIdfierPage{CGAL::Data_access<Map>}\\
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\ccRefIdfierPage{CGAL::sibson_gradient_fitting} \\
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\ccRefIdfierPage{CGAL::linear_interpolation} \\
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%\ccRefIdfierPage{CGAL::farin_c1_interpolation} \\
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%\ccRefIdfierPage{CGAL::quadratic_interpolation} \\
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\ccRefIdfierPage{CGAL::Interpolation_traits_2<K>} \\
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\ccRefIdfierPage{CGAL::Interpolation_gradient_fitting_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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