CGAL::sibson_c1_interpolation

Definition

The function sibson_c1_interpolation interpolates the function values and the gradients that are provided by functors following the method described in [Sib81].

Parameters

#include <CGAL/interpolation_functions.h>

template < class ForwardIterator, class Functor, class GradFunctor, class Traits>
std::pair< typename Functor::result_type, bool>
	sibson_c1_interpolation ( ForwardIterator first, ForwardIterator beyond, typename std::iterator_traits<ForwardIterator>::value_type::second_type norm, typename std::iterator_traits<ForwardIterator>::value_type:: first_type p, Functor function_value, GradFunctor function_gradient, Traits traits)
		This function generates the interpolated function value at the point p using Sibson's $$Z1 interpolant [Sib81]. If the functor function_gradient cannot supply the gradient of a point, the function returns a pair where the boolean is set to false. If the interpolation was successful, the pair contains the interpolated function value as first and true as second value. Precondition: norm $$ 0. function_value(p).second == true for all points p of the point/coordinate pairs in the range $$[.first, beyond$$.).

Requirements

1. Traits is a model of the concept InterpolationTraits .
2. ForwardIterator::value_type is a point/coordinate pair. Precisely ForwardIterator::value_type::first_type is equivalent to Traits::Point_d and ForwardIterator::value_type::second_type is equivalent to Traits::FT.
3. 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.
4. 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.
5. 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. STL std::map) having the point type as key_type and the function value type (resp. function gradient type) as mapped_type.
6. The number type FT provided by Traits must support the square root operation sqrt().

template < class ForwardIterator, class Functor, class GradFunctor, class Traits>
typename Functor::result_type
	sibson_c1_interpolation_square ( ForwardIterator first, ForwardIterator beyond, typename std::iterator_traits<ForwardIterator>::value_type::second_type norm, Functor function_value, GradFunctor function_gradient, Traits traits)
		The same as above except that no square root operation is needed for FT.

See Also