libcgal-dev 4.2-5ubuntu1 / usr / include / CGAL / interpolation_functions.h

// Copyright (c) 2003  INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
// You can redistribute it and/or modify it under the terms of the GNU
// General Public License as published by the Free Software Foundation,
// either version 3 of the License, or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
//
//
// Author(s)     : Julia Floetotto

#ifndef CGAL_INTERPOLATION_FUNCTIONS_H
#define CGAL_INTERPOLATION_FUNCTIONS_H

#include <utility>
#include <CGAL/double.h>
#include <CGAL/use.h>

namespace CGAL {

//Functor class for accessing the function values/gradients
template< class Map >
struct Data_access : public std::unary_function< typename Map::key_type,
		     std::pair< typename Map::mapped_type, bool> >
{
  typedef typename Map::mapped_type Data_type;
  typedef typename Map::key_type  Key_type;

  Data_access< Map >(const Map& m): map(m){};

  std::pair< Data_type, bool>
  operator()(const Key_type& p) const {
    typename Map::const_iterator mit = map.find(p);
    if(mit!= map.end())
      return std::make_pair(mit->second, true);
    return std::make_pair(Data_type(), false);
  };

  const Map& map;
};

//the interpolation functions:
template < class ForwardIterator, class Functor>
typename Functor::result_type::first_type
linear_interpolation(ForwardIterator first, ForwardIterator beyond,
		     const typename
		     std::iterator_traits<ForwardIterator>::value_type::
		     second_type& norm, Functor function_value)
{
  CGAL_precondition(norm>0);
  typedef typename Functor::result_type::first_type Value_type;
  Value_type result(0);
  typename Functor::result_type val;
  for(; first !=beyond; ++first){
    val = function_value(first->first);
    CGAL_assertion(val.second);
    result += (first->second/norm) * val.first;
  }
  return result;
}


template < class ForwardIterator, class Functor, class GradFunctor,
           class Traits>
std::pair< typename Functor::result_type::first_type, bool>
quadratic_interpolation(ForwardIterator first, ForwardIterator beyond,
			const typename
			std::iterator_traits<ForwardIterator>::
			value_type::second_type& norm, const typename
			std::iterator_traits<ForwardIterator>::value_type::
			first_type& p, Functor function_value,
			GradFunctor function_gradient,
			const Traits& traits)
{
  CGAL_precondition(norm >0);
  typedef typename Functor::result_type::first_type Value_type;
  Value_type result(0);
  typename Functor::result_type f;
  typename GradFunctor::result_type grad;
  for(; first !=beyond; ++first){
    f = function_value(first->first);
    grad = function_gradient(first->first);
    //test if value and gradient are correctly retrieved:
    CGAL_assertion(f.second);
    if(!grad.second)
      return std::make_pair(Value_type(0), false);
    result += (first->second/norm)
      *( f.first + grad.first*
	 traits.construct_scaled_vector_d_object()
	 (traits.construct_vector_d_object()(first->first, p),0.5));
  }
  return std::make_pair(result, true);
}


template < class ForwardIterator, class Functor, class GradFunctor,
           class Traits>
std::pair< typename Functor::result_type::first_type, bool>
sibson_c1_interpolation(ForwardIterator first, ForwardIterator beyond,
			const typename
			std::iterator_traits<ForwardIterator>::
			value_type::second_type&
			norm, const typename
			std::iterator_traits<ForwardIterator>::value_type::
			first_type& p,
			Functor function_value,
			GradFunctor function_gradient,
			const Traits& traits)
{
  CGAL_precondition(norm >0);
  typedef typename Functor::result_type::first_type Value_type;
  typedef typename Traits::FT                       Coord_type;

  Coord_type term1(0), term2(term1), term3(term1), term4(term1);
  Value_type linear_int(0),gradient_int(0);
  typename Functor::result_type f;
  typename GradFunctor::result_type grad;

  for(; first !=beyond; ++first){
    f = function_value(first->first);
    grad = function_gradient(first->first);
    CGAL_assertion(f.second);
    if(!grad.second)
      //the values are not correct:
      return std::make_pair(Value_type(0), false);

    Coord_type coeff = first->second/norm;
    Coord_type squared_dist = traits.
      compute_squared_distance_d_object()(first->first, p);
    Coord_type dist = CGAL_NTS sqrt(squared_dist);

    if(squared_dist ==0){
      ForwardIterator it = first;
      CGAL_USE(it);
      CGAL_assertion(++it==beyond);
      return std::make_pair(f.first, true);
    }
    //three different terms to mix linear and gradient
    //interpolation
    term1 +=  coeff/dist;
    term2 +=  coeff * squared_dist;
    term3 +=  coeff * dist;

    linear_int += coeff * f.first;

    gradient_int += (coeff/dist)
      * (f.first + grad.first *
      traits.construct_vector_d_object()(first->first, p));
  }

  term4 = term3/ term1;
  gradient_int = gradient_int / term1;

  return std::make_pair((term4* linear_int + term2 * gradient_int)/
			(term4 + term2), true);
}

//this method works with rational number types:
//modification of Sibson's interpolant without sqrt
//following a proposition by Gunther Rote:
//
// the general scheme:
//  Coord_type inv_weight = f(dist); //i.e. dist^2
//   	term1 +=  coeff/inv_weight;
//	term2 +=  coeff * squared_dist;
//	term3 +=  coeff*(squared_dist/inv_weight);
// 	gradient_int +=  (coeff/inv_weight)*
// 	  (vh->get_value()+  vh->get_gradient()
// 	   *(p - vh->point()));

template < class ForwardIterator, class Functor, class GradFunctor,
           class Traits>
std::pair< typename Functor::result_type::first_type, bool>
sibson_c1_interpolation_square(ForwardIterator first, ForwardIterator
			       beyond, const typename
			       std::iterator_traits<ForwardIterator>::
			       value_type::second_type& norm,
			       const typename
			       std::iterator_traits<ForwardIterator>::
			       value_type::first_type& p,
			       Functor function_value,
			       GradFunctor function_gradient,
			       const Traits& traits)
{
  CGAL_precondition(norm >0);
  typedef typename Functor::result_type::first_type Value_type;
  typedef typename Traits::FT                       Coord_type;

  Coord_type term1(0), term2(term1), term3(term1), term4(term1);
  Value_type linear_int(0),gradient_int(0);
  typename Functor::result_type f;
  typename GradFunctor::result_type grad;

  for(; first !=beyond; ++first){
    f = function_value(first->first);
    grad = function_gradient(first->first);
    CGAL_assertion(f.second);
    if(!grad.second)
      //the gradient is not known
      return std::make_pair(Value_type(0), false);

    Coord_type coeff = first->second/norm;
    Coord_type squared_dist = traits.
      compute_squared_distance_d_object()(first->first, p);

    if(squared_dist ==0){
      ForwardIterator it = first;
      CGAL_USE(it);
      CGAL_assertion(++it==beyond);
      return std::make_pair(f.first,true);
    }
    //three different terms to mix linear and gradient
    //interpolation
    term1 +=  coeff/squared_dist;
    term2 +=  coeff * squared_dist;
    term3 +=  coeff;

    linear_int += coeff * f.first;

    gradient_int += (coeff/squared_dist)
      *(f.first + grad.first*
	traits.construct_vector_d_object()(first->first, p));
  }

  term4 = term3/ term1;
  gradient_int = gradient_int / term1;

  return std::make_pair((term4* linear_int + term2 * gradient_int)/
			(term4 + term2), true);
}


template < class RandomAccessIterator, class Functor, class
GradFunctor, class Traits>
std::pair< typename Functor::result_type::first_type, bool>
farin_c1_interpolation(RandomAccessIterator first,
		       RandomAccessIterator beyond,
		       const typename
		       std::iterator_traits<RandomAccessIterator>::
		       value_type::second_type& norm, const typename
		       std::iterator_traits<RandomAccessIterator>::
		       value_type::first_type& /*p*/,
		       Functor function_value, GradFunctor
		       function_gradient,
		       const Traits& traits)
{
  CGAL_precondition(norm >0);
  //the function value is available for all points
  //if a gradient value is not availble: function returns false
  typedef typename Functor::result_type::first_type  Value_type;
  typedef typename Traits::FT                        Coord_type;

  typename Functor::result_type f;
  typename GradFunctor::result_type grad;

  int n= static_cast<int>(beyond - first);
  if( n==1){
    f= function_value(first->first);
    CGAL_assertion(f.second);
    return std::make_pair(f.first, true);
  }

  //there must be one or at least three NN-neighbors:
  CGAL_assertion(n > 2);

  RandomAccessIterator it2, it;

  Value_type result(0);
  const Coord_type fac3(3);

  std::vector< std::vector<Value_type> >
    ordinates(n,std::vector<Value_type>(n, Value_type(0)));

  for(int i =0; i<n; ++i){
    it = first+i;
    Coord_type coord_i_square = CGAL_NTS square(it->second);

    //for later: the function value of it->first:
    f = function_value(it->first);
    CGAL_assertion(f.second);
    ordinates[i][i] = f.first;

    //control point = data point
    result += coord_i_square * it->second* ordinates[i][i];

    //compute tangent plane control point (one 2, one 1 entry)
    Value_type res_i(0);
    for(int j =0; j<n; ++j){
      if(i!=j){
	it2 = first+j;

	grad = function_gradient(it->first);
	if(!grad.second)
	  //the gradient is not known
	  return std::make_pair(Value_type(0), false);

	//ordinates[i][j] = (p_j - p_i) * g_i
	ordinates[i][j] = grad.first *
	  traits.construct_vector_d_object()(it->first,it2->first);

	// a point in the tangent plane:
	// 3( f(p_i) + (1/3)(p_j - p_i) * g_i)
	// => 3*f(p_i) + (p_j - p_i) * g_i
	res_i += (fac3 * ordinates[i][i] + ordinates[i][j])* it2->second;
      }
    }
    //res_i already multiplied by three
    result += coord_i_square *res_i;
  }

  //the third type of control points: three 1 entries i,j,k
  for(int i=0; i< n; ++i)
    for(int j=i+1; j< n; ++j)
      for(int k=j+1; k<n; ++k){
	// add 6* (u_i*u_j*u_k) * b_ijk
	//  b_ijk = 1.5 * a - 0.5*c
	//where
	//c : average of the three data control points
	//a : 1.5*a = 1/12 * (ord[i][j] + ord[i][k] + ord[j][i] +
	//            ord[j][k] + ord[k][i]+ ord[k][j])
	// =>  6 * b_ijk = 3*(f_i + f_j + f_k) + 0.5*a
	result += (Coord_type(2.0)*( ordinates[i][i]+ ordinates[j][j]+
				     ordinates[k][k])
		   + Coord_type(0.5)*(ordinates[i][j] + ordinates[i][k]
				      + ordinates[j][i] +
				      ordinates[j][k] + ordinates[k][i]+
				      ordinates[k][j]))
	  *(first+i)->second *(first+j)->second *(first+k)->second ;
      }

  return std::make_pair(result/(CGAL_NTS square(norm)*norm), true);
}

} //namespace CGAL

#endif // CGAL_INTERPOLATION_FUNCTIONS_H