\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D and Surface Function Interpolation

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Interpolation/surface_neighbor_coordinates_3.cpp
// example with random points on a sphere
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/point_generators_3.h>
#include <CGAL/algorithm.h>
#include <CGAL/Origin.h>
#include <CGAL/surface_neighbor_coordinates_3.h>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef K::FT Coord_type;
typedef K::Point_3 Point_3;
typedef K::Vector_3 Vector_3;
typedef std::vector< std::pair< Point_3, K::FT > >
Point_coordinate_vector;
int main()
{
int n=100;
std::vector< Point_3> points;
points.reserve(n);
std::cout << "Generate " << n << " random points on a sphere."
<< std::endl;
CGAL::Random_points_on_sphere_3<Point_3> g(1);
CGAL::cpp11::copy_n( g, n, std::back_inserter(points));
Point_3 p(1, 0,0);
Vector_3 normal(p-CGAL::ORIGIN);
std::cout << "Compute surface neighbor coordinates for "
<< p << std::endl;
Point_coordinate_vector coords;
CGAL::Triple< std::back_insert_iterator<Point_coordinate_vector>,
K::FT, bool> result =
CGAL::surface_neighbor_coordinates_3(points.begin(), points.end(),
p, normal,
std::back_inserter(coords),
K());
if(!result.third){
//Undersampling:
std::cout << "The coordinate computation was not successful."
<< std::endl;
return 0;
}
K::FT norm = result.second;
std::cout << "Testing the barycentric property " << std::endl;
Point_3 b(0, 0,0);
for(std::vector< std::pair< Point_3, Coord_type > >::const_iterator
it = coords.begin(); it!=coords.end(); ++it)
b = b + (it->second/norm)* (it->first - CGAL::ORIGIN);
std::cout <<" weighted barycenter: " << b <<std::endl;
std::cout << " squared distance: " <<
CGAL::squared_distance(p,b) <<std::endl;
std::cout << "done" << std::endl;
return 0;
}