1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
|
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/natural_neighbor_coordinates_2.h>
#include <CGAL/Interpolation_gradient_fitting_traits_2.h>
#include <CGAL/sibson_gradient_fitting.h>
#include <CGAL/interpolation_functions.h>
#include <CGAL/Triangulation_vertex_base_with_info_2.h>
#include <CGAL/Regular_triangulation_2.h>
#include <boost/iterator/function_output_iterator.hpp>
#include <iostream>
#include <iterator>
#include <utility>
#include <vector>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Interpolation_gradient_fitting_traits_2<K> Traits;
typedef K::FT Coord_type;
typedef K::Point_2 Bare_point;
typedef K::Weighted_point_2 Weighted_point;
typedef K::Vector_2 Vector;
template <typename V, typename G>
struct Value_and_gradient
{
Value_and_gradient() : value(), gradient(CGAL::NULL_VECTOR) {}
V value;
G gradient;
};
typedef CGAL::Triangulation_vertex_base_with_info_2<
Value_and_gradient<Coord_type, Vector>, K,
CGAL::Regular_triangulation_vertex_base_2<K> > Vb;
typedef CGAL::Regular_triangulation_face_base_2<K> Fb;
typedef CGAL::Triangulation_data_structure_2<Vb, Fb> Tds;
typedef CGAL::Regular_triangulation_2<K, Tds> Regular_triangulation;
typedef Regular_triangulation::Vertex_handle Vertex_handle;
int main()
{
Regular_triangulation rt;
auto value_function = [](const Vertex_handle& a) -> std::pair<Coord_type, bool>
{
return std::make_pair(a->info().value, true);
};
auto gradient_function = [](const Vertex_handle& a) -> std::pair<Vector, bool>
{
return std::make_pair(a->info().gradient, a->info().gradient != CGAL::NULL_VECTOR);
};
auto gradient_output_iterator
= boost::make_function_output_iterator
([](const std::pair<Vertex_handle, Vector>& p)
{
p.first->info().gradient = p.second;
});
// parameters for spherical function:
Coord_type a(0.25), bx(1.3), by(-0.7), c(0.2);
for (int y=0; y<4; y++) {
for (int x=0; x<4; x++) {
Weighted_point p(Bare_point(x,y), (x-y)/3. /*weight*/);
Vertex_handle vh = rt.insert(p);
Coord_type value = a + bx*x + by*y + c*(x*x+y*y);
vh->info().value = value;
}
}
CGAL::sibson_gradient_fitting_rn_2(rt,
gradient_output_iterator,
CGAL::Identity<std::pair<Vertex_handle, Vector> >(),
value_function,
Traits());
// coordinate computation
Weighted_point p(Bare_point(1.6, 1.4), -0.3 /*weight*/);
std::vector<std::pair<Vertex_handle, Coord_type> > coords;
typedef CGAL::Identity<std::pair<Vertex_handle, Coord_type> > Identity;
Coord_type norm = CGAL::regular_neighbor_coordinates_2(rt,
p,
std::back_inserter(coords),
Identity()).second;
// Sibson interpolant: version without sqrt:
std::pair<Coord_type, bool> res = CGAL::sibson_c1_interpolation_square(coords.begin(),
coords.end(),
norm,
p,
value_function,
gradient_function,
Traits());
if(res.second)
std::cout << "Tested interpolation on " << p
<< " interpolation: " << res.first << " exact: "
<< a + bx * p.x()+ by * p.y()+ c*(p.x()*p.x()+p.y()*p.y())
<< std::endl;
else
std::cout << "C^1 Interpolation not successful." << std::endl
<< " not all gradients are provided." << std::endl
<< " You may resort to linear interpolation." << std::endl;
return EXIT_SUCCESS;
}
|
