int main()
{
Delaunay_triangulation dt;
for(int y=0; y<3; ++y)
for(int x=0; x<3; ++x)
dt.insert(K::Point_2(x, y));
// coordinates computation
K::Point_2 p(1.2, 0.7); // query point
Point_coordinate_vector coords;
CGAL::Triple<std::back_insert_iterator<Point_coordinate_vector>, K::FT, bool> result =
CGAL::natural_neighbor_coordinates_2(dt, p, std::back_inserter(coords));
if(!result.third)
{
std::cout << "The coordinate computation was not successful." << std::endl;
std::cout << "The point (" << p << ") lies outside the convex hull." << std::endl;
}
K::FT norm = result.second;
std::cout << "Coordinate computation successful." << std::endl;
std::cout << "Normalization factor: " << norm << std::endl;
std::cout << "Coordinates for point: (" << p << ") are the following: " << std::endl;
for(std::size_t i=0; i<coords.size(); ++i)
std::cout << " Point: (" << coords[i].first << ") coeff: " << coords[i].second << std::endl;
return EXIT_SUCCESS;
}
int main()
{
Delaunay_triangulation T;
Point_value_map value_function;
Point_vector_map gradient_function;
//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++) {
K::Point_2 p(x,y);
T.insert(p);
value_function.insert(std::make_pair(p,a + bx* x+ by*y + c*(x*x+y*y)));
}
}
sibson_gradient_fitting_nn_2(T, std::inserter(gradient_function,
gradient_function.begin()),
CGAL:: Data_access<Point_value_map>(value_function),
Traits());
for(Point_vector_map::iterator it = gradient_function.begin(); it != gradient_function.end(); ++it)
{
std::cout << it->first << " " << it->second << std::endl;
}
// coordinate computation
K::Point_2 p(1.6, 1.4);
std::vector< std::pair< Point, Coord_type > > coords;
Coord_type norm = CGAL::natural_neighbor_coordinates_2(T, p, std::back_inserter(coords)).second;
//Sibson interpolant: version without sqrt:
std::pair<Coord_type, bool> res =
CGAL::sibson_c1_interpolation_square(coords.begin(),
coords.end(), norm, p,
CGAL::Data_access<Point_value_map>(value_function),
CGAL::Data_access<Point_vector_map>(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;
}
int main()
{
Delaunay_triangulation T;
std::map<Point, Coord_type, K::Less_xy_2> function_values;
typedef CGAL::Data_access< std::map<Point, Coord_type, K::Less_xy_2 > >
Value_access;
Coord_type a(0.25), bx(1.3), by(-0.7);
for (int y=0 ; y<3 ; y++)
for (int x=0 ; x<3 ; x++){
K::Point_2 p(x,y);
T.insert(p);
function_values.insert(std::make_pair(p,a + bx* x+ by*y));
}
//coordinate computation
K::Point_2 p(1.3,0.34);
std::vector< std::pair< Point, Coord_type > > coords;
Coord_type norm =
CGAL::natural_neighbor_coordinates_2
(T, p,std::back_inserter(coords)).second;
Coord_type res = CGAL::linear_interpolation(coords.begin(), coords.end(),
norm,
Value_access(function_values));
std::cout << " Tested interpolation on " << p << " interpolation: "
<< res << " exact: " << a + bx* p.x()+ by* p.y()<< std::endl;
std::cout << "done" << std::endl;
//////////////////////////////////////////////////////////////////////
// own version
return 0;
}
tphysvar goft(const tphysvar logT, const tphysvar logrho, const cube gofttab)
{
// uses the log(T), because the G(T) is also stored using those values.
typedef CGAL::Delaunay_triangulation_2<K> Delaunay_triangulation;
typedef CGAL::Interpolation_traits_2<K> Traits;
typedef K::FT Coord_type;
typedef K::Point_2 Point;
std::map<Point, Coord_type, K::Less_xy_2> function_values;
typedef CGAL::Data_access< std::map<Point, Coord_type, K::Less_xy_2 > > Value_access;
tgrid grid=gofttab.readgrid();
tphysvar tempgrid=grid[0];
tphysvar rhogrid=grid[1];
tphysvar goftvec=gofttab.readvar(0);
// put the temperature and density grid from the gofttab into the CGAL data structures
vector<Point> delaunaygrid;
Point temporarygridpoint;
tphysvar::const_iterator tempit=tempgrid.begin();
tphysvar::const_iterator rhoit=rhogrid.begin();
tphysvar::const_iterator goftit=goftvec.begin();
for (; tempit != tempgrid.end(); ++tempit)
{
temporarygridpoint=Point(*tempit,*rhoit);
delaunaygrid.push_back(temporarygridpoint);
function_values.insert(std::make_pair(temporarygridpoint,Coord_type(*goftit)));
++rhoit;
++goftit;
}
Value_access tempmap=Value_access(function_values);
// compute the Delaunay triangulation
Delaunay_triangulation DT;
DT.insert(delaunaygrid.begin(),delaunaygrid.end());
tphysvar g;
int ng=logT.size();
// the reservation of the size is necessary, otherwise the vector reallocates in the openmp threads with segfaults as consequence
g.resize(ng);
cout << "Doing G(T) interpolation: " << flush;
// If MPI is available, we should divide the work between nodes, we can just use a geometric division by the commsize
int commrank,commsize;
#ifdef HAVEMPI
MPI_Comm_rank(MPI_COMM_WORLD,&commrank);
MPI_Comm_size(MPI_COMM_WORLD,&commsize);
#else
commrank = 0;
commsize = 1;
#endif
int mpimin, mpimax;
// MPE_Decomp1d decomposes a vector into more or less equal parts
// The only restriction is that it takes the vector from 1:ng, rather than 0:ng-1
// Therefore, the mpimin and mpimax are decreases afterwards.
MPE_Decomp1d(ng,commsize, commrank, &mpimin, &mpimax);
mpimin--;
mpimax--;
boost::progress_display show_progress((mpimax-mpimin+1)/10);
#ifdef _OPENMP
#pragma omp parallel for schedule(dynamic)
#endif
for (int i=mpimin; i<mpimax; i++)
{
Point p(logT[i],logrho[i]);
// a possible linear interpolation
// see http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Interpolation/Chapter_main.html#Subsection_70.3.3
// make sure to use small interpolation file. If not, this takes hours!
std::vector< std::pair< Point, Coord_type > > coords;
Coord_type norm = CGAL::natural_neighbor_coordinates_2(DT, p,std::back_inserter(coords)).second;
Coord_type res = CGAL::linear_interpolation(coords.begin(), coords.end(),
norm,
Value_access(function_values));
g[i]=res;
// let's not do nearest neighbour
// it is much faster than the linear interpolation
// but the spacing in temperature is too broad too handle this
/*Delaunay_triangulation::Vertex_handle v=DT.nearest_vertex(p);
Point nearest=v->point();
std::pair<Coord_type,bool> funcval=tempmap(nearest);
g[i]=funcval.first;*/
// This introduces a race condition between threads, but since it's only a counter, it doesn't really matter.
if ((i-mpimin)%10 == 0) ++show_progress;
}
cout << " Done!" << endl << flush;
return g;
}
void clear() { data.clear(); T.clear(); }
float interpolNearest(const Point &p) { return data[T.nearest_vertex(p)->point()]; }
