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////////////////////////////////////////////////////////////////////////
//
// Copyright (C) 2002-2021 The Octave Project Developers
//
// See the file COPYRIGHT.md in the top-level directory of this
// distribution or <https://octave.org/copyright/>.
//
// This file is part of Octave.
//
// Octave is free software: 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.
//
// Octave is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with Octave; see the file COPYING. If not, see
// <https://www.gnu.org/licenses/>.
//
////////////////////////////////////////////////////////////////////////
#if defined (HAVE_CONFIG_H)
# include "config.h"
#endif
#include <cmath>
#include "lo-ieee.h"
#include "defun.h"
#include "error.h"
#include "ovl.h"
inline double max (double a, double b, double c)
{
if (a < b)
return (b < c ? c : b);
else
return (a < c ? c : a);
}
inline double min (double a, double b, double c)
{
if (a > b)
return (b > c ? c : b);
else
return (a > c ? c : a);
}
#define REF(x,k,i) x(static_cast<octave_idx_type> (elem((k), (i))) - 1)
// for large data set the algorithm is very slow
// one should presort (how?) either the elements of the points of evaluation
// to cut down the time needed to decide which triangle contains the
// given point
// e.g., build up a neighbouring triangle structure and use a simplex-like
// method to traverse it
DEFUN (tsearch, args, ,
doc: /* -*- texinfo -*-
@deftypefn {} {@var{idx} =} tsearch (@var{x}, @var{y}, @var{t}, @var{xi}, @var{yi})
Search for the enclosing Delaunay convex hull.
For @code{@var{t} = delaunay (@var{x}, @var{y})}, finds the index in @var{t}
containing the points @code{(@var{xi}, @var{yi})}. For points outside the
convex hull, @var{idx} is NaN.
@seealso{delaunay, delaunayn}
@end deftypefn */)
{
if (args.length () != 5)
print_usage ();
const double eps = 1.0e-12;
const ColumnVector x (args(0).vector_value ());
const ColumnVector y (args(1).vector_value ());
const Matrix elem (args(2).matrix_value ());
const ColumnVector xi (args(3).vector_value ());
const ColumnVector yi (args(4).vector_value ());
const octave_idx_type nelem = elem.rows ();
ColumnVector minx (nelem);
ColumnVector maxx (nelem);
ColumnVector miny (nelem);
ColumnVector maxy (nelem);
for (octave_idx_type k = 0; k < nelem; k++)
{
minx(k) = min (REF (x, k, 0), REF (x, k, 1), REF (x, k, 2)) - eps;
maxx(k) = max (REF (x, k, 0), REF (x, k, 1), REF (x, k, 2)) + eps;
miny(k) = min (REF (y, k, 0), REF (y, k, 1), REF (y, k, 2)) - eps;
maxy(k) = max (REF (y, k, 0), REF (y, k, 1), REF (y, k, 2)) + eps;
}
const octave_idx_type np = xi.numel ();
ColumnVector values (np);
double x0, y0, a11, a12, a21, a22, det;
x0 = y0 = 0.0;
a11 = a12 = a21 = a22 = 0.0;
det = 0.0;
octave_idx_type k = nelem; // k is a counter of elements
for (octave_idx_type kp = 0; kp < np; kp++)
{
const double xt = xi(kp);
const double yt = yi(kp);
// check if last triangle contains the next point
if (k < nelem)
{
const double dx1 = xt - x0;
const double dx2 = yt - y0;
const double c1 = (a22 * dx1 - a21 * dx2) / det;
const double c2 = (-a12 * dx1 + a11 * dx2) / det;
if (c1 >= -eps && c2 >= -eps && (c1 + c2) <= (1 + eps))
{
values(kp) = double(k+1);
continue;
}
}
// it doesn't, so go through all elements
for (k = 0; k < nelem; k++)
{
octave_quit ();
if (xt >= minx(k) && xt <= maxx(k) && yt >= miny(k) && yt <= maxy(k))
{
// element inside the minimum rectangle: examine it closely
x0 = REF (x, k, 0);
y0 = REF (y, k, 0);
a11 = REF (x, k, 1) - x0;
a12 = REF (y, k, 1) - y0;
a21 = REF (x, k, 2) - x0;
a22 = REF (y, k, 2) - y0;
det = a11 * a22 - a21 * a12;
// solve the system
const double dx1 = xt - x0;
const double dx2 = yt - y0;
const double c1 = (a22 * dx1 - a21 * dx2) / det;
const double c2 = (-a12 * dx1 + a11 * dx2) / det;
if ((c1 >= -eps) && (c2 >= -eps) && ((c1 + c2) <= (1 + eps)))
{
values(kp) = double(k+1);
break;
}
} //endif # examine this element closely
} //endfor # each element
if (k == nelem)
values(kp) = lo_ieee_nan_value ();
} //endfor # kp
return ovl (values);
}
/*
%!shared x, y, tri
%! x = [-1;-1;1];
%! y = [-1;1;-1];
%! tri = [1, 2, 3];
%!assert (tsearch (x,y,tri,-1,-1), 1)
%!assert (tsearch (x,y,tri, 1,-1), 1)
%!assert (tsearch (x,y,tri,-1, 1), 1)
%!assert (tsearch (x,y,tri,-1/3, -1/3), 1)
%!assert (tsearch (x,y,tri, 1, 1), NaN)
%!error tsearch ()
*/
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