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annotate libinterp/corefcn/tsearch.cc @ 25054:6652d3823428 stable

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maint: Update copyright dates in all source files.
author John W. Eaton <jwe@octave.org>
date Fri, 30 Mar 2018 09:19:05 -0400
parents 194eb4bd202b
children b2917b7858ba
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1 /*
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2
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3 Copyright (C) 2002-2018 Andreas Stahel
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4
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5 This file is part of Octave.
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6
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7 Octave is free software: you can redistribute it and/or modify it
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8 under the terms of the GNU General Public License as published by
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9 the Free Software Foundation, either version 3 of the License, or
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10 (at your option) any later version.
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11
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12 Octave is distributed in the hope that it will be useful, but
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13 WITHOUT ANY WARRANTY; without even the implied warranty of
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14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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15 GNU General Public License for more details.
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16
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17 You should have received a copy of the GNU General Public License
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18 along with Octave; see the file COPYING. If not, see
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19 <https://www.gnu.org/licenses/>.
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20
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21 */
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22
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23 // Author: Andreas Stahel <Andreas.Stahel@hta-bi.bfh.ch>
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24
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25 #if defined (HAVE_CONFIG_H)
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26 # include "config.h"
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27 #endif
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28
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29 #include <cmath>
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30
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31 #include "lo-ieee.h"
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32
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33 #include "defun.h"
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34 #include "error.h"
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35 #include "ovl.h"
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36
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37 inline double max (double a, double b, double c)
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38 {
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39 if (a < b)
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40 return (b < c ? c : b);
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41 else
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42 return (a < c ? c : a);
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43 }
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44
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45 inline double min (double a, double b, double c)
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46 {
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47 if (a > b)
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48 return (b > c ? c : b);
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49 else
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50 return (a > c ? c : a);
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51 }
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52
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53 #define REF(x,k,i) x(static_cast<octave_idx_type>(elem((k), (i))) - 1)
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54
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55 // for large data set the algorithm is very slow
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56 // one should presort (how?) either the elements of the points of evaluation
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57 // to cut down the time needed to decide which triangle contains the
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58 // given point
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59
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60 // e.g., build up a neighbouring triangle structure and use a simplex-like
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61 // method to traverse it
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62
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63 DEFUN (tsearch, args, ,
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64 doc: /* -*- texinfo -*-
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65 @deftypefn {} {@var{idx} =} tsearch (@var{x}, @var{y}, @var{t}, @var{xi}, @var{yi})
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66 Search for the enclosing Delaunay convex hull.
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67
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68 For @code{@var{t} = delaunay (@var{x}, @var{y})}, finds the index in @var{t}
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69 containing the points @code{(@var{xi}, @var{yi})}. For points outside the
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70 convex hull, @var{idx} is NaN.
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71 @seealso{delaunay, delaunayn}
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72 @end deftypefn */)
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73 {
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74 if (args.length () != 5)
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75 print_usage ();
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76
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77 const double eps = 1.0e-12;
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78
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79 const ColumnVector x (args(0).vector_value ());
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80 const ColumnVector y (args(1).vector_value ());
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81 const Matrix elem (args(2).matrix_value ());
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82 const ColumnVector xi (args(3).vector_value ());
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83 const ColumnVector yi (args(4).vector_value ());
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84
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85 const octave_idx_type nelem = elem.rows ();
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86
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87 ColumnVector minx (nelem);
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88 ColumnVector maxx (nelem);
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89 ColumnVector miny (nelem);
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90 ColumnVector maxy (nelem);
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91 for (octave_idx_type k = 0; k < nelem; k++)
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92 {
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93 minx(k) = min (REF (x, k, 0), REF (x, k, 1), REF (x, k, 2)) - eps;
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94 maxx(k) = max (REF (x, k, 0), REF (x, k, 1), REF (x, k, 2)) + eps;
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95 miny(k) = min (REF (y, k, 0), REF (y, k, 1), REF (y, k, 2)) - eps;
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96 maxy(k) = max (REF (y, k, 0), REF (y, k, 1), REF (y, k, 2)) + eps;
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97 }
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98
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99 const octave_idx_type np = xi.numel ();
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100 ColumnVector values (np);
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101
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102 double x0, y0, a11, a12, a21, a22, det;
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103 x0 = y0 = 0.0;
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104 a11 = a12 = a21 = a22 = 0.0;
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105 det = 0.0;
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106
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107 octave_idx_type k = nelem; // k is a counter of elements
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108 for (octave_idx_type kp = 0; kp < np; kp++)
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109 {
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110 const double xt = xi(kp);
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111 const double yt = yi(kp);
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112
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113 // check if last triangle contains the next point
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114 if (k < nelem)
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115 {
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116 const double dx1 = xt - x0;
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117 const double dx2 = yt - y0;
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118 const double c1 = (a22 * dx1 - a21 * dx2) / det;
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119 const double c2 = (-a12 * dx1 + a11 * dx2) / det;
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120 if (c1 >= -eps && c2 >= -eps && (c1 + c2) <= (1 + eps))
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121 {
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122 values(kp) = double(k+1);
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123 continue;
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124 }
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125 }
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126
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127 // it doesn't, so go through all elements
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128 for (k = 0; k < nelem; k++)
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129 {
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130 octave_quit ();
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131
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132 if (xt >= minx(k) && xt <= maxx(k) && yt >= miny(k) && yt <= maxy(k))
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133 {
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134 // element inside the minimum rectangle: examine it closely
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135 x0 = REF (x, k, 0);
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136 y0 = REF (y, k, 0);
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137 a11 = REF (x, k, 1) - x0;
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138 a12 = REF (y, k, 1) - y0;
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139 a21 = REF (x, k, 2) - x0;
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140 a22 = REF (y, k, 2) - y0;
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141 det = a11 * a22 - a21 * a12;
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142
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143 // solve the system
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144 const double dx1 = xt - x0;
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145 const double dx2 = yt - y0;
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146 const double c1 = (a22 * dx1 - a21 * dx2) / det;
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147 const double c2 = (-a12 * dx1 + a11 * dx2) / det;
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148 if ((c1 >= -eps) && (c2 >= -eps) && ((c1 + c2) <= (1 + eps)))
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149 {
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150 values(kp) = double(k+1);
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151 break;
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152 }
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153 } //endif # examine this element closely
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154 } //endfor # each element
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155
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156 if (k == nelem)
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157 values(kp) = lo_ieee_nan_value ();
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158
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159 } //endfor # kp
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160
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161 return ovl (values);
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162 }
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163
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164 /*
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165 %!shared x, y, tri
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166 %! x = [-1;-1;1];
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167 %! y = [-1;1;-1];
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168 %! tri = [1, 2, 3];
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169 %!assert (tsearch (x,y,tri,-1,-1), 1)
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170 %!assert (tsearch (x,y,tri, 1,-1), 1)
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171 %!assert (tsearch (x,y,tri,-1, 1), 1)
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172 %!assert (tsearch (x,y,tri,-1/3, -1/3), 1)
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173 %!assert (tsearch (x,y,tri, 1, 1), NaN)
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174
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175 %!error tsearch ()
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176 */