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
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
|
## Copyright (C) 1999-2013 Kai Habel
##
## 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
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{zi} =} griddata (@var{x}, @var{y}, @var{z}, @var{xi}, @var{yi})
## @deftypefnx {Function File} {@var{zi} =} griddata (@var{x}, @var{y}, @var{z}, @var{xi}, @var{yi}, @var{method})
## @deftypefnx {Function File} {[@var{xi}, @var{yi}, @var{zi}] =} griddata (@dots{})
##
## Generate a regular mesh from irregular data using interpolation.
## The function is defined by @code{@var{z} = f (@var{x}, @var{y})}.
## Inputs @code{@var{x}, @var{y}, @var{z}} are vectors of the same length
## or @code{@var{x}, @var{y}} are vectors and @code{@var{z}} is matrix.
##
## The interpolation points are all @code{(@var{xi}, @var{yi})}. If
## @var{xi}, @var{yi} are vectors then they are made into a 2-D mesh.
##
## The interpolation method can be @qcode{"nearest"}, @qcode{"cubic"} or
## @qcode{"linear"}. If method is omitted it defaults to @qcode{"linear"}.
## @seealso{griddata3, griddatan, delaunay}
## @end deftypefn
## Author: Kai Habel <kai.habel@gmx.de>
## Adapted-by: Alexander Barth <barth.alexander@gmail.com>
## xi and yi are not "meshgridded" if both are vectors
## of the same size (for compatibility)
function [rx, ry, rz] = griddata (x, y, z, xi, yi, method = "linear")
if (nargin < 5 || nargin > 7)
print_usage ();
endif
if (ischar (method))
method = tolower (method);
endif
## Meshgrid if x and y are vectors but z is matrix
if (isvector (x) && isvector (y) && all ([numel(y), numel(x)] == size (z)))
[x, y] = meshgrid (x, y);
endif
if (isvector (x) && isvector (y) && isvector (z))
if (! isequal (length (x), length (y), length (z)))
error ("griddata: X, Y, and Z must be vectors of the same length");
endif
elseif (! size_equal (x, y, z))
error ("griddata: lengths of X, Y must match the columns and rows of Z");
endif
## Meshgrid xi and yi if they are a row and column vector.
if (rows (xi) == 1 && columns (yi) == 1)
[xi, yi] = meshgrid (xi, yi);
elseif (isvector (xi) && isvector (yi))
## Otherwise, convert to column vectors
xi = xi(:);
yi = yi(:);
endif
if (! size_equal (xi, yi))
error ("griddata: XI and YI must be vectors or matrices of same size");
endif
x = x(:);
y = y(:);
z = z(:);
## Triangulate data.
tri = delaunay (x, y);
zi = NaN (size (xi));
if (strcmp (method, "cubic"))
error ("griddata: cubic interpolation not yet implemented");
elseif (strcmp (method, "nearest"))
## Search index of nearest point.
idx = dsearch (x, y, tri, xi, yi);
valid = !isnan (idx);
zi(valid) = z(idx(valid));
elseif (strcmp (method, "linear"))
## Search for every point the enclosing triangle.
tri_list = tsearch (x, y, tri, xi(:), yi(:));
## Only keep the points within triangles.
valid = !isnan (tri_list);
tri_list = tri_list(valid);
nr_t = rows (tri_list);
tri = tri(tri_list,:);
## Assign x,y,z for each point of triangle.
x1 = x(tri(:,1));
x2 = x(tri(:,2));
x3 = x(tri(:,3));
y1 = y(tri(:,1));
y2 = y(tri(:,2));
y3 = y(tri(:,3));
z1 = z(tri(:,1));
z2 = z(tri(:,2));
z3 = z(tri(:,3));
## Calculate norm vector.
N = cross ([x2-x1, y2-y1, z2-z1], [x3-x1, y3-y1, z3-z1]);
## Normalize.
N = diag (norm (N, "rows")) \ N;
## Calculate D of plane equation
## Ax+By+Cz+D = 0;
D = -(N(:,1) .* x1 + N(:,2) .* y1 + N(:,3) .* z1);
## Calculate zi by solving plane equation for xi, yi.
zi(valid) = -(N(:,1).*xi(:)(valid) + N(:,2).*yi(:)(valid) + D) ./ N(:,3);
else
error ("griddata: unknown interpolation METHOD");
endif
if (nargout == 3)
rx = xi;
ry = yi;
rz = zi;
elseif (nargout == 1)
rx = zi;
elseif (nargout == 0)
mesh (xi, yi, zi);
endif
endfunction
%!demo
%! clf;
%! colormap ("default");
%! x = 2*rand (100,1) - 1;
%! y = 2*rand (size (x)) - 1;
%! z = sin (2*(x.^2 + y.^2));
%! [xx,yy] = meshgrid (linspace (-1,1,32));
%! griddata (x,y,z,xx,yy);
%! title ("nonuniform grid sampled at 100 points");
%!demo
%! clf;
%! colormap ("default");
%! x = 2*rand (1000,1) - 1;
%! y = 2*rand (size (x)) - 1;
%! z = sin (2*(x.^2 + y.^2));
%! [xx,yy] = meshgrid (linspace (-1,1,32));
%! griddata (x,y,z,xx,yy);
%! title ("nonuniform grid sampled at 1000 points");
%!demo
%! clf;
%! colormap ("default");
%! x = 2*rand (1000,1) - 1;
%! y = 2*rand (size (x)) - 1;
%! z = sin (2*(x.^2 + y.^2));
%! [xx,yy] = meshgrid (linspace (-1,1,32));
%! griddata (x,y,z,xx,yy,"nearest");
%! title ("nonuniform grid sampled at 1000 points with nearest neighbor");
%!testif HAVE_QHULL
%! [xx,yy] = meshgrid (linspace (-1,1,32));
%! x = xx(:);
%! x = x + 10*(2*round (rand (size (x))) - 1) * eps;
%! y = yy(:);
%! y = y + 10*(2*round (rand (size (y))) - 1) * eps;
%! z = sin (2*(x.^2 + y.^2));
%! zz = griddata (x,y,z,xx,yy,"linear");
%! zz2 = sin (2*(xx.^2 + yy.^2));
%! zz2(isnan (zz)) = NaN;
%! assert (zz, zz2, 100*eps);
%% Test input validation
%!error griddata ()
%!error griddata (1)
%!error griddata (1,2)
%!error griddata (1,2,3)
%!error griddata (1,2,3,4)
%!error griddata (1,2,3,4,5,6,7)
%!error <vectors of the same length> griddata (1:3, 1:3, 1:4, 1:3, 1:3)
%!error <vectors of the same length> griddata (1:3, 1:4, 1:3, 1:3, 1:3)
%!error <vectors of the same length> griddata (1:4, 1:3, 1:3, 1:3, 1:3)
%!error <the columns and rows of Z> griddata (1:4, 1:3, ones (4,4), 1:3, 1:3)
%!error <the columns and rows of Z> griddata (1:4, 1:3, ones (3,5), 1:3, 1:3)
%!error <matrices of same size> griddata (1:3, 1:3, 1:3, 1:4, 1:3)
%!error <matrices of same size> griddata (1:3, 1:3, 1:3, 1:3, 1:4)
|
