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1 ## Copyright (C) 2007 David Bateman |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 2, or (at your option) |
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8 ## any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, write to the Free |
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17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {@var{vi} =} interp3 (@var{x}, @var{y},@var{z}, @var{v}, @var{xi}, @var{yi}, @var{zi}) |
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22 ## @deftypefnx {Function File} {@var{vi} =} interp3 (@var{v}, @var{xi}, @var{yi}, @var{zi}) |
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23 ## @deftypefnx {Function File} {@var{vi} =} interp3 (@var{v}, @var{m}) |
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24 ## @deftypefnx {Function File} {@var{vi} =} interp3 (@var{v}) |
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25 ## @deftypefnx {Function File} {@var{vi} =} interp3 (@dots{}, @var{method}) |
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26 ## @deftypefnx {Function File} {@var{vi} =} interp3 (@dots{}, @var{method}, @var{extrapval}) |
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27 ## |
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28 ## Perform 3-dimensional interpolation. Each element of then 3-dimensional |
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29 ## array @var{v} represents a value at a location given by the parameters |
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30 ## @var{x}, @var{y}, and @var{z}. The parameters @var{x}, @var{x}, and |
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31 ## @var{z} are either 3-dimensional arrays of the same size as the array |
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32 ## @var{v} in the 'meshgrid' format or vectors. The parameters @var{xi}, etc |
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33 ## respect a similar format to @var{x}, etc, and they represent the points |
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34 ## at which the array @var{vi} is interpolated. |
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35 ## |
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36 ## If @var{x}, @var{y}, @var{z} are ommitted, they are assumed to be |
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37 ## @code{x = 1 : size (@var{v}, 2)}, @code{y = 1 : size (@var{v}, 1)} and |
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38 ## @code{z = 1 : size (@var{v}, 3)}. If @var{m} is specified, then |
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39 ## the interpolation adds a point half way between each of the interplation |
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40 ## points. This process is performed @var{m} times. If only @var{v} is |
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41 ## specified, then @var{m} is assumed to be @code{1}. |
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42 ## |
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43 ## Method is one of: |
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44 ## |
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45 ## @table @asis |
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46 ## @item 'nearest' |
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47 ## Return the nearest neighbour. |
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48 ## @item 'linear' |
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49 ## Linear interpolation from nearest neighbours. |
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50 ## @item 'cubic' |
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51 ## Cubic interpolation from four nearest neighbours (not implemented yet). |
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52 ## @item 'spline' |
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53 ## Cubic spline interpolation--smooth first and second derivatives |
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54 ## throughout the curve. |
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55 ## @end table |
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56 ## |
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57 ## The default method is 'linear'. |
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58 ## |
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59 ## If @var{extrap} is the string 'extrap', then extrapolate values beyond |
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60 ## the endpoints. If @var{extrap} is a number, replace values beyond the |
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61 ## endpoints with that number. If @var{extrap} is missing, assume NaN. |
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62 ## @seealso{interp1, interp2, spline, meshgrid} |
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63 ## @end deftypefn |
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64 |
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65 function vi = interp3 (varargin) |
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66 method = "linear"; |
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67 extrapval = NaN; |
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68 nargs = nargin; |
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69 |
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70 if (nargin < 1) |
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71 print_usage (); |
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72 endif |
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73 |
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74 if (ischar (varargin {end})) |
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75 method = varargin {end}; |
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76 nargs = nargs - 1; |
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77 elseif (ischar (varargin {end - 1})) |
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78 if (! isnumeric (varargin {end}) || ! isscalar (varargin {end})) |
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79 error ("extrapal is expected to be a numeric scalar"); |
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80 endif |
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81 extrapval = varargin {end}; |
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82 method = varargin {end - 1}; |
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83 nargs = nargs - 2; |
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84 endif |
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85 |
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86 if (nargs < 3 || (nargs == 4 && ! isvector (varargin {1}) && |
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87 nargs == (ndims (varargin {1}) + 1))) |
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88 if (ndims (v) != 3) |
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89 error ("expect 3-dimensional array of values"); |
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90 endif |
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91 x = varargin (2:4); |
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92 if (any (! cellfun (@isvector, x))) |
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93 for i = 2 : 3 |
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94 if (! size_equal (x{1}, x{i}) || ! size_equal (x{i}, v)) |
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95 error ("dimensional mismatch"); |
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96 endif |
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97 x{i} = permute (x{i}, [2, 1, 3]); |
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98 endfor |
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99 x{1} = permute (x{1}, [2, 1, 3]); |
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100 endif |
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101 v = permute (v, [2, 1, 3]); |
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102 vi = ipermute (interpn (v, x{:}, method, extrapval), [2, 1, 3]); |
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103 elseif (nargs == 7 && nargs == (2 * ndims (varargin {ceil (nargs / 2)})) + 1) |
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104 v = varargin {4}; |
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105 if (ndims (v) != 3) |
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106 error ("expect 3-dimensional array of values"); |
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107 endif |
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108 x = varargin (1:3); |
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109 if (any (! cellfun (@isvector, x))) |
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110 for i = 2 : 3 |
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111 if (! size_equal (x{1}, x{i}) || ! size_equal (x{i}, v)) |
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112 error ("dimensional mismatch"); |
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113 endif |
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114 x{i} = permute (x{i}, [2, 1, 3]); |
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115 endfor |
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116 x{1} = permute (x{1}, [2, 1, 3]); |
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117 endif |
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118 y = varargin (5:7); |
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119 if (any (! cellfun (@isvector, y))) |
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120 for i = 2 : 3 |
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121 if (! size_equal (y{1}, y{i})) |
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122 error ("dimensional mismatch"); |
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123 endif |
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124 y{i} = permute (y{i}, [2, 1, 3]); |
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125 endfor |
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126 y{1} = permute (y{1}, [2, 1, 3]); |
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127 endif |
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128 v = permute (v, [2, 1, 3]); |
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129 vi = ipermute (interpn (x{:}, v, y{:}, method, extrapval), [2,1,3]); |
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130 else |
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131 error ("wrong number or incorrectly formatted input arguments"); |
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132 endif |
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133 endfunction |
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134 |
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135 %!test |
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136 %! x = y = z = -1:1; |
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137 %! f = @(x,y,z) x.^2 - y - z.^2; |
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138 %! [xx, yy, zz] = meshgrid (x, y, z); |
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139 %! v = f (xx,yy,zz); |
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140 %! xi = yi = zi = -1:0.5:1; |
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141 %! [xxi, yyi, zzi] = meshgrid (xi, yi, zi); |
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142 %! vi = interp3(x, y, z, v, xxi, yyi, zzi); |
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143 %! [xxi, yyi, zzi] = ndgrid (xi, yi, zi); |
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144 %! vi2 = interpn(x, y, z, v, xxi, yyi, zzi); |
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145 %! assert (vi, vi2); |
