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surfnorm.m: Return unnormalized vectors for Matlab compatibility. * NEWS: Announce change. surfnorm.m: Return unnormalized vectors if output arguments requested. If plotting immediately, new algorithm for determining normals takes into account the data aspect ratio of the plot.
author Rik <rik@octave.org>
date Mon, 25 May 2015 16:48:47 -0700
parents 9fc020886ae9
children 5b7643257978
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rev   line source
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4197fc428c7d maint: Update copyright notices for 2015.
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1 ## Copyright (C) 2007-2015 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 3 of the License, or (at
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8 ## your option) 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, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} surfnorm (@var{x}, @var{y}, @var{z})
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21 ## @deftypefnx {Function File} {} surfnorm (@var{z})
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22 ## @deftypefnx {Function File} {} surfnorm (@dots{}, @var{prop}, @var{val}, @dots{})
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23 ## @deftypefnx {Function File} {} surfnorm (@var{hax}, @dots{})
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24 ## @deftypefnx {Function File} {[@var{nx}, @var{ny}, @var{nz}] =} surfnorm (@dots{})
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25 ## Find the vectors normal to a meshgridded surface.
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26 ##
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27 ## If @var{x} and @var{y} are vectors, then a typical vertex is
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28 ## (@var{x}(j), @var{y}(i), @var{z}(i,j)). Thus, columns of @var{z} correspond
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29 ## to different @var{x} values and rows of @var{z} correspond to different
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30 ## @var{y} values. If only a single input @var{z} is given then @var{x} is
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31 ## taken to be @code{1:rows (@var{z})} and @var{y} is
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32 ## @code{1:columns (@var{z})}.
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33 ##
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34 ## If no return arguments are requested, a surface plot with the normal
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35 ## vectors to the surface is plotted.
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36 ##
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37 ## Any property/value input pairs are assigned to the surface object.
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38 ##
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39 ## If the first argument @var{hax} is an axes handle, then plot into this axis,
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40 ## rather than the current axes returned by @code{gca}.
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41 ##
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42 ## If output arguments are requested then the components of the normal
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43 ## vectors are returned in @var{nx}, @var{ny}, and @var{nz} and no plot is
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44 ## made. The normal vectors are unnormalized (magnitude != 1). To normalize,
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45 ## use
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46 ##
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47 ## @example
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48 ## mag = sqrt (nx.^2 + ny.^2 + nz.^2);
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49 ## nx ./= len; ny ./= len; nz ./= len;
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50 ## @end example
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51 ##
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52 ## An example of the use of @code{surfnorm} is
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53 ##
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54 ## @example
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55 ## surfnorm (peaks (25));
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56 ## @end example
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57 ##
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58 ## Algorithm: The normal vectors are calculated by taking the cross product
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59 ## of the diagonals of each of the quadrilateral faces in the meshgrid to find
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60 ## the normal vectors at the center of each face. Next, for each meshgrid
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61 ## point the four nearest normal vectors are averaged to obtain the final
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62 ## normal to the surface at the meshgrid point.
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63 ##
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64 ## For surface objects, the @qcode{"VertexNormals"} property contains
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65 ## equivalent information, except possibly near the boundary of the surface
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66 ## where different interpolation schemes may yield slightly different values.
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67 ##
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68 ## @seealso{isonormals, quiver3, surf, meshgrid}
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69 ## @end deftypefn
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70
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71 function [Nx, Ny, Nz] = surfnorm (varargin)
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72
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73 [hax, varargin, nargin] = __plt_get_axis_arg__ ("surfnorm", varargin{:});
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74
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75 if (nargin == 0 || nargin == 2)
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76 print_usage ();
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77 endif
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78
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79 if (nargin == 1)
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80 z = varargin{1};
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81 [x, y] = meshgrid (1:columns (z), 1:rows (z));
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82 ioff = 2;
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83 else
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84 x = varargin{1};
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85 y = varargin{2};
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86 z = varargin{3};
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87 ioff = 4;
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88 endif
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89
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90 if (iscomplex (z) || iscomplex (x) || iscomplex (y))
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91 error ("surfnorm: X, Y, and Z must be 2-D real matrices");
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92 endif
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93 if (! size_equal (x, y, z))
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94 error ("surfnorm: X, Y, and Z must have the same dimensions");
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95 endif
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96
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97 ## FIXME: Matlab uses a bicubic interpolation, not linear, along the boundary.
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98 ## Do a linear extrapolation for mesh points on the boundary so that the mesh
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99 ## is increased by 1 on each side. This allows each original meshgrid point
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100 ## to be surrounded by four quadrilaterals and the same calculation can be
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101 ## used for interior and boundary points. The extrapolation works badly for
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102 ## closed surfaces like spheres.
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103 xx = [2 * x(:,1) - x(:,2), x, 2 * x(:,end) - x(:,end-1)];
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104 xx = [2 * xx(1,:) - xx(2,:); xx; 2 * xx(end,:) - xx(end-1,:)];
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105 yy = [2 * y(:,1) - y(:,2), y, 2 * y(:,end) - y(:,end-1)];
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106 yy = [2 * yy(1,:) - yy(2,:); yy; 2 * yy(end,:) - yy(end-1,:)];
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107 zz = [2 * z(:,1) - z(:,2), z, 2 * z(:,end) - z(:,end-1)];
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108 zz = [2 * zz(1,:) - zz(2,:); zz; 2 * zz(end,:) - zz(end-1,:)];
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109
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110 u.x = xx(1:end-1,1:end-1) - xx(2:end,2:end);
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111 u.y = yy(1:end-1,1:end-1) - yy(2:end,2:end);
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112 u.z = zz(1:end-1,1:end-1) - zz(2:end,2:end);
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113 v.x = xx(1:end-1,2:end) - xx(2:end,1:end-1);
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114 v.y = yy(1:end-1,2:end) - yy(2:end,1:end-1);
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115 v.z = zz(1:end-1,2:end) - zz(2:end,1:end-1);
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116
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117 c = cross ([u.x(:), u.y(:), u.z(:)], [v.x(:), v.y(:), v.z(:)]);
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118 w.x = reshape (c(:,1), size (u.x));
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119 w.y = reshape (c(:,2), size (u.y));
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120 w.z = reshape (c(:,3), size (u.z));
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121
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122 ## Create normal vectors as mesh vectices from normals at mesh centers
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123 nx = (w.x(1:end-1,1:end-1) + w.x(1:end-1,2:end) +
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124 w.x(2:end,1:end-1) + w.x(2:end,2:end)) / 4;
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125 ny = (w.y(1:end-1,1:end-1) + w.y(1:end-1,2:end) +
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126 w.y(2:end,1:end-1) + w.y(2:end,2:end)) / 4;
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127 nz = (w.z(1:end-1,1:end-1) + w.z(1:end-1,2:end) +
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128 w.z(2:end,1:end-1) + w.z(2:end,2:end)) / 4;
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129
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130 if (nargout == 0)
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131 oldfig = [];
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132 if (! isempty (hax))
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133 oldfig = get (0, "currentfigure");
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134 endif
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135 unwind_protect
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136 hax = newplot (hax);
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137
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138 surf (x, y, z, varargin{ioff:end});
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139 old_hold_state = get (hax, "nextplot");
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140 unwind_protect
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141 set (hax, "nextplot", "add");
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142
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143 ## Normalize the normal vectors
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144 nmag = sqrt (nx.^2 + ny.^2 + nz.^2);
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145
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146 ## And correct for the aspect ratio of the display
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147 daratio = daspect (hax);
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148 damag = sqrt (sumsq (daratio));
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149
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150 ## FIXME: May also want to normalize the vectors relative to the size
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151 ## of the diagonal.
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152
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153 nx ./= nmag / (daratio(1)^2 / damag);
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154 ny ./= nmag / (daratio(2)^2 / damag);
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155 nz ./= nmag / (daratio(3)^2 / damag);
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156
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157 plot3 ([x(:).'; x(:).' + nx(:).' ; NaN(size(x(:).'))](:),
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158 [y(:).'; y(:).' + ny(:).' ; NaN(size(y(:).'))](:),
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159 [z(:).'; z(:).' + nz(:).' ; NaN(size(z(:).'))](:),
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160 "r");
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161 unwind_protect_cleanup
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162 set (hax, "nextplot", old_hold_state);
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163 end_unwind_protect
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164
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165 unwind_protect_cleanup
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166 if (! isempty (oldfig))
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167 set (0, "currentfigure", oldfig);
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168 endif
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169 end_unwind_protect
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170 else
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171 Nx = nx;
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172 Ny = ny;
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173 Nz = nz;
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174 endif
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175
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176 endfunction
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177
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178
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179 %!demo
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180 %! clf;
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181 %! colormap ('default');
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182 %! surfnorm (peaks (19));
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183 %! shading faceted;
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184 %! title ({'surfnorm() shows surface and normals at each vertex', ...
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185 %! 'peaks() function with 19 faces'});
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186
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187 %!demo
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188 %! clf;
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189 %! colormap ('default');
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190 %! [x, y, z] = sombrero (10);
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191 %! surfnorm (x, y, z);
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192
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193 ## Test input validation
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194 %!error surfnorm ()
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195 %!error surfnorm (1,2)
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196 %!error <X, Y, and Z must be 2-D real matrices> surfnorm (i)
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197 %!error <X, Y, and Z must be 2-D real matrices> surfnorm (i, 1, 1)
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198 %!error <X, Y, and Z must be 2-D real matrices> surfnorm (1, i, 1)
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199 %!error <X, Y, and Z must be 2-D real matrices> surfnorm (1, 1, i)
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200 %!error <X, Y, and Z must have the same dimensions> surfnorm ([1 2], 1, 1)
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201 %!error <X, Y, and Z must have the same dimensions> surfnorm (1, [1 2], 1)
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202 %!error <X, Y, and Z must have the same dimensions> surfnorm (1, 1, [1 2])
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203