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view scripts/plot/draw/isosurface.m @ 30564:796f54d4ddbf stable
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2021.
In all .txi and .texi files except gpl.txi and gpl.texi in the
doc/liboctave and doc/interpreter directories, change the copyright
to "Octave Project Developers", the same as used for other source
files. Update copyright notices for 2022 (not done since 2019). For
gpl.txi and gpl.texi, change the copyright notice to be "Free Software
Foundation, Inc." and leave the date at 2007 only because this file
only contains the text of the GPL, not anything created by the Octave
Project Developers.
Add Paul Thomas to contributors.in.
author | John W. Eaton <jwe@octave.org> |
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date | Tue, 28 Dec 2021 18:22:40 -0500 |
parents | 363fb10055df |
children |
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######################################################################## ## ## Copyright (C) 2009-2022 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/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {@var{fv} =} isosurface (@var{v}, @var{isoval}) ## @deftypefnx {} {@var{fv} =} isosurface (@var{v}) ## @deftypefnx {} {@var{fv} =} isosurface (@var{x}, @var{y}, @var{z}, @var{v}, @var{isoval}) ## @deftypefnx {} {@var{fv} =} isosurface (@var{x}, @var{y}, @var{z}, @var{v}) ## @deftypefnx {} {@var{fvc} =} isosurface (@dots{}, @var{col}) ## @deftypefnx {} {@var{fv} =} isosurface (@dots{}, "noshare") ## @deftypefnx {} {@var{fv} =} isosurface (@dots{}, "verbose") ## @deftypefnx {} {[@var{f}, @var{v}] =} isosurface (@dots{}) ## @deftypefnx {} {[@var{f}, @var{v}, @var{c}] =} isosurface (@dots{}) ## @deftypefnx {} {} isosurface (@dots{}) ## ## Calculate isosurface of 3-D volume data. ## ## An isosurface connects points with the same value and is analogous to a ## contour plot, but in three dimensions. ## ## The input argument @var{v} is a three-dimensional array that contains data ## sampled over a volume. ## ## The input @var{isoval} is a scalar that specifies the value for the ## isosurface. If @var{isoval} is omitted or empty, a @nospell{"good"} value ## for an isosurface is determined from @var{v}. ## ## When called with a single output argument @code{isosurface} returns a ## structure array @var{fv} that contains the fields @var{faces} and ## @var{vertices} computed at the points ## @code{[@var{x}, @var{y}, @var{z}] = meshgrid (1:l, 1:m, 1:n)} where ## @code{[l, m, n] = size (@var{v})}. The output @var{fv} can be ## used directly as input to the @code{patch} function. ## ## If called with additional input arguments @var{x}, @var{y}, and @var{z} ## that are three-dimensional arrays with the same size as @var{v} or ## vectors with lengths corresponding to the dimensions of @var{v}, then the ## volume data is taken at the specified points. If @var{x}, @var{y}, or ## @var{z} are empty, the grid corresponds to the indices (@code{1:n}) in ## the respective direction (@pxref{XREFmeshgrid,,@code{meshgrid}}). ## ## The optional input argument @var{col}, which is a three-dimensional array ## of the same size as @var{v}, specifies coloring of the isosurface. The ## color data is interpolated, as necessary, to match @var{isoval}. The ## output structure array, in this case, has the additional field ## @var{facevertexcdata}. ## ## If given the string input argument @qcode{"noshare"}, vertices may be ## returned multiple times for different faces. The default behavior is to ## eliminate vertices shared by adjacent faces. ## ## The string input argument @qcode{"verbose"} is supported for @sc{matlab} ## compatibility, but has no effect. ## ## Any string arguments must be passed after the other arguments. ## ## If called with two or three output arguments, return the information about ## the faces @var{f}, vertices @var{v}, and color data @var{c} as separate ## arrays instead of a single structure array. ## ## If called with no output argument, the isosurface geometry is directly ## plotted with the @code{patch} command and a light object is added to ## the axes if not yet present. ## ## For example, ## ## @example ## @group ## [x, y, z] = meshgrid (1:5, 1:5, 1:5); ## v = rand (5, 5, 5); ## isosurface (x, y, z, v, .5); ## @end group ## @end example ## ## @noindent ## will directly draw a random isosurface geometry in a graphics window. ## ## An example of an isosurface geometry with different additional coloring: ## @c Set example in small font to prevent overfull line ## ## @smallexample ## N = 15; # Increase number of vertices in each direction ## iso = .4; # Change isovalue to .1 to display a sphere ## lin = linspace (0, 2, N); ## [x, y, z] = meshgrid (lin, lin, lin); ## v = abs ((x-.5).^2 + (y-.5).^2 + (z-.5).^2); ## figure (); ## ## subplot (2,2,1); view (-38, 20); ## [f, vert] = isosurface (x, y, z, v, iso); ## p = patch ("Faces", f, "Vertices", vert, "EdgeColor", "none"); ## pbaspect ([1 1 1]); ## isonormals (x, y, z, v, p) ## set (p, "FaceColor", "green", "FaceLighting", "gouraud"); ## light ("Position", [1 1 5]); ## ## subplot (2,2,2); view (-38, 20); ## p = patch ("Faces", f, "Vertices", vert, "EdgeColor", "blue"); ## pbaspect ([1 1 1]); ## isonormals (x, y, z, v, p) ## set (p, "FaceColor", "none", "EdgeLighting", "gouraud"); ## light ("Position", [1 1 5]); ## ## subplot (2,2,3); view (-38, 20); ## [f, vert, c] = isosurface (x, y, z, v, iso, y); ## p = patch ("Faces", f, "Vertices", vert, "FaceVertexCData", c, ... ## "FaceColor", "interp", "EdgeColor", "none"); ## pbaspect ([1 1 1]); ## isonormals (x, y, z, v, p) ## set (p, "FaceLighting", "gouraud"); ## light ("Position", [1 1 5]); ## ## subplot (2,2,4); view (-38, 20); ## p = patch ("Faces", f, "Vertices", vert, "FaceVertexCData", c, ... ## "FaceColor", "interp", "EdgeColor", "blue"); ## pbaspect ([1 1 1]); ## isonormals (x, y, z, v, p) ## set (p, "FaceLighting", "gouraud"); ## light ("Position", [1 1 5]); ## @end smallexample ## ## @seealso{isonormals, isocolors, isocaps, smooth3, reducevolume, reducepatch, ## patch} ## @end deftypefn ## FIXME: Add support for string input argument "verbose" ## (needs changes to __marching_cube__.m) function varargout = isosurface (varargin) if (nargin < 1 || nargin > 8) print_usage (); endif [x, y, z, v, isoval, colors, noshare, verbose] = ... __get_check_isosurface_args__ (nargout, varargin{:}); calc_colors = ! isempty (colors); if (calc_colors) [fvc.faces, fvc.vertices, fvc.facevertexcdata] = ... __marching_cube__ (x, y, z, v, isoval, colors); else [fvc.faces, fvc.vertices] = __marching_cube__ (x, y, z, v, isoval); endif if (isempty (fvc.vertices) || isempty (fvc.faces)) warning ("isosurface: triangulation is empty"); endif ## remove faces for which at least one of the vertices is NaN vert_nan = 1:size (fvc.vertices, 1); vert_nan(any (isnan (fvc.vertices), 2)) = NaN; fvc.faces = vert_nan(fvc.faces); fvc.faces(any (isnan (fvc.faces), 2), :) = []; if (! noshare) [fvc.faces, fvc.vertices, J] = __unite_shared_vertices__ (fvc.faces, fvc.vertices); if (calc_colors) fvc.facevertexcdata = fvc.facevertexcdata(J); # share very close vertices endif endif switch (nargout) case 0 ## plot the calculated surface if (calc_colors) fc = fvc.facevertexcdata; else fc = isoval; endif ## Matlab uses "EdgeColor", "none", but that looks odd in gnuplot. hax = gca (); if (strcmp (get (gcf, "__graphics_toolkit__"), "gnuplot")) ec = "k"; else ec = "none"; endif pa = patch ("Faces", fvc.faces, "Vertices", fvc.vertices, "FaceVertexCData", fc, "FaceColor", "flat", "EdgeColor", ec, "FaceLighting", "gouraud"); if (! ishold ()) set (hax, "View", [-37.5, 30]); endif isonormals (x, y, z, v, pa); lights = findobj (hax, "Type", "light"); if (isempty (lights)) camlight (); endif case 1 varargout = {fvc}; case 2 varargout = {fvc.faces, fvc.vertices}; otherwise # 3 args or more varargout = {fvc.faces, fvc.vertices, fvc.facevertexcdata}; endswitch endfunction function [x, y, z, v, isoval, colors, noshare, verbose] = __get_check_isosurface_args__ (nout, varargin) ## get arguments from input and check values x = y = z = []; v = []; isoval = []; colors = []; ## default values noshare = false; verbose = false; nin = length (varargin); num_string_inputs = 0; ## check whether last 2 input arguments are strings and assign parameters for i_arg = (nin:-1:nin-1) if (! ischar (varargin{i_arg}) || i_arg < 1) break; # no string arguments at end, exit checking endif switch (tolower (varargin{i_arg})) case {"v", "verbose"} verbose = true; num_string_inputs++; case {"n", "noshare"} noshare = true; num_string_inputs++; case "" num_string_inputs++; ## silently ignore empty strings otherwise error ("isosurface: parameter '%s' not supported", varargin{i_arg}); endswitch endfor ## assign arguments switch (nin - num_string_inputs) case 1 # isosurface (v, ...) v = varargin{1}; case 2 # isosurface (v, isoval, ...) or isosurface (v, col, ...) v = varargin{1}; if (isscalar (varargin{2}) || isempty (varargin{2})) isoval = varargin{2}; else colors = varargin{2}; endif case 3 # isosurface (v, isoval, col, ...) v = varargin{1}; isoval = varargin{2}; colors = varargin{3}; case 4 # isosurface (x, y, z, v, ...) x = varargin{1}; y = varargin{2}; z = varargin{3}; v = varargin{4}; case 5 # isosurface (x, y, z, v, isoval, ...) or # isosurface (x, y, z, v, col, ...) x = varargin{1}; y = varargin{2}; z = varargin{3}; v = varargin{4}; if (isscalar (varargin{5}) || isempty (varargin{5})) isoval = varargin{5}; else colors = varargin{5}; endif case 6 # isosurface (x, y, z, v, isoval, col, ...) x = varargin{1}; y = varargin{2}; z = varargin{3}; v = varargin{4}; isoval = varargin{5}; colors = varargin{6}; otherwise error ("isosurface: incorrect number of input arguments"); endswitch ## check dimensions of v v_sz = size (v); if (ndims (v) != 3 || any (v_sz(1:3) < 2)) error ("isosurface: V must be a non-singleton 3-dimensional matrix"); endif if (isempty (x)) x = 1:columns (v); endif if (isempty (y)) y = 1:rows (v); endif if (isempty (z)) z = 1:size (v, 3); endif ## check x if (isvector (x) && length (x) == v_sz(2)) x = repmat (x(:)', [v_sz(1) 1 v_sz(3)]); elseif (! size_equal (v, x)) error ("isosurface: X must match the size of V"); endif ## check y if (isvector (y) && length (y) == v_sz(1)) y = repmat (y(:), [1 v_sz(2) v_sz(3)]); elseif (! size_equal (v, y)) error ("isosurface: Y must match the size of V"); endif ## check z if (isvector (z) && length (z) == v_sz(3)) z = repmat (reshape (z(:), [1 1 length(z)]), [v_sz(1) v_sz(2) 1]); elseif (! size_equal (v, z)) error ("isosurface: Z must match the size of V"); endif ## check isoval if (isempty (isoval)) ## calculate "good" isoval value from v isoval = __calc_isovalue_from_data__ (v); endif if (! isscalar (isoval)) error ("isosurface: ISOVAL must be a scalar"); endif ## check colors if (! isempty (colors)) if (! size_equal (v, colors)) error ("isosurface: COL must match the size of V"); endif if (nout == 2) warning ("isosurface: colors will be calculated, but no output argument to receive it"); endif elseif (nout >= 3) error ("isosurface: COL must be passed to return C"); endif endfunction %!demo %! clf; %! [x,y,z] = meshgrid (-2:0.5:2, -2:0.5:2, -2:0.5:2); %! v = x.^2 + y.^2 + z.^2; %! isosurface (x, y, z, v, 1); %! axis equal; %! title ("isosurface() of a sphere"); %!demo %! clf; %! [x,y,z] = meshgrid (-2:0.5:2, -2:0.5:2, -2:0.5:2); %! v = x.^2 + y.^2 + z.^2; %! isosurface (x, y, z, v, 3); %! isosurface (x, y, z, v, 5); %! axis equal; %! title ("isosurface() of two nested spheres"); %!demo %! clf; %! x = 0:2; %! y = 0:3; %! z = 0:1; %! [xx, yy, zz] = meshgrid (x, y, z); %! v = [0, 0, 0; 0, 0, 0; 0, 0, 1; 0, 0, 1]; %! v(:,:,2) = [0, 0, 0; 0, 0, 1; 0, 1, 2; 0, 1, 2]; %! iso = 0.8; %! %! ## Three arguments, no output %! subplot (2, 2, 1); %! fvc = isosurface (v, iso, yy); %! patch (fvc); %! shading faceted; %! view (110, 40); %! ## six arguments, no output (x, y, z are vectors) %! subplot (2, 2, 2); %! fvc = isosurface (x, y, z, v, iso, yy); %! patch (fvc); %! shading faceted; %! view (110, 40); %! ## six arguments, no output (x, y, z are matrices) %! subplot (2, 2, 3); %! fvc = isosurface (xx, yy, zz, v, iso, yy); %! patch (fvc); %! shading faceted; %! view (110, 40); %! ## six arguments, no output (mixed x, y, z) and option "noshare" %! subplot (2, 2, 4); %! fvc = isosurface (x, yy, z, v, iso, yy, "noshare"); %! patch (fvc); %! shading faceted; %! view (110, 40); %! annotation ("textbox", [0.41 0.9 0.9 0.1], ... %! "String", "isosurface() called 4 ways", ... %! "HorizontalAlignment", "center", ... %! "FontSize", 12); %! annotation ("textbox", [0.1 0.45 0.9 0.1], ... %! "String", {["Apart from the first plot having a different scale, " ... %! "all four plots must look the same."], %! ["The last plot might have different colors but must " ... %! "have the same shape."]}, ... %! "HorizontalAlignment", "left", ... %! "FontSize", 12); %!shared x, y, z, xx, yy, zz, val, iso %! x = 0:2; %! y = 0:3; %! z = 0:1; %! [xx, yy, zz] = meshgrid (x, y, z); %! val = [0, 0, 0; 0, 0, 0; 0, 0, 1; 0, 0, 1]; %! val(:,:,2) = [0, 0, 0; 0, 0, 1; 0, 1, 2; 0, 1, 2]; %! iso = 0.8; ## one argument, one output %!test %! fv = isosurface (val); %! assert (isfield (fv, "vertices"), true); %! assert (isfield (fv, "faces"), true); %! assert (size (fv.vertices), [5 3]); %! assert (size (fv.faces), [3 3]); ## two arguments (second is ISO), one output %!test %! fv = isosurface (val, iso); %! assert (isfield (fv, "vertices"), true); %! assert (isfield (fv, "faces"), true); %! assert (size (fv.vertices), [11 3]); %! assert (size (fv.faces), [10 3]); ## two arguments (second is COL), one output %!test %! fvc = isosurface (val, yy); %! assert (isfield (fvc, "vertices"), true); %! assert (isfield (fvc, "faces"), true); %! assert (isfield (fvc, "facevertexcdata"), true); %! assert (size (fvc.vertices), [5 3]); %! assert (size (fvc.faces), [3 3]); %! assert (size (fvc.facevertexcdata), [5 1]); ## three arguments, one output %!test %! fvc = isosurface (val, iso, yy); %! assert (isfield (fvc, "vertices"), true); %! assert (isfield (fvc, "faces"), true); %! assert (isfield (fvc, "facevertexcdata"), true); %! assert (size (fvc.vertices), [11 3]); %! assert (size (fvc.faces), [10 3]); %! assert (size (fvc.facevertexcdata), [11 1]); ## four arguments, one output %!test %! fv = isosurface (x, [], z, val); %! assert (isfield (fv, "vertices"), true); %! assert (isfield (fv, "faces"), true); %! assert (size (fv.vertices), [5 3]); %! assert (size (fv.faces), [3 3]); ## five arguments (fifth is ISO), one output %!test %! fv = isosurface (xx, y, [], val, iso); %! assert (isfield (fv, "vertices"), true); %! assert (isfield (fv, "faces"), true); %! assert (size (fv.vertices), [11 3]); %! assert (size (fv.faces), [10 3]); ## five arguments (fifth is COL), one output %!test %! fvc = isosurface ([], yy, z, val, yy); %! assert (isfield (fvc, "vertices"), true); %! assert (isfield (fvc, "faces"), true); %! assert (isfield (fvc, "facevertexcdata"), true); %! assert (size (fvc.vertices), [5 3]); %! assert (size (fvc.faces), [3 3]); %! assert (size (fvc.facevertexcdata), [5 1]); ## six arguments, one output %!test %! fvc = isosurface (xx, yy, zz, val, iso, yy); %! assert (isfield (fvc, "vertices"), true); %! assert (isfield (fvc, "faces"), true); %! assert (isfield (fvc, "facevertexcdata"), true); %! assert (size (fvc.vertices), [11 3]); %! assert (size (fvc.faces), [10 3]); %! assert (size (fvc.facevertexcdata), [11 1]); ## five arguments (fifth is ISO), two outputs %!test %! [f, v] = isosurface (x, y, z, val, iso); %! assert (size (f), [10 3]); %! assert (size (v), [11 3]); ## six arguments, three outputs %!test %! [f, v, c] = isosurface (x, y, z, val, iso, yy); %! assert (size (f), [10 3]); %! assert (size (v), [11 3]); %! assert (size (c), [11 1]); ## two arguments (second is ISO) and one string, one output %!test %! fv = isosurface (val, iso, "verbose"); %! assert (isfield (fv, "vertices"), true); %! assert (isfield (fv, "faces"), true); %! assert (size (fv.vertices), [11 3]); %! assert (size (fv.faces), [10 3]); ## six arguments and two strings, one output %!test %! fvc = isosurface (xx, yy, zz, val, iso, yy, "v", "noshare"); %! assert (isfield (fvc, "vertices"), true); %! assert (isfield (fvc, "faces"), true); %! assert (isfield (fvc, "facevertexcdata"), true); %! assert (size (fvc.vertices), [20 3]); %! assert (size (fvc.faces), [10 3]); %! assert (size (fvc.facevertexcdata), [20 1]); ## five arguments (fifth is COL) and two strings (different order), one output %!test %! fvc = isosurface (xx, yy, zz, val, yy, "n", "v"); %! assert (isfield (fvc, "vertices"), true); %! assert (isfield (fvc, "faces"), true); %! assert (isfield (fvc, "facevertexcdata"), true); %! assert (size (fvc.vertices), [7 3]); %! assert (size (fvc.faces), [3 3]); %! assert (size (fvc.facevertexcdata), [7 1]); ## test for each error and warning %!error <Invalid call> isosurface () %!error <Invalid call> isosurface (1,2,3,4,5,6,7,8,9) %!error <parameter 'foobar' not supported> %! fvc = isosurface (val, iso, "foobar"); %!error <incorrect number of input arguments> %! fvc = isosurface (xx, yy, zz, val, iso, yy, 5); %!error <V must be a non-singleton 3-dimensional matrix> %! v = reshape (1:6*8, [6 8]); %! fvc = isosurface (v, iso); %!error <V must be a non-singleton 3-dimensional matrix> %! v = reshape(1:6*8, [6 1 8]); fvc = isosurface (v, iso); %!error <X must match the size of V> %! x = 1:2:24; %! fvc = isosurface (x, y, z, val, iso); %!error <Y must match the size of V> %! y = -14:6:11; %! fvc = isosurface (x, y, z, val, iso); %!error <Z must match the size of V> %! z = linspace (16, 18, 5); %! fvc = isosurface (x, y, z, val, iso); %!error <X must match the size of V> %! x = 1:2:24; %! [xx, yy, zz] = meshgrid (x, y, z); %! fvc = isosurface (xx, yy, zz, val, iso); %!error <X must match the size of V> %! y = -14:6:11; %! [xx, yy, zz] = meshgrid (x, y, z); %! fvc = isosurface (xx, yy, zz, val, iso); %!error <X must match the size of V> %! z = linspace (16, 18, 3); %! [xx, yy, zz] = meshgrid (x, y, z); %! fvc = isosurface (xx, yy, zz, val, iso); %!error <ISOVAL must be a scalar> fvc = isosurface (val, [iso iso], yy) %!error <COL must match the size of V> fvc = isosurface (val, [iso iso]) %!error <COL must be passed to return C> [f, v, c] = isosurface (val, iso) %!warning <colors will be calculated, but no output argument to receive it> %! [f, v] = isosurface (val, iso, yy); ## test for __calc_isovalue_from_data__ ## FIXME: private function cannot be tested, unless bug #38776 is resolved. %!test <38776> %! assert (__calc_isovalue_from_data__ (1:5), 3.02);