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view scripts/plot/draw/surfnorm.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 | 7854d5752dd2 |
children | 5d3faba0342e |
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######################################################################## ## ## Copyright (C) 2007-2022 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 {} {} surfnorm (@var{x}, @var{y}, @var{z}) ## @deftypefnx {} {} surfnorm (@var{z}) ## @deftypefnx {} {} surfnorm (@dots{}, @var{prop}, @var{val}, @dots{}) ## @deftypefnx {} {} surfnorm (@var{hax}, @dots{}) ## @deftypefnx {} {[@var{nx}, @var{ny}, @var{nz}] =} surfnorm (@dots{}) ## Find the vectors normal to a meshgridded surface. ## ## If @var{x} and @var{y} are vectors, then a typical vertex is ## (@var{x}(j), @var{y}(i), @var{z}(i,j)). Thus, columns of @var{z} correspond ## to different @var{x} values and rows of @var{z} correspond to different ## @var{y} values. If only a single input @var{z} is given then @var{x} is ## taken to be @code{1:columns (@var{z})} and @var{y} is ## @code{1:rows (@var{z})}. ## ## If no return arguments are requested, a surface plot with the normal ## vectors to the surface is plotted. ## ## Any property/value input pairs are assigned to the surface object. The full ## list of properties is documented at @ref{Surface Properties}. ## ## If the first argument @var{hax} is an axes handle, then plot into this axes, ## rather than the current axes returned by @code{gca}. ## ## If output arguments are requested then the components of the normal ## vectors are returned in @var{nx}, @var{ny}, and @var{nz} and no plot is ## made. The normal vectors are unnormalized (magnitude != 1). To normalize, ## use ## ## @example ## @group ## len = sqrt (nx.^2 + ny.^2 + nz.^2); ## nx ./= len; ny ./= len; nz ./= len; ## @end group ## @end example ## ## An example of the use of @code{surfnorm} is ## ## @example ## surfnorm (peaks (25)); ## @end example ## ## Algorithm: The normal vectors are calculated by taking the cross product ## of the diagonals of each of the quadrilateral faces in the meshgrid to find ## the normal vectors at the center of each face. Next, for each meshgrid ## point the four nearest normal vectors are averaged to obtain the final ## normal to the surface at the meshgrid point. ## ## For surface objects, the @qcode{"VertexNormals"} property contains ## equivalent information, except possibly near the boundary of the surface ## where different interpolation schemes may yield slightly different values. ## ## @seealso{isonormals, quiver3, surf, meshgrid} ## @end deftypefn function [Nx, Ny, Nz] = surfnorm (varargin) [hax, varargin, nargin] = __plt_get_axis_arg__ ("surfnorm", varargin{:}); if (nargin == 0 || nargin == 2) print_usage (); endif if (nargin == 1) z = varargin{1}; [x, y] = meshgrid (1:columns (z), 1:rows (z)); ioff = 2; else x = varargin{1}; y = varargin{2}; z = varargin{3}; ioff = 4; endif if (iscomplex (z) || iscomplex (x) || iscomplex (y)) error ("surfnorm: X, Y, and Z must be 2-D real matrices"); endif if (! size_equal (x, y, z)) error ("surfnorm: X, Y, and Z must have the same dimensions"); endif ## FIXME: Matlab uses a bicubic interpolation, not linear, along the boundary. ## Do a linear extrapolation for mesh points on the boundary so that the mesh ## is increased by 1 on each side. This allows each original meshgrid point ## to be surrounded by four quadrilaterals and the same calculation can be ## used for interior and boundary points. The extrapolation works badly for ## closed surfaces like spheres. xx = [2 * x(:,1) - x(:,2), x, 2 * x(:,end) - x(:,end-1)]; xx = [2 * xx(1,:) - xx(2,:); xx; 2 * xx(end,:) - xx(end-1,:)]; yy = [2 * y(:,1) - y(:,2), y, 2 * y(:,end) - y(:,end-1)]; yy = [2 * yy(1,:) - yy(2,:); yy; 2 * yy(end,:) - yy(end-1,:)]; zz = [2 * z(:,1) - z(:,2), z, 2 * z(:,end) - z(:,end-1)]; zz = [2 * zz(1,:) - zz(2,:); zz; 2 * zz(end,:) - zz(end-1,:)]; u.x = xx(1:end-1,1:end-1) - xx(2:end,2:end); u.y = yy(1:end-1,1:end-1) - yy(2:end,2:end); u.z = zz(1:end-1,1:end-1) - zz(2:end,2:end); v.x = xx(1:end-1,2:end) - xx(2:end,1:end-1); v.y = yy(1:end-1,2:end) - yy(2:end,1:end-1); v.z = zz(1:end-1,2:end) - zz(2:end,1:end-1); c = cross ([u.x(:), u.y(:), u.z(:)], [v.x(:), v.y(:), v.z(:)]); w.x = reshape (c(:,1), size (u.x)); w.y = reshape (c(:,2), size (u.y)); w.z = reshape (c(:,3), size (u.z)); ## Create normal vectors as mesh vectices from normals at mesh centers nx = (w.x(1:end-1,1:end-1) + w.x(1:end-1,2:end) + w.x(2:end,1:end-1) + w.x(2:end,2:end)) / 4; ny = (w.y(1:end-1,1:end-1) + w.y(1:end-1,2:end) + w.y(2:end,1:end-1) + w.y(2:end,2:end)) / 4; nz = (w.z(1:end-1,1:end-1) + w.z(1:end-1,2:end) + w.z(2:end,1:end-1) + w.z(2:end,2:end)) / 4; if (nargout == 0) oldfig = []; if (! isempty (hax)) oldfig = get (0, "currentfigure"); endif unwind_protect hax = newplot (hax); surf (x, y, z, varargin{ioff:end}); old_hold_state = get (hax, "nextplot"); unwind_protect set (hax, "nextplot", "add"); ## Normalize the normal vectors nmag = sqrt (nx.^2 + ny.^2 + nz.^2); ## And correct for the aspect ratio of the display daratio = daspect (hax); damag = sqrt (sumsq (daratio)); ## FIXME: May also want to normalize the vectors relative to the size ## of the diagonal. nx ./= nmag / (daratio(1)^2 / damag); ny ./= nmag / (daratio(2)^2 / damag); nz ./= nmag / (daratio(3)^2 / damag); plot3 ([x(:).'; x(:).' + nx(:).' ; NaN(size(x(:).'))](:), [y(:).'; y(:).' + ny(:).' ; NaN(size(y(:).'))](:), [z(:).'; z(:).' + nz(:).' ; NaN(size(z(:).'))](:), "r"); unwind_protect_cleanup set (hax, "nextplot", old_hold_state); end_unwind_protect unwind_protect_cleanup if (! isempty (oldfig)) set (0, "currentfigure", oldfig); endif end_unwind_protect else Nx = nx; Ny = ny; Nz = nz; endif endfunction %!demo %! clf; %! colormap ("default"); %! surfnorm (peaks (19)); %! shading faceted; %! title ({"surfnorm() shows surface and normals at each vertex", ... %! "peaks() function with 19 faces"}); %!demo %! clf; %! colormap ("default"); %! [x, y, z] = sombrero (10); %! surfnorm (x, y, z); %! title ({"surfnorm() shows surface and normals at each vertex", ... %! "sombrero() function with 10 faces"}); ## Test input validation %!error <Invalid call> surfnorm () %!error <Invalid call> surfnorm (1,2) %!error <X, Y, and Z must be 2-D real matrices> surfnorm (i) %!error <X, Y, and Z must be 2-D real matrices> surfnorm (i, 1, 1) %!error <X, Y, and Z must be 2-D real matrices> surfnorm (1, i, 1) %!error <X, Y, and Z must be 2-D real matrices> surfnorm (1, 1, i) %!error <X, Y, and Z must have the same dimensions> surfnorm ([1 2], 1, 1) %!error <X, Y, and Z must have the same dimensions> surfnorm (1, [1 2], 1) %!error <X, Y, and Z must have the same dimensions> surfnorm (1, 1, [1 2])