Mercurial > octave
view scripts/plot/draw/private/__ezplot__.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> |
---|---|
date | Tue, 28 Dec 2021 18:22:40 -0500 |
parents | 363fb10055df |
children | e1788b1a315f |
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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 {} {[@var{h}, @var{needusage}] =} __ezplot__ (@var{pltfunc}, @var{varargin}) ## Undocumented internal function. ## @end deftypefn ## Overview: This function is the back-end for the 9 ez* plot functions. ## As such, most of the function is actually dedicated to sorting ## out the inputs and verifying that the particular ez* function ## called was called correctly. The actual plotting occurs near ## the end in an unwind_protect block. function [h, needusage] = __ezplot__ (pltfunc, varargin) ezfunc = ["ez" pltfunc]; [hax, varargin, nargin] = __plt_get_axis_arg__ (ezfunc, varargin{:}); ## Define outputs early in case of shorting out of function with return; h = []; needusage = false; if (nargin < 1) needusage = true; return; endif iscontour = strncmp (pltfunc, "contour", 7); ## Defaults for ezplot isplot = true; isplot3 = false; ispolar = false; nargs = 1; switch (pltfunc) case "plot" ## defaults already set case "plot3" isplot = false; isplot3 = true; case "polar" isplot = false; ispolar = true; otherwise ## contour, mesh, surf plots isplot = false; nargs = 2; endswitch parametric = false; fun = varargin{1}; if (ischar (fun)) if (exist (fun, "file") || exist (fun, "builtin")) fun = str2func (fun); # convert to function handle else fun = vectorize (inline (fun)); # convert to inline function endif endif if (isa (fun, "inline")) argids = argnames (fun); if (isplot && length (argids) == 2) nargs = 2; elseif (numel (argids) != nargs) error ("%s: expecting a function of %d arguments", ezfunc, nargs); endif fun = vectorize (fun); fstr = formula (fun); if (isplot) xarg = argids{1}; if (nargs == 2) yarg = argids{2}; else yarg = ""; endif elseif (isplot3) xarg = "x"; yarg = "y"; elseif (isplot || ispolar) xarg = ""; yarg = ""; else xarg = argids{1}; yarg = argids{2}; endif elseif (is_function_handle (fun)) fstr = func2str (fun); idx = index (fstr, ')'); if (idx != 0) args = regexp (fstr(3:(idx-1)), '\w+', 'match'); fstr = fstr(idx+2:end); # remove '@(x) ' from string name else args = {"x"}; try if (builtin ("nargin", fun) == 2) args{2} = "y"; endif end_try_catch endif if (isplot && length (args) == 2) nargs = 2; elseif (numel (args) != nargs) error ("%s: expecting a function of %d arguments", ezfunc, nargs); endif if (isplot) xarg = args{1}; if (nargs == 2) yarg = args{2}; else yarg = ""; endif elseif (isplot3) xarg = "x"; yarg = "y"; elseif (ispolar) xarg = ""; yarg = ""; else xarg = args{1}; yarg = args{2}; endif else error ("%s: F must be a string or function handle", ezfunc); endif if (nargin > 2 || (nargin == 2 && isplot)) funx = fun; fstrx = fstr; funy = varargin{2}; if (ischar (funy) && ! strcmp (funy, "circ") && ! strcmp (funy, "animate")) parametric = true; if (exist (funy, "file") || exist (funy, "builtin")) funy = inline ([funy "(t)"]); else funy = vectorize (inline (funy)); endif if (numel (argnames (funy)) != nargs) error ("%s: expecting a function of %d arguments", ezfunc, nargs); endif fstry = formula (funy); elseif (isa (funy, "inline")) parametric = true; if (numel (argnames (funy)) != nargs) error ("%s: expecting a function of %d arguments", ezfunc, nargs); endif funy = vectorize (funy); fstry = formula (funy); elseif (is_function_handle (funy)) parametric = true; fstry = func2str (funy); idx = index (fstry, ')'); if (idx != 0) args = regexp (fstry(3:(idx-1)), '\w+', 'match'); fstry = fstry(idx+2:end); # remove '@(x) ' from string name else args = {"y"}; endif if (numel (args) != nargs) error ("%s: expecting a function of %d arguments", ezfunc, nargs); endif endif if (! parametric && isplot3) needusage = true; # Can't call non-parametric ezplot3 return; elseif (parametric && isplot) if (nargs == 2) error ("%s: can not define a parametric function in this manner", ezfunc); else xarg = "x"; yarg = "y"; endif elseif (parametric) funz = varargin{3}; if (ischar (funz) && ! strcmp (funz, "circ") && ! strcmp (funz, "animate")) if (exist (funz, "file") || exist (funz, "builtin")) funz = inline ([funz "(t)"]); else funz = vectorize (inline (funz)); endif if (numel (argnames (funz)) > nargs) error ("%s: expecting a function of %d arguments", ezfunc, nargs); endif fstrz = formula (funz); elseif (isa (funz, "inline")) if (numel (argnames (funz)) != nargs) error ("%s: expecting a function of %d arguments", ezfunc, nargs); endif funz = vectorize (funz); fstrz = formula (funz); elseif (is_function_handle (funz)) fstrz = func2str (funz); idx = index (fstrz, ')'); if (idx != 0) args = regexp (fstrz(3:(idx-1)), '\w+', 'match'); fstrz = fstrz(idx+2:end); # remove '@(x) ' from string name else args = {"z"}; endif if (numel (args) != nargs) error ("%s: expecting a function of %d arguments", ezfunc, nargs); endif else error ("%s: parametric plots require 3 functions", ezfunc); endif endif endif if ((isplot && nargs != 2) || isplot3 || ispolar) n = 500; # default for point-style functions like plot else n = 60; # default for meshgrid style functions like contour, surf endif domain = []; circ = false; animate = false; if (parametric) if (isplot) iarg = 3; else iarg = 4; endif else iarg = 2; endif while (iarg <= nargin) arg = varargin{iarg++}; if (ischar (arg) && strcmp (arg, "circ")) circ = true; elseif (ischar (arg) && strcmp (arg, "animate")) animate = true; elseif (isscalar (arg) && (n == 60 || n == 500)) n = arg; elseif (numel (arg) == 2 && isempty (domain)) domain = [arg(1) arg(2) arg(1) arg(2)]; elseif (numel (arg) == 4 && isempty (domain)) domain = arg(:).'; else error ("%s: expecting scalar N, or 2-/4-element vector DOM", ezfunc); endif endwhile if (circ && (iscontour || isplot3 || isplot)) needusage = true; return; elseif (circ && parametric) error ("%s: can not have both circular domain and parametric function", ezfunc); endif if (animate && ! isplot3) error ("%s: animate option only valid for ezplot3", ezfunc); endif if (parametric) ## Make the label strings pretty by removing extra spaces between base ## and exponent, the '.' in vectorized code, and the '*' for multiply. fstrx = regexprep (regexprep (regexprep (fstrx, '\s*\.?(?:\^|\*\*)\s*','^'), '\.([/+-])', '$1'), '\s*\.?\*\s*', ' '); fstry = regexprep (regexprep (regexprep (fstry, '\s*\.?(?:\^|\*\*)\s*','^'), '\.([/+-])', '$1'), '\s*\.?\*\s*', ' '); if (isplot) fstr = ["x = " fstrx ", y = " fstry]; else fstrz = regexprep (regexprep (regexprep (fstrz, '\s*\.?(?:\^|\*\*)\s*','^'), '\.([/+-])', '$1'), '\s*\.?\*\s*', ' '); fstr = ["x = " fstrx ", y = " fstry ", z = " fstrz]; endif else fstr = regexprep (regexprep (regexprep (fstr, '\s*\.?(?:\^|\*\*)\s*','^'), '\.([/+-])', '$1'), '\s*\.?\*\s*', ' '); if (isplot && nargs == 2) fstr = [fstr " = 0"]; # make title string of implicit function elseif (ispolar) fstr = ["r = " fstr]; endif endif if (isempty (domain)) auto_domain = true; if (isplot3 || ispolar) domain = [0, 2*pi, 0, 2*pi]; else domain = [-2*pi, 2*pi, -2*pi, 2*pi]; endif else auto_domain = false; endif auto_domain_done = false; do domain_ok = true; if ((isplot && nargs == 1) || isplot3 || ispolar) X = linspace (domain(1), domain(2), n); elseif (isplot && numel (domain) == 2) x = linspace (domain(1), domain(2), n); [X, Y] = meshgrid (x, x); elseif (circ) ## To plot on circular domain develop grid in polar coordinates ## and then switch these to Cartesian coordinates. cent = [domain(1) + domain(2), domain(3) + domain(4)] / 2; rmax = sqrt ((domain(2) - cent(1))^2 + (domain(4) - cent(2))^2); r = linspace (0, rmax, n); t = linspace (0, 2*pi, n); [T, R] = meshgrid (t, r); X = R .* cos (T) + cent(1); Y = R .* sin (T) + cent(2); domain = [-rmax+cent(1), +rmax+cent(1), -rmax+cent(2), +rmax+cent(2)]; else # contour, mesh, surf plots x = linspace (domain(1), domain(2), n); y = linspace (domain(3), domain(4), n); [X, Y] = meshgrid (x, y); endif if (parametric) if (isplot) XX = feval (funx, X); Z = feval (funy, X); X = XX; elseif (isplot3) Z = feval (funz, X); XX = feval (funx, X); YY = feval (funy, X); X = XX; Y = YY; else Z = feval (funz, X, Y); XX = feval (funx, X, Y); YY = feval (funy, X, Y); X = XX; Y = YY; ## Eliminate the singularities X = __eliminate_sing__ (X); Y = __eliminate_sing__ (Y); Z = __eliminate_sing__ (Z); endif else # non-parametric plots if (isplot && nargs == 2) Z = feval (fun, X, Y); ## Matlab returns line objects for this case and so can't call ## contour directly as it returns patch objects to allow colormaps ## to work with contours. Therefore recreate the lines from the ## output for contourc, and store in cell arrays. [c, ~] = contourc (X, Y, Z, [0, 0]); i = 1; XX = YY = {}; while (i < length (c)) clev = c(1,i); clen = c(2,i); XX = [XX, {c(1, i+1:i+clen)}]; YY = [YY, {c(2, i+1:i+clen)}]; i += clen+1; endwhile else if (ispolar) Z = feval (fun, X); ## FIXME: Why aren't singularities eliminated for polar plots? elseif (isplot) Z = feval (fun, X); ## Eliminate the singularities Z = __eliminate_sing__ (Z); domain = find_valid_domain (X, [], Z); elseif (iscontour) Z = feval (fun, X, Y); Z = __eliminate_sing__ (Z); else # mesh, surf plots Z = feval (fun, X, Y); Z = __eliminate_sing__ (Z); if (circ) ## Use domain calculated at the start. ## The X, Y grids are non-monotonic after conversion from polar ## coordinates and find_valid_domain fails. elseif (auto_domain && ! auto_domain_done) valid_domain = find_valid_domain (X, Y, Z); domain_ok = all (domain == valid_domain); domain = valid_domain; auto_domain_done = true; # ensures only 1 round of do loop done else if (! auto_domain_done) domain = find_valid_domain (X, Y, Z); endif endif endif endif endif until (domain_ok) ## Now, actually call the correct plot function with valid data and domain. oldfig = []; if (! isempty (hax)) oldfig = get (0, "currentfigure"); endif unwind_protect hax = newplot (hax); if (iscontour) [~, h] = feval (pltfunc, hax, X, Y, Z); elseif (isplot && nargs == 2) h = zeros (length (XX), 1); hold_state = get (hax, "nextplot"); for i = 1 : length (XX) if (i == 1) h(1) = plot (hax, XX{1}, YY{1}); set (hax, "nextplot", "add"); color = get (h(1), "color"); else h(i) = plot (hax, XX{i}, YY{i}, "color", color); endif endfor set (hax, "nextplot", hold_state); axis (hax, domain); elseif (isplot || ispolar) h = feval (pltfunc, hax, X, Z); if (isplot) if (! parametric) axis (hax, domain); else axis ("equal"); endif endif elseif (isplot3) if (animate) comet3 (hax, X, Y, Z); else h = feval (pltfunc, hax, X, Y, Z); endif grid (hax, "on"); zlabel (hax, "z"); else # mesh and surf plots h = feval (pltfunc, hax, X, Y, Z); ## FIXME: surf, mesh should really do a better job of setting zlim if (! parametric) axis (hax, domain); endif endif xlabel (hax, xarg); ylabel (hax, yarg); title (hax, fstr); unwind_protect_cleanup if (! isempty (oldfig)) set (0, "currentfigure", oldfig); endif end_unwind_protect endfunction ## Eliminate bad data (complex values, infinities, singularities) function x = __eliminate_sing__ (x) if (iscomplex (x)) x(imag (x) != 0) = NaN; endif x(isinf (x)) = NaN; ## High rates of curvature are treated as singularities threshold = 0.2 * (max (x(:)) - min (x(:))); x(abs (del2 (x)) > threshold) = NaN; endfunction ## Find: 1) range of function where there are not NaN values, ## 2) function is changing (not just flat surface) function domain = find_valid_domain (X, Y, Z) if (isvector (Z)) ## 2-D data for isplot domain = [X(1) X(end)]; ## Guess a range which includes the "mass" of the data by using a ## median-based approach. The center 3/4 of the data is used to ## determine the range of the data. ## This seems to be vaguely what Matlab does, but can't be sure. XX = sort (Z(isfinite (Z))); if (length (X) > 4) irlo = XX(fix (1/8 * length (XX))); irhi = XX(fix (7/8 * length (XX))); d = irhi - irlo; domain(3) = max (XX(1) - d/8, irlo - d); domain(4) = min (XX(end) + d/8, irhi + d); else domain(3:4) = [XX(1), XX(end)]; endif ## Handle exceptional case of constant function if (domain(3) == domain(4)) domain(3) -= 1; domain(4) += 1; endif else ## 3-D data such as mesh, surf Zfinite = ! isnan (Z); Zrows = any (Zfinite, 2); rmin = find (Zrows, 1, "first"); rmax = find (Zrows, 1, "last"); Zcols = any (Zfinite, 1); cmin = find (Zcols, 1, "first"); cmax = find (Zcols, 1, "last"); ## Handle nasty case of all NaNs if (isempty (rmin)) rmin = 1; rmax = rows (Z); endif if (isempty (cmin)) cmin = 1; cmax = columns (Z); endif if ( ! any (isnan (Z([rmin, rmax],:)(:))) && ! any (isnan (Z(:, [cmin, cmax])(:)))) ## Exclude surfaces along borders which are flat (gradient =~ 0). ## Technically, this calculation might be better done with actual ## deltaX, deltaY values. But, data is usually meshgridded ## (constant spacing) so working with deltaROW#, deltaCOL# is fine. [Zx, Zy] = gradient (Z(rmin:rmax, cmin:cmax)); Zgrad = sqrt (Zx.^2 + Zy.^2); slope = ((max (Z(:)) - min (Z(:))) / sqrt ((rmax - rmin)^2 + (cmax - cmin)^2)); slope /= 125; # threshold for discarding points. Zrows = any (Zgrad > slope, 2); rmin += find (Zrows, 1, "first") - 1; rmax += find (Zrows, 1, "last") - rows (Zrows); Zcols = any (Zgrad > slope, 1); cmin += find (Zcols, 1, "first") - 1; cmax += find (Zcols, 1, "last") - columns (Zcols); endif domain = [X(1,cmin) X(1,cmax) Y(rmin,1) Y(rmax,1)]; endif endfunction