Implement contour3 for spherefun

@chebfun2/contour3.m

@@ -8,7 +8,7 @@
 %   The values V are still chosen automatically.
 %
 %   CONTOUR3(F, V) draws LENGTH(V) contour lines at the values specified in
-%   vector V. Use CONTOUR3(F, [V V]) to compute a single contour at the
+%   the vector V. Use CONTOUR3(F, [V V]) to compute a single contour at the
 %   level V.
 %
 %   CONTOUR3(X, Y, F, ...), CONTOUR3(X, Y, F, N, ...), and
@@ -19,7 +19,7 @@
 %   CONTOURC and a handle H to a contour object. This handle can be used as
 %   input to CLABEL.
 %
-%   CONTOUR3(F, 'NUMPTS', N) plots the contour lines on a N by N uniform
+%   CONTOUR3(F, 'NUMPTS', N) plots the contour lines on an N by N uniform
 %   grid. If NUMPTS is not given then we plot on a 200 by 200 grid.
 %
 %   CONTOUR3(F, 'PIVOTS', STR) plots the contour lines with the pivot

@diskfun/contour3.m

@@ -8,7 +8,7 @@
 %   The values V are still chosen automatically.
 %   
 %   CONTOUR3(F, V) draws LENGTH(V) contour lines at the values specified in
-%   vector V. Use CONTOUR3(F, [V V]) to compute a single contour at the
+%   the vector V. Use CONTOUR3(F, [V V]) to compute a single contour at the
 %   level V.
 %
 %   CONTOUR3(X, Y, F, ...), CONTOUR3(X, Y, F, N, ...), and
@@ -19,7 +19,7 @@
 %   CONTOURC and a handle H to a contour object. This handle can be used as
 %   input to CLABEL.
 %
-%   CONTOUR3(F, 'NUMPTS', N) plots the contour lines on a N by N uniform
+%   CONTOUR3(F, 'NUMPTS', N) plots the contour lines on an N by N uniform
 %   grid. If NUMPTS is not given then we plot on a 200 by 200 grid.
 %
 %   CONTOUR3(F, 'PIVOTS', STR) plots the contour lines with the pivot

@separableApprox/contour3.m

@@ -8,7 +8,7 @@
 %   The values V are still chosen automatically.
 %   
 %   CONTOUR3(F, V) draws LENGTH(V) contour lines at the values specified in
-%   vector V. Use CONTOUR3(F, [V V]) to compute a single contour at the
+%   the vector V. Use CONTOUR3(F, [V V]) to compute a single contour at the
 %   level V.
 %
 %   CONTOUR3(X, Y, F, ...), CONTOUR3(X, Y, F, N, ...), and
@@ -19,7 +19,7 @@
 %   CONTOURC and a handle H to a contour object. This handle can be used as
 %   input to CLABEL.
 %
-%   CONTOUR3(F, 'NUMPTS', N) plots the contour lines on a N by N uniform
+%   CONTOUR3(F, 'NUMPTS', N) plots the contour lines on an N by N uniform
 %   grid. If NUMPTS is not given then we plot on a 200 by 200 grid.
 %
 %   CONTOUR3(F, 'PIVOTS', STR) plots the contour lines with the pivot

@spherefun/contour3.m

@@ -0,0 +1,136 @@
+function varargout = contour3( f, varargin )
+%CONTOUR3   3-D contour plot of a SPHEREFUN.
+%   CONTOUR3(F) is a contour plot of F treating the values of F as heights
+%   above the sphere. A contour plot shows the level curves of F for some
+%   values V. The values V are chosen automatically.
+%
+%   CONTOUR3(F, N) draws N contour lines, overriding the automatic number.
+%   The values V are still chosen automatically.
+%   
+%   CONTOUR3(F, V) draws LENGTH(V) contour lines at the values specified in
+%   the vector V. Use CONTOUR3(F, [V V]) to compute a single contour at the
+%   level V.
+%
+%   CONTOUR3(F, 'NUMPTS', N) plots the contour lines on an N by N uniform
+%   grid. If NUMPTS is not given then we plot on a 200 by 200 grid.
+%
+% See also CONTOUR, CONTOURF.
+
+% Copyright 2020 by The University of Oxford and The Chebfun Developers.
+% See http://www.chebfun.org/ for Chebfun information.
+
+if ( isempty(f) )  % Empty check.
+    contour3([]);
+    return
+end
+
+holdState = ishold;
+
+% Minimum number of plotting points:
+minplotnum = 200;
+
+% Extract from the inputs the user defined options: 
+j = 1; 
+argin = {};
+while ( ~isempty(varargin) )
+    if ( strcmpi(varargin{1}, 'numpts') ) % If given numpts then use them.
+        minplotnum = varargin{2};
+        varargin(1:2) = [];
+    else
+        argin{j} = varargin{1};
+        varargin(1) = [];
+        j = j+1;
+    end
+end
+
+if ( isa(f, 'spherefun') )
+    dom = f.domain;
+    % Evaluate at equally spaced grid: 
+    x = linspace(dom(1), dom(2), minplotnum);
+    y = linspace(dom(3), dom(4), minplotnum);
+    vals = sample(f, minplotnum-1, minplotnum);
+    vals = [vals vals(:,1)];
+else
+    error('CHEBFUN:SPHEREFUN:contour3:inputs', ...
+        'Input must be a spherefun.');
+end
+
+if ( iscolat(f) )
+    xc = @(ll,tt,rr) rr.*cos(ll).*sin(tt);
+    yc = @(ll,tt,rr) rr.*sin(ll).*sin(tt);
+    zc = @(tt,rr) rr.*cos(tt);
+else
+    xc = @(ll,tt,rr) rr.*cos(ll).*cos(tt);
+    yc = @(ll,tt,rr) rr.*sin(ll).*cos(tt);
+    zc = @(tt,rr) rr.*sin(tt);
+end
+
+% Use contour rather than contourc so that it can handle parsing the inputs
+% correctly.
+[c, h] = contour( x', y', vals, argin{:} );
+
+% Extract out the options we need to plot the contours with plot3.
+LW = 'LineWidth'; 
+lw = h.LineWidth;
+LS = 'LineStyle'; 
+ls = h.LineStyle;
+LC = 'Color'; 
+lc = h.LineColor;
+levelList = h.LevelList;
+clrmap = parula(numel(levelList));
+
+% Remove the contour plot that was generated.
+delete(h);
+
+scl = 0.15;           % Match the bumpy parameter in SPHEREFUN/SURF().
+lim = [-1-scl 1+scl]; % Pad the axis limits.
+m = minandmax2(f);
+
+% If the plot is not being added to another, then set the axis properties.
+if ( ~holdState )
+    xlim(lim), ylim(lim), zlim(lim)
+    daspect([1 1 1])
+    grid on, box off
+    hold on
+end
+view(3)
+
+cl = size(c,2);
+k = 1;
+while ( k < cl )
+    kl = c(2,k);
+    v = k+1:k+kl;
+
+    % Bump out the radial components according to the function values.
+    rr = rescale(c(1,k), 1-scl, 1+scl, 'InputMin', m(1), 'InputMax', m(2));
+    xv = xc(c(1,v), c(2,v), rr);
+    yv = yc(c(1,v), c(2,v), rr);
+    zv = zc(c(2,v), rr);
+
+    % If the line color is a float then we are plotting all contours in a
+    % single color.
+    if ( isfloat(lc) )
+        plot3(xv, yv, zv, LW, lw, LC, lc, LS, ls);
+    else
+        % We need to plot each contour in a color using the default 
+        % colormap.
+        % Determine the color for the level being plotted.
+        clr = clrmap(abs(c(1, k) - levelList) < 10*eps, :);
+        plot3(xv, yv, zv, LW, lw, LC, clr, LS, ls);
+    end
+
+    k = k+kl+1;
+end
+
+if ( ~holdState )
+    hold off
+end
+
+% Return plot handle if appropriate.
+if ( nargout >= 1 )
+    warning('CHEBFUN:SPHEREFUN:contour3:outputs', ...
+        'Outputs from contour3 are not supported');
+    varargout = { [], [] };
+end
+
+end