causet_saveas_tikz.m

function causet_saveas_tikz( coordinates, L, filename, ...
    flags, drawingstyles, linkselectors, dimensions, fadingdepth )
%CAUSET_SAVEAS_TIKZ converts causet COORDINATES and links L to a TikZ 
% picture file where only the first two (or three) coordinates are used.
% 
% Arguments:
% COORDINATES         positions of the points.
% L                   logical upper triangular (direct) link matrix.
% FILENAME            location and filename.
% 
% Optional arguments:
% FLAGS               structure of flags. 
%   'unit'            factor to convert from numeric coordinates to cm.
%                     If it is a non-positive number, it will be assumed 
%                     that parameters are set externally.
%                     Default: 1
%   'IsSubPicture'    boolean flag to skip the \begin and \end macros of
%                     the tikzpicture environment.
%                     Default: false
%   'StartupCommands' text to be printed right after the start of the 
%                     tikzpicture.
%                     Default: (none)
%   'EndCommands'     text to be printed right before the end of the 
%                     tikzpicture.
%                     Default: (none)
% DRAWINGSTYLES       cell vector with length of the causet cardinality.
%                     Every cell is a vector of drawing style indices
%                     (starting from 1). If the input is a numeric vector,
%                     it is converted to a cell vector automatically. 
%                     Default: all events, style 1
% LINKSELECTORS       cell array of logical event selection vectors for 
%                     differently coloured links. 
%                     Default: all events, style 1
% DIMENSIONS          vector, which sets the dimensions to be printed.
%                     Default: [ 2, 1 ]
% FADINGRANGE         sets the coordinate-range for fading in 3D graphics.
% 
% Copyright 2021, C. Minz. BSD 3-Clause License.
    
    N = size( L, 1 );
    if ( nargin < 4 ) || isempty( flags )
        flags = struct( 'unit', 1 );
    end
    if ~isfield( flags, 'IsSubPicture' )
        flags.IsSubPicture = false;
    end
    if nargin < 5
        drawingstyles = ones( 1, N );
    end
    if ~iscell( drawingstyles )
        drawingstyles = num2cell( drawingstyles );
    end
    if nargin < 6
        linkselectors = { true( 1, N ) };
    end
    if nargin < 7
        dimensions = [ 2, 1 ];
    end
    is3D = false;
    if length( dimensions ) > 2
        is3D = true;
        % third dimension offset for planar coordinates:
        offsetscaling3D = [ 0.3, 0.2 ];
        % foreground-most and background-most fading:
        fading3D = [ 1, 0 ];
        scalings3D = coordinates( :, dimensions( 3 ) );
        scalings3D = scalings3D - min( coordinates( :, dimensions( 3 ) ) );
        scalings3D = 1 - scalings3D / max( scalings3D );
        if nargin < 8
            fadingdepth = 1;
        end
        ignore_faded = fadingdepth == 1;
    end
    linkcount = sum( sum( L ) );
    pt_digits = floor( log10( N ) ) + 1;
    pt_nameformat = [ '%0', num2str( pt_digits ), 'u' ];
    % start picture:
    fileID = fopen( filename, 'w' );
    if ~flags.IsSubPicture
        fprintf( fileID, '\\begin{tikzpicture}\n' );
    end
    fprintf( fileID, '\t%% ### This graphic is generated by causet_saveas_tikz.m\n' );
    fprintf( fileID, '\t%% ###   Number of elements: %d\n', N );
    fprintf( fileID, '\t%% ###   Number of links: %d\n', linkcount );
    fprintf( fileID, '\t%% ###   Average link density: %0.3f\n', linkcount / N );
    if isfield( flags, 'StartupCommands' )
        fprintf( fileID, '\t%% start-up commands:\n' );
        fprintf( fileID, flags.StartupCommands );
    end
    fprintf( fileID, '\t%% parameters:\n' );
    fprintf( fileID, '\t\\providecommand{\\firstHiddenEvent}{%d}\n', N + 1 );
    if isfield( flags, 'unit') && ( flags.unit > 0 )
        fprintf( fileID, '\t\\def\\CSunit{%0.3fcm}\n', flags.unit );
        fprintf( fileID, '\t\\def\\CScoordinatesystem{%0.3f}\n', 1 );
        fprintf( fileID, '\t\\def\\CScoordinatesystemshift{%0.3f}\n', -0.2 );
        if is3D
            fprintf( fileID, '\t\\def\\CSminscaling{%0.3f}\n', 0.3 );
            fprintf( fileID, '\t\\def\\CSlblscaling{%0.3f}\n', 1 );
            fprintf( fileID, '\t\\def\\CSlinkopacity{%0.3f}\n', 0.8 );
            fprintf( fileID, '\t\\def\\CSmaxopacity{%0.3f}\n', fading3D( 1 ) );
            fprintf( fileID, '\t\\def\\CSlblopacityfill{%0.3f}\n', 0.8 );
            fprintf( fileID, '\t\\def\\CSlblopacitytext{%0.3f}\n', 1 );
            fprintf( fileID, '\t\\def\\CSfading{%0.3f}\n', ( fading3D( 1 ) - fading3D( 2 ) ) / fadingdepth );
        end
    else
        fprintf( fileID, '\t%% -- expected global definitions of:\n' );
        if is3D
            fprintf( fileID, '\t%%    \\CSunit, \\CSminscaling, \\CSlblscaling, ' );
            fprintf( fileID, '\\CSlinkopacity, \\CSmaxopacity, \\CSlblopacityfill, ' );
            fprintf( fileID, '\\CSlblopacitytext, \\CSfading\n' );
        else
            fprintf( fileID, '\t%%    \\CSunit\n' );
        end
    end
    % define causet coordinate format:
    pt_coordformat = [ '\t\\coordinate (p', pt_nameformat, ') at ', ...
        '( %0.3f*\\CSunit, %0.3f*\\CSunit );\n' ];
    % draw coordinate axes:
    cs_xaxisformat = [ '\t\t\\draw[%s] ( \\CScoordinatesystemshift*\\CSunit, \\CScoordinatesystemshift*\\CSunit ) -- ', ...
            '( %0.3f*\\CSunit-\\CScoordinatesystemshift*\\CSunit, \\CScoordinatesystemshift*\\CSunit ) ', ...
            'node[%slbl, below] {$x_{%u}$};\n' ];
    cs_yaxisformat = [ '\t\t\\draw[%s] ( \\CScoordinatesystemshift*\\CSunit, \\CScoordinatesystemshift*\\CSunit ) -- ', ...
            '( \\CScoordinatesystemshift*\\CSunit, %0.3f*\\CSunit-\\CScoordinatesystemshift*\\CSunit ) ', ...
            'node[%slbl, left] {$x_{%u}$};\n' ];
    cs_zaxisformat = [ '\t\t\\draw[%s] ( \\CScoordinatesystemshift*\\CSunit, \\CScoordinatesystemshift*\\CSunit ) -- ', ...
            '( %0.3f*\\CSunit+%0.3f*\\CScoordinatesystemshift*\\CSunit, %0.3f*\\CSunit+%0.3f*\\CScoordinatesystemshift*\\CSunit ) ', ...
            'node[%slbl, above left] {$x_{%u}$};\n' ];
    fprintf( fileID, '\t%% draw coordinate system:\n' );
    fprintf( fileID, '\t\\ifdrawcoordinateaxes\n' );
    if is3D
        axismax = max( coordinates( :, dimensions( 3 ) ) );
        fprintf( fileID, cs_zaxisformat, 'axis', axismax * offsetscaling3D( 1 ), 1 + offsetscaling3D( 1 ), ...
            axismax * offsetscaling3D( 2 ), 1 + offsetscaling3D( 2 ), 'axis', dimensions( 3 ) - 1 );
    end
    axismax = max( coordinates( :, dimensions( 1 ) ) );
    fprintf( fileID, cs_xaxisformat, 'axis', axismax, 'axis', dimensions( 1 ) - 1 );
    axismax = max( coordinates( :, dimensions( 2 ) ) );
    fprintf( fileID, cs_yaxisformat, 'axis', axismax, 'axis', dimensions( 2 ) - 1 );
    fprintf( fileID, '\t\\fi\n' );
    fprintf( fileID, '\t\\ifdrawcoordinatemap\n' );
    if is3D
        fprintf( fileID, cs_zaxisformat, 'axesmap', offsetscaling3D( 1 ), 1 - offsetscaling3D( 1 ), ...
            offsetscaling3D( 2 ), 1 - offsetscaling3D( 2 ), 'axesmap', dimensions( 3 ) - 1 );
    end
    fprintf( fileID, cs_xaxisformat, 'axesmap', 1, 'axesmap', dimensions( 1 ) - 1 );
    fprintf( fileID, cs_yaxisformat, 'axesmap', 1, 'axesmap', dimensions( 2 ) - 1 );
    fprintf( fileID, '\t\\fi\n' );
    if is3D
        % put point coordinates:
        fprintf( fileID, '\t%% define coordinates:\n' );
        for i = 1 : N
            fprintf( fileID, pt_coordformat, i, ...
                coordinates( i, dimensions( 1 : 2 ) ) + ...
                coordinates( i, dimensions( 3 ) ) * offsetscaling3D );
        end
        % draw causal set from background to foreground:
        fprintf( fileID, '\t\\pgfmathsetmacro{\\CSlinkopacityoffset}{\\CSmaxopacity*\\CSlinkopacity-\\CSfading*\\CSlinkopacity}\n' );
        fprintf( fileID, '\t\\pgfmathsetmacro{\\CSlinkopacityfactor}{\\CSfading*\\CSlinkopacity}\n' );
        [ sorted3D, idx3D ] = sort( scalings3D, 'ascend' ); %#ok<ASGLU>
        elementsdrawn = false( N, 1 );
        draw_event = [ '\t\\ifnum\\firstHiddenEvent>%d \\node[%s, scale=\\CSeventscaling, opacity=\\CSeventopacity] (pn', pt_nameformat, ') at (p', pt_nameformat, ') {};\n' ];
        draw_link = [ '\t\t\\draw[causalrel%d, opacity=%0.3f*\\CSlinkopacityfactor+\\CSlinkopacityoffset] (pn', pt_nameformat, ') -- (pn', pt_nameformat, ');\n' ];
        draw_label = [ '\t\t\\ifdraweventlabels\\node[eventlbl, scale=\\CSeventscaling*\\CSlblscaling, fill opacity=\\CSeventopacity*\\CSlblopacityfill, text opacity=\\CSeventopacity*\\CSlblopacitytext] at (pn', pt_nameformat, '.east) {%d};\\fi\\fi\n' ];
        for i = transpose( idx3D )
            if ( ignore_faded == false ) || scalings3D( i ) > fadingdepth
                fprintf( fileID, '\t%% draw element #%d and its links:\n', i );
                fprintf( fileID, '\t\\pgfmathsetmacro{\\CSeventopacity}{%0.3f*\\CSfading+\\CSmaxopacity-\\CSfading}\n', scalings3D( i ) );
                fprintf( fileID, '\t\\pgfmathsetmacro{\\CSeventscaling}{%0.3f+%0.3f*\\CSminscaling}\n', scalings3D( i ), 1 - scalings3D( i ) );
                fprintf( fileID, draw_event, i, ...
                    EventStyleString( drawingstyles{ i } ), i, i );
                for s = 1 : length( linkselectors )
                    for j = 1 : N
                        if elementsdrawn( j ) && ...
                                linkselectors{ s }( i ) && ...
                                linkselectors{ s }( j ) && ...
                                ( L( i, j ) || L( j, i ) )
                            fprintf( fileID, draw_link, ...
                                s, scalings3D( j ), i, j );
                        end
                    end
                end
                fprintf( fileID, draw_label, i, i );
                elementsdrawn( i ) = true;
            end
        end
    else
        % put point coordinates:
        fprintf( fileID, '\t%% define coordinates:\n' );
        for i = 1 : N
            fprintf( fileID, pt_coordformat, i, coordinates( i, dimensions ) );
        end
        % draw causal set relations:
        fprintf( fileID, '\t%% draw links:\n' );
        for s = 1 : length( linkselectors )
            fprintf( fileID, replace( causet_saveas_links2tikz( ...
                L, linkselectors{ s }, s ), '\', '\\' ) );
        end
        % draw point coordinates:
        fprintf( fileID, '\t%% draw elements:\n' );
        draw_event = [ '\t\\ifnum\\firstHiddenEvent>%d \\node[%s] (pn', pt_nameformat, ') at (p', pt_nameformat, ') {};\n' ];
        draw_label = [ '\t\t\\ifdraweventlabels\\node[eventlbl] at (pn', pt_nameformat, '.east) {%d};\\fi\\fi\n' ];
        for i = 1 : N
            fprintf( fileID, draw_event, i, ...
                EventStyleString( drawingstyles{ i } ), i, i );
            fprintf( fileID, draw_label, i, i );
        end
%         for idig = 1 : pt_digits
%             if idig < pt_digits
%                 pt_namepadding = sprintf( [ '%0', num2str( pt_digits - idig ), 'u' ], 0 );
%             else
%                 pt_namepadding = '';
%             end
%             fprintf( fileID, '\t\\foreach \\pi in {%d, ..., %d} {\n', 10^( idig - 1 ), min( 10^idig - 1, N ) );
%             fprintf( fileID, [ '\t\t\\node[event] (pn', pt_namepadding, '\\pi) at (p', pt_namepadding, '\\pi) {};\n' ] );
%             fprintf( fileID, [ '\t\t\\ifdraweventlabels\\node[eventlbl] at ($(pn', pt_namepadding, '\\pi.east)$) {\\pi};\\fi\n' ] );
%             fprintf( fileID, '\t}\n' );
%         end
    end
    % end picture:
    if isfield( flags, 'EndCommands' )
        fprintf( fileID, '\t%% end commands:\n' );
        fprintf( fileID, flags.EndCommands );
    end
    if ~flags.IsSubPicture
        fprintf( fileID, '\\end{tikzpicture}\n' );
    end
    fclose( fileID );
end

function s = EventStyleString( dstyles )
    s = '';
    draw_eventstyles_count = length( dstyles );
    for j = 1 : draw_eventstyles_count
        if j < draw_eventstyles_count
            s = sprintf( '%sevent%d, ', s, dstyles( j ) );
        else
            s = sprintf( '%sevent%d', s, dstyles( j ) );
        end
    end
end