├── .gitignore ├── COPYING ├── README.md ├── deg2rad.m ├── extractpositional.m ├── extractpositionalTest.m ├── fractions.m ├── simpletri.m ├── ternaxes.m ├── terncontour.m ├── terncoords.m ├── terndemo.m ├── ternlabel.m ├── ternpcolor.m ├── ternplot.m ├── ternplot.png ├── ternplot_pro.m ├── ternsurf.m └── vertexlabel.m /.gitignore: -------------------------------------------------------------------------------- 1 | *~ 2 | *.asv 3 | .DS_Store 4 | *.mat 5 | -------------------------------------------------------------------------------- /COPYING: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007, 2011 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | Ternary plotting for Matlab 2 | =========================== 3 | 4 | [![DOI](https://zenodo.org/badge/31416657.svg)](https://zenodo.org/badge/latestdoi/31416657) 5 | 6 | This code helps you to plot ternary phase data on a ternary phase diagram. 7 | 8 | This package is also avialable [from File Exchange](http://www.mathworks.com/matlabcentral/fileexchange/2299-ternplot). 9 | 10 | It acts like plot (responds to hold, etc), also includes `ternlabel.m` 11 | to label all three axes. There are also functions to plot three 12 | dimensional plots and contours. 13 | -------------------------------------------------------------------------------- /deg2rad.m: -------------------------------------------------------------------------------- 1 | function rad = deg2rad(deg) 2 | rad = deg / 180 * pi; -------------------------------------------------------------------------------- /extractpositional.m: -------------------------------------------------------------------------------- 1 | function [remainingargs, value] = extractpositional(args, name, default) 2 | remainingargs = {}; 3 | skipping = false; 4 | value = default; 5 | for i = 1:length(args) 6 | if strcmp(args{i}, name) 7 | value = args{i+1}; 8 | skipping = true; 9 | elseif skipping 10 | skipping = false; 11 | else 12 | remainingargs{end+1} = args{i}; 13 | end 14 | end 15 | -------------------------------------------------------------------------------- /extractpositionalTest.m: -------------------------------------------------------------------------------- 1 | testargs = {'this', 'is', 'a', 'majors', 20, 'test'}; 2 | outputargs = {'this', 'is', 'a', 'test'}; 3 | 4 | %% Normal parsing 5 | [args, value] = extractpositional(testargs, 'majors', 10); 6 | assert(all(strcmp(args, outputargs)), 'Incorrect arguments passed back'); 7 | assert(value == 20, 'Incorrect value extracted'); 8 | 9 | %% Default behaviour 10 | [args, value] = extractpositional(outputargs, 'majors', 10); 11 | assert(all(strcmp(args, outputargs)), 'Args changed'); 12 | assert(value == 10, 'Incorrect value extracted'); 13 | 14 | %% Edge case: empty list 15 | [args, value] = extractpositional({}, 'majors', 10); 16 | assert(isempty(args), 'Empty args not handled correctly'); 17 | assert(value == 10, 'Empty args not handled correctly'); 18 | -------------------------------------------------------------------------------- /fractions.m: -------------------------------------------------------------------------------- 1 | % FRACTIONS normalise ternary data 2 | % [fA, fB, fC] = FRACTIONS(A, B, C) calculates fractional values for 3 | 4 | function [fA, fB, fC] = fractions(A, B, C) 5 | Total = (A+B+C); 6 | fA = A./Total; 7 | fB = B./Total; 8 | fC = 1-(fA+fB); 9 | -------------------------------------------------------------------------------- /simpletri.m: -------------------------------------------------------------------------------- 1 | % SIMPLETRI return simple triangulation for square datasets 2 | % TRI = SIMPLETRI(N) returns a matrix containing indexes to the 3 | % vertices of triangles fitted onto a square grid of size NxN. 4 | % 5 | % See also TERNSURF 6 | 7 | 8 | % Method: 9 | 10 | 11 | % Author Carl Sandrock 20031006 12 | 13 | % To do 14 | 15 | % Modifications 16 | 17 | % Modifiers 18 | % (CS) Carl Sandrock 19 | 20 | function tri = simpletri(N) 21 | 22 | % for each square, divide diagonally from top left to bottom right 23 | % The two triangles have their top left and bottom right points in common, 24 | % with the remaining point being either top right or bottom left 25 | % 26 | % tl--tr 27 | % |\ | 28 | % | \| 29 | % bl--br 30 | % 31 | 32 | % Remember that increasing i goes with increasing x, so from bottom to top 33 | 34 | [row, col] = meshgrid(1:N-1); 35 | 36 | bl = sub2ind([N, N], row, col); 37 | bl = bl(:); 38 | br = bl + 1; 39 | tl = bl + N; 40 | tr = tl + 1; 41 | 42 | tri = [tl bl br; tl tr br]; 43 | -------------------------------------------------------------------------------- /ternaxes.m: -------------------------------------------------------------------------------- 1 | % TERNAXES create ternary axis 2 | % HOLD_STATE = TERNAXES(MAJORS) creates a ternary axis system using the system 3 | % defaults and with MAJORS major tickmarks. 4 | 5 | % Author: Carl Sandrock 20050211 6 | 7 | % To Do 8 | 9 | % Modifications 10 | % 20160405 (SA) Added lines to change the order/direction of axes (i.e. 11 | % clockwise or counter-clockwise) cooresponding to user-specified 12 | % option on terncoords 13 | 14 | % Modifiers 15 | % (CS) Carl Sandrock 16 | % (SA) Shahab Afshari 17 | 18 | function [hold_state, cax, next] = ternaxes(majors) 19 | if nargin < 1 20 | majors = 10; 21 | end 22 | 23 | % TODO: Handle these as options 24 | direction = 'clockwise'; 25 | percentage = false; 26 | 27 | %TODO: Get a better way of offsetting the labels 28 | xoffset = 0.25; 29 | yoffset = 0.01; 30 | 31 | % get hold state 32 | cax = newplot; 33 | next = lower(get(cax,'NextPlot')); 34 | hold_state = ishold; 35 | 36 | % get x-axis text color so grid is in same color 37 | tc = get(cax,'xcolor'); 38 | ls = get(cax,'gridlinestyle'); 39 | 40 | % Hold on to current Text defaults, reset them to the 41 | % Axes' font attributes so tick marks use them. 42 | fAngle = get(cax, 'DefaultTextFontAngle'); 43 | fName = get(cax, 'DefaultTextFontName'); 44 | fSize = get(cax, 'DefaultTextFontSize'); 45 | fWeight = get(cax, 'DefaultTextFontWeight'); 46 | fUnits = get(cax, 'DefaultTextUnits'); 47 | 48 | set(cax, 'DefaultTextFontAngle', get(cax, 'FontAngle'), ... 49 | 'DefaultTextFontName', get(cax, 'FontName'), ... 50 | 'DefaultTextFontSize', get(cax, 'FontSize'), ... 51 | 'DefaultTextFontWeight', get(cax, 'FontWeight'), ... 52 | 'DefaultTextUnits','data') 53 | 54 | % only do grids if hold is off 55 | if ~hold_state 56 | %plot axis lines 57 | hold on; 58 | plot ([0 1 0.5 0],[0 0 sin(1/3*pi) 0], 'color', tc, 'linewidth',1,... 59 | 'handlevisibility','off'); 60 | set(gca, 'visible', 'off'); 61 | 62 | % plot background if necessary 63 | if ~ischar(get(cax,'color')) 64 | patch('xdata', [0 1 0.5 0], 'ydata', [0 0 sin(1/3*pi) 0], ... 65 | 'edgecolor',tc,'facecolor',get(gca,'color'),... 66 | 'handlevisibility','off'); 67 | end 68 | 69 | % Generate labels 70 | majorticks = linspace(0, 1, majors + 1); 71 | majorticks = majorticks(1:end-1); 72 | 73 | if percentage 74 | multiplier = 100; 75 | else 76 | multiplier = 1; 77 | end 78 | 79 | if ~strcmp(direction, 'clockwise') 80 | labels = num2str(majorticks'*multiplier); 81 | else 82 | labels = num2str(majorticks(end:-1:1)'*multiplier); 83 | end 84 | 85 | zerocomp = zeros(size(majorticks)); % represents zero composition 86 | 87 | % Plot right labels (no c - only b a) 88 | [lxc, lyc] = terncoords(1-majorticks, majorticks, zerocomp); 89 | text(lxc+0.05, lyc-0.025, [repmat(' ', length(labels), 1) labels]); 90 | 91 | % Plot bottom labels (no b - only a c) 92 | [lxb, lyb] = terncoords(majorticks, zerocomp, 1-majorticks); % fB = 1-fA 93 | text(lxb-0.115, lyb-0.065, labels, 'VerticalAlignment', 'Top'); 94 | 95 | % Plot left labels (no a, only c b) 96 | [lxa, lya] = terncoords(zerocomp, 1-majorticks, majorticks); 97 | text(lxa-0.035, lya+0.09, labels); 98 | 99 | nlabels = length(labels)-1; 100 | for i = 1:nlabels 101 | plot([lxa(i+1) lxb(nlabels - i + 2)], [lya(i+1) lyb(nlabels - i + 2)], ls, 'color', tc, 'linewidth',0.25,... 102 | 'handlevisibility','off'); 103 | plot([lxb(i+1) lxc(nlabels - i + 2)], [lyb(i+1) lyc(nlabels - i + 2)], ls, 'color', tc, 'linewidth',0.25,... 104 | 'handlevisibility','off'); 105 | plot([lxc(i+1) lxa(nlabels - i + 2)], [lyc(i+1) lya(nlabels - i + 2)], ls, 'color', tc, 'linewidth',0.25,... 106 | 'handlevisibility','off'); 107 | end; 108 | end; 109 | 110 | % Reset defaults 111 | set(cax, 'DefaultTextFontAngle', fAngle , ... 112 | 'DefaultTextFontName', fName , ... 113 | 'DefaultTextFontSize', fSize, ... 114 | 'DefaultTextFontWeight', fWeight, ... 115 | 'DefaultTextUnits', fUnits ); 116 | -------------------------------------------------------------------------------- /terncontour.m: -------------------------------------------------------------------------------- 1 | % TERNCONTOUR plot contours on ternary phase diagram 2 | % TERNCONTOUR(A, B, Z) plots contours of Z on ternary phase diagram for three components. C is calculated 3 | % as 1 - A - B. 4 | % 5 | % TERNCONTOUR(A, B, C, Z) plots contours of Z on ternary phase data for three components A B and C. If the values 6 | % are not fractions, the values are normalised by dividing by the total. 7 | % 8 | % TERNPLOT(A, B, C, Z, I) the same as the above, but with a user specified contour interval (see CONTOUR 9 | % for specification). 10 | % 11 | % NOTES 12 | % - An attempt is made to keep the plot close to the default contour type. The code has been based largely on the 13 | % code for TERNPLOT. 14 | % - The regular TITLE and LEGEND commands work with the plot from this function, as well as incrimental plotting 15 | % using HOLD. Labels can be placed on the axes using TERNLABEL 16 | % 17 | % See also TERNCONTOURF TERNPLOT TERNLABEL PLOT POLAR CONTOUR CONTOURF 18 | 19 | % b 20 | % / \ 21 | % / \ 22 | % c --- a 23 | 24 | % Author: Peter Selkin 20030507 based on TERNPLOT by Carl Sandrock 20020827 25 | 26 | % To do 27 | % Make TERNCONTOURF and TERNSURF 28 | 29 | % Modifications 30 | % 20070107 (CS) Modified to use new structure (more subroutines) 31 | 32 | % Modifiers 33 | % CS Carl Sandrock 34 | 35 | function [Hcl, Hha] = terncontour(A, B, C, Z, I) 36 | majors = 5; 37 | 38 | if nargin < 4 39 | Z = C; 40 | C = 1 - (A+B); 41 | end; 42 | 43 | if nargin < 5 44 | I=10; 45 | end; 46 | 47 | [fA, fB, fC] = fractions(A, B, C); 48 | [x, y] = terncoords(fA, fB, fC); 49 | 50 | % Sort data points in x order 51 | [x, i] = sort(x); 52 | y = y(i); 53 | Z = Z(i); 54 | 55 | % Now we have X, Y, Z as vectors. 56 | % use meshgrid to generate a grid 57 | Ngrid = 100; 58 | xr = linspace(min(x), max(x), Ngrid); 59 | yr = linspace(min(y), max(y), Ngrid); 60 | [xg ,yg] = meshgrid(xr, yr); 61 | 62 | % ...then use griddata to get a plottable array 63 | zg = griddata(x, y, Z, xg, yg, 'cubic'); 64 | 65 | [hold_state, cax, next] = ternaxes(majors); 66 | 67 | % plot data 68 | [Cl, Ha] = contour(xg, yg, zg, I, 'k-'); 69 | 70 | 71 | if nargout > 0 72 | Hcl=Cl; 73 | Hha=Ha; 74 | end 75 | 76 | if ~hold_state 77 | set(gca,'dataaspectratio',[1 1 1]), axis off; set(cax,'NextPlot',next); 78 | end 79 | -------------------------------------------------------------------------------- /terncoords.m: -------------------------------------------------------------------------------- 1 | % TERNCOORDS calculate rectangular coordinates of fractions on a ternary plot 2 | % [X, Y] = TERNCOORDS(FA, FB) returns the rectangular X and Y coordinates 3 | % for the point with a fraction defined by FA and FB. It is assumed that 4 | % FA and FB are sensible fractions. 5 | % 6 | % [X, Y] = TERNCOORDS(FA, FB, FC) returns the same. FC is assumed to be 7 | % the remainder when subtracting FA and FB from 1. 8 | 9 | % b 10 | % / \ 11 | % / \ 12 | % c --- a 13 | 14 | % Author: Carl Sandrock 20050211 15 | 16 | % Modifications 17 | % 20160405 (SA) rotation of the ternary axes in clockwise/counter-clockwise order 18 | % (User must directly switch to either options via 19 | % commenting/uncommenting the associated lines. 20 | % Moreover, any modification on terncoords must be adjusted 21 | % with associated lines on ternaxes) 22 | 23 | % Modifiers 24 | % SA Shahab Afshari 25 | 26 | function [x, y] = terncoords(fA, fB, fC) 27 | if nargin < 3 28 | fC = 1 - (fA + fB); 29 | end 30 | 31 | direction = 'clockwise'; 32 | 33 | if ~strcmp(direction, 'clockwise') 34 | y = fB*sin(deg2rad(60)); 35 | x = fA + y*cot(deg2rad(60)); 36 | else 37 | y = fC*sin(deg2rad(60)); 38 | x = 1 - fA - y*cot(deg2rad(60)); 39 | end -------------------------------------------------------------------------------- /terndemo.m: -------------------------------------------------------------------------------- 1 | %% Simple two-d plot 2 | 3 | dataA = linspace(0.1, 0.7, 20); 4 | dataB = -dataA.^2 + dataA + (rand(size(dataA)) - 0.5)/7; 5 | dataC = 1 - dataA - dataB; 6 | 7 | A = linspace(0, 1, 100); 8 | B = -A.^2+A; 9 | 10 | ternplot(dataA, dataB, dataC, 'r.', 'majors', 5); 11 | hold on 12 | ternplot(A, B) 13 | ternlabel('A', 'B', 'C') 14 | legend('Data', 'Fit') 15 | hold off 16 | 17 | %% Simple two-d density plot 18 | num_axes_steps = 5; 19 | num_color_classes = 5; 20 | ternplot_pro(dataA, dataB, dataC, num_axes_steps, num_color_classes); 21 | ternlabel('A', 'B', 'C'); 22 | hold on 23 | ternplot(dataA, dataB, dataC, 'r.'); 24 | hold off 25 | 26 | %% Three D plot for viscosity of HIPS, ABS and PETG polymer blends 27 | experimental = [... 28 | 1.000 0.000 0.000 29 | 0.000 1.000 0.000 30 | 0.000 0.000 1.000 31 | 0.500 0.500 0.000 32 | 0.500 0.000 0.500 33 | 0.000 0.500 0.500 34 | 0.333 0.333 0.333 35 | 0.750 0.250 0.000 36 | 0.250 0.750 0.000 37 | 0.750 0.000 0.250 38 | 0.250 0.000 0.750 39 | 0.000 0.750 0.250 40 | 0.000 0.250 0.750 41 | 0.667 0.167 0.167 42 | 0.167 0.667 0.167 43 | 0.167 0.167 0.667 44 | 0.000 0.900 0.100]; 45 | data = [... 46 | 0.139 47 | 0.373 48 | 0.089 49 | 0.151 50 | 0.056 51 | 0.679 52 | 0.095 53 | 0.153 54 | 0.178 55 | 0.084 56 | 0.040 57 | 0.463 58 | 0.163 59 | 0.111 60 | 0.170 61 | 0.072 62 | 0.333]; 63 | 64 | A = experimental(:, 1)'; 65 | B = experimental(:, 2)'; 66 | C = 1 - (A + B); 67 | 68 | figure 69 | subplot(2, 2, 1) 70 | ternplot(A, B, C, '.'); ternlabel('HIPS', 'ABS', 'PETG'); 71 | subplot(2, 2, 2) 72 | ternpcolor(A, B, data); ternlabel('HIPS', 'ABS', 'PETG'); 73 | shading interp 74 | subplot(2, 2, 3) 75 | terncontour(A, B, data); ternlabel('HIPS', 'ABS', 'PETG'); 76 | subplot(2, 2, 4) 77 | ternsurf(A, B, data); 78 | -------------------------------------------------------------------------------- /ternlabel.m: -------------------------------------------------------------------------------- 1 | % TERNLABEL label ternary phase diagram 2 | % TERNLABEL('ALABEL', 'BLABEL', 'CLABEL') labels a ternary phase diagram created using TERNPLOT 3 | % 4 | % H = TERNLABEL('ALABEL', 'BLABEL', 'CLABEL') returns handles to the text objects created. 5 | % with the labels provided. TeX escape codes are accepted. 6 | % 7 | % See also TERNPLOT 8 | 9 | % Author: Carl Sandrock 20020827 10 | 11 | % To Do 12 | 13 | % Modifications 14 | 15 | % Modifiers 16 | 17 | function h = ternlabel(A, B, C) 18 | r(1) = text(0.5, -0.05, A, 'horizontalalignment', 'center'); 19 | r(2) = text(1-0.45*sin(deg2rad(30)), 0.5, B, 'rotation', -60, 'horizontalalignment', 'center'); 20 | r(3) = text(0.45*sin(deg2rad(30)), 0.5, C, 'rotation', 60, 'horizontalalignment', 'center'); 21 | 22 | if nargout > 0 23 | h = r; 24 | end; -------------------------------------------------------------------------------- /ternpcolor.m: -------------------------------------------------------------------------------- 1 | % TERNPCOLOR plot pseudo color diagram on ternary axes 2 | % TERNPCOLOR(A, B, Z) plots surface fitted over Z on ternary phase diagram for three components. C is calculated 3 | % as 1 - A - B. 4 | % 5 | % TERNPCOLOR(A, B, C, Z) plots surface of Z on ternary phase data for three components A B and C. If the values 6 | % are not fractions, the values are normalised by dividing by the total. 7 | % 8 | % NOTES 9 | % - An attempt is made to keep the plot close to the default trisurf type. The code has been based largely on the 10 | % code for TERNPLOT. 11 | % - The regular TITLE and LEGEND commands work with the plot from this function, as well as incrimental plotting 12 | % using HOLD. Labels can be placed on the axes using TERNLABEL 13 | % 14 | % See also TERNSURF TERNCONTOUR 15 | 16 | % Author : Carl Sandrock 20070107 17 | 18 | % To do: Better error checking 19 | 20 | function ternpcolor(varargin) 21 | ternsurf(varargin{:}); 22 | view(0, 90); -------------------------------------------------------------------------------- /ternplot.m: -------------------------------------------------------------------------------- 1 | % TERNPLOT plot ternary phase diagram 2 | % TERNPLOT(A, B) plots ternary phase diagram for three components. C is calculated 3 | % as 1 - A - B. 4 | % 5 | % TERNPLOT(A, B, C) plots ternary phase data for three components A B and C. If the values 6 | % are not fractions, the values are normalised by dividing by the 7 | % total. 8 | % 9 | % TERNPLOT(A, B, C, LINETYPE) the same as the above, but with a user specified LINETYPE (see PLOT 10 | % for valid linetypes). 11 | % 12 | % The parameters above can be followed by parameter/value pairs to 13 | % specify additional properties as with the PLOT function. All 14 | % unrecognized options will be passed through to the PLOT command. The 15 | % following options are used by this function: 16 | % 17 | % Parameter Default Description 18 | % --------- ------- ----------- 19 | % majors 10 The number of major intervals to divide the plot grid into. 20 | % sortpoints false Sort points in x order before plotting 21 | % 22 | % Example 23 | % 24 | % plot(x, y, 'majors', 10) 25 | % 26 | % NOTES 27 | % - An attempt is made to keep the plot close to the default plot type. The code has been based largely on the 28 | % code for POLAR. 29 | % - The regular TITLE and LEGEND commands work with the plot from this function, as well as incrimental plotting 30 | % using HOLD. Labels can be placed on the axes using TERNLABEL 31 | % 32 | % See also TERNLABEL PLOT POLAR 33 | 34 | % b 35 | % / \ 36 | % / \ 37 | % c --- a 38 | 39 | % Author: Carl Sandrock 20020827 40 | 41 | % To do 42 | 43 | % Modifications 44 | % 20160405 (SA) Added an input argument 'major' 45 | 46 | % Modifiers 47 | % CS Carl Sandrock 48 | % SA Shahab Afshari 49 | 50 | function handles = ternplot(A, B, C, varargin) 51 | 52 | if nargin < 3 53 | C = 1 - (A+B); 54 | end; 55 | 56 | [varargin, majors] = extractpositional(varargin, 'majors', 10); 57 | [varargin, sortpoints] = extractpositional(varargin, 'sortpoints', false); 58 | 59 | [fA, fB, fC] = fractions(A, B, C); 60 | 61 | [x, y] = terncoords(fA, fB, fC); 62 | 63 | % Sort data points in x order 64 | if sortpoints 65 | [x, i] = sort(x); 66 | y = y(i); 67 | end 68 | 69 | % Make ternary axes 70 | [hold_state, cax, next] = ternaxes(majors); 71 | 72 | % plot data 73 | q = plot(x, y, varargin{:}); 74 | if nargout > 0 75 | handles = q; 76 | end 77 | if ~hold_state 78 | set(gca,'dataaspectratio',[1 1 1]), axis off; set(cax,'NextPlot',next); 79 | end 80 | -------------------------------------------------------------------------------- /ternplot.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/alchemyst/ternplot/9c72b9007977caf5f5b00cd236334ab39026000c/ternplot.png -------------------------------------------------------------------------------- /ternplot_pro.m: -------------------------------------------------------------------------------- 1 | % TERNPLOT_PRO plot ternary phase diagram, where the facecolors of the 2 | % triangular cells (in grey scale) represent density of points with respect 3 | % to overall counts of data. 4 | 5 | % b 6 | % / \ 7 | % / \ 8 | % c --- a 9 | 10 | % HFINAL = TERNPLOT_PRO(dataA, dataB, dataC, NUM_AXES_STEPS, NUM_COLOR_CLASSES) 11 | % plots ternary phase diagram for three components,i.e. dataA,dataB, 12 | % and dataC, each being as Nx1 vector, where N is overall counts of data. 13 | % NUM_AXES_STEPS, is a user specified number of steps (major ticks) on a-c, c-b, and b-a axes. 14 | % NUM_COLOR_CLASSES, is a user specified number of classes of assigned 15 | % facecolor of triangulare cells corresponding to computed point density within a particular cell. 16 | % For example, NUM_AXES_STEPS = 10, will divide a-c, c-b, and b-a axes into 17 | % 10 axial steps, and NUM_COLOR_CLASSES = 20 will make a colorbar of 20 different 18 | % colors (grey-scaled), where each color represent a particular density range. 19 | 20 | % Note: the main goal of the this code is to: first, capturing the triangular cells 21 | % and treat them as polygons using PATCH function (a pre-defined function in MATLAB). 22 | % The next steps are employing the INPOLYGON fucntion (a pre-defined function in MATLAB) 23 | % for counting the number of points within each polygon, and application of 24 | % TERNPLOT along with PATCH function to plot the final density ternary plot. 25 | 26 | % Author: Shahab Afshari 20160428 27 | % City University of New York/City College 28 | % Civil Engineering Department 29 | 30 | % To Do 31 | 32 | % Modifications 33 | % SA The value of 'majors' at the final plot is fixed to 10 to avoid tick 34 | % label interruption 35 | 36 | % Modifiers 37 | % (SA) Shahab Afshari 38 | 39 | function hfinal = ternplot_pro(dataA, dataB, dataC, num_axes_steps, num_color_classes) 40 | % preliminary effort for getting the indices of values of verticies and faces of 41 | % each triangular cell generated according to desired number of axial steps 42 | h0 = figure; 43 | elev = zeros(num_axes_steps,1); 44 | experimental = [linspace(0,1,num_axes_steps)',linspace(1,0,num_axes_steps)',elev]; 45 | %%%% 46 | Z = experimental(:, 3)'; 47 | [fA, fB, fC] = fractions(experimental(:, 1)', experimental(:, 2)', experimental(:, 3)'); 48 | [x, y] = terncoords(fA, fB, fC); 49 | % Sort data points in x order 50 | [x, i] = sort(x); 51 | y = y(i); 52 | Z = Z(i); 53 | % The matrixes we work with should be square for the triangulation to work 54 | N = num_axes_steps+1; 55 | % Now we have X, Y, Z as vectors. 56 | % use meshgrid to generate a grid 57 | Ar = linspace(min(fA), max(fA), N); 58 | Br = linspace(min(fB), max(fB), N); 59 | [Ag, Bg] = meshgrid(Ar, Br); 60 | [xg, yg] = terncoords(Ag, Bg); 61 | % ...then use griddata to get a plottable array 62 | zg = griddata(x, y, Z, xg, yg, 'v4'); 63 | zg(Ag + Bg > 1) = nan; 64 | % Make ternary axes 65 | [hold_state, cax, next] = ternaxes(num_axes_steps); 66 | % plot data 67 | tri = simpletri(N); 68 | h = trisurf(tri, xg, yg, zg); 69 | view([-37.5, 30]); 70 | if ~hold_state 71 | set(gca,'dataaspectratio',[1 1 1]), axis off; 72 | set(cax,'NextPlot',next); 73 | end 74 | view(0, 90); 75 | set(h, 'FaceColor', 'none'); 76 | v = get(h, 'Vertices'); 77 | f = get(h, 'Faces'); 78 | close(h0) 79 | clear fA fB fC x y N Ag Bg Ar Br xg yg hold_state cax next 80 | %%%% 81 | f2 = f; 82 | f2(ismember(f2(:,1),find(isnan(v(:,3)))),:)=[]; 83 | f2(ismember(f2(:,2),find(isnan(v(:,3)))),:)=[]; 84 | f2(ismember(f2(:,3),find(isnan(v(:,3)))),:)=[]; 85 | 86 | [fA, fB, fC] = fractions(dataA, dataB, dataC); 87 | [x, y] = terncoords(fA, fB, fC); 88 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 89 | 90 | total_data_count = length(dataA); 91 | % count points located within polygon extent 92 | for i = 1:size(f2, 1) 93 | inpoly_data_count = inpolygon(x, y, v(f2(i, :), 1), v(f2(i, :), 2)); 94 | density_i(i, 1) = sum(inpoly_data_count)/total_data_count; 95 | end 96 | % 97 | % specify the RGB ranges of the colorbar (here grey scale is applied) 98 | c_mat_down = 0; 99 | c_mat_up = round(1.05*max(density_i), 2, 'significant'); 100 | c_mat = repmat(linspace(1, 0, num_color_classes-1)', 1, 3); 101 | c_mat_1 = linspace(c_mat_down, c_mat_up, size(c_mat,1) + 1)'; 102 | c_mat = [c_mat_1(1:end-1), c_mat_1(2:end), c_mat]; 103 | % 104 | % Plot Ternary Diagram 105 | hfinal = figure; 106 | % here the 'majors' is fixed to 10 to avoid text-lable interruption. 107 | ternplot(dataA, dataB, dataC, 'majors', 10, '.', 'color', 'none') 108 | set(gca, 'visible', 'off'); 109 | hold on 110 | for i = 1: size(f2,1) 111 | if i < 2 112 | inpoly_data_count = sum(inpolygon(x, y,v(f2(i,:),1),v(f2(i,:),2))); 113 | density_i_dum = inpoly_data_count/total_data_count; 114 | patch('Faces',f2(1,:),'Vertices',v,'FaceColor',c_mat(find(density_i_dum 1) = nan; 66 | 67 | % Make ternary axes 68 | [hold_state, cax, next] = ternaxes(majors); 69 | 70 | % plot data 71 | tri = simpletri(N); 72 | 73 | %tri = delaunay(xg, yg, zg); 74 | handle = trisurf(tri, xg, yg, zg); 75 | %h = trimesh(tri, xg, yg, zg); 76 | view([-37.5, 30]); 77 | 78 | if ~hold_state 79 | set(gca,'dataaspectratio',[1 1 1]), axis off; set(cax,'NextPlot',next); 80 | end 81 | -------------------------------------------------------------------------------- /vertexlabel.m: -------------------------------------------------------------------------------- 1 | % VERTEXLABEL label ternary phase diagram at vertices 2 | % VERTEXLABEL('ALABEL', 'BLABEL', 'CLABEL') puts labels at vertices of ternary phase diagrams created using TERNPLOT 3 | % 4 | % VERTEXLABEL('ALABEL','BLABEL','CLABEL',OFFSET) sets the labels OFFSET units away from the vertices. 5 | % H = VERTEXLABEL('ALABEL', 'BLABEL', 'CLABEL') returns handles to the text objects created. 6 | % with the labels provided. TeX escape codes are accepted. 7 | % 8 | % See also TERNLABEL TERNPLOT TERNCONTOUR TERNCONTOURF 9 | 10 | % b 11 | % / \ 12 | % / \ 13 | % c --- a 14 | 15 | % Author: Peter Selkin 20030508 Modified from Carl Sandrock 20020827 16 | 17 | % To Do 18 | 19 | % Modifications 20 | 21 | % Modifiers 22 | 23 | function h = vertexlabel(A, B, C, offset) 24 | 25 | if (nargin~=4) 26 | offset=0.03; 27 | end 28 | 29 | r(1) = text(-offset, -offset, C, 'horizontalalignment', 'right'); 30 | r(2) = text(1+offset, -offset, A, 'horizontalalignment', 'left'); 31 | r(3) = text(0.5, sin(deg2rad(60))+offset, B, 'horizontalalignment', 'center'); 32 | 33 | if nargout > 0 34 | h = r; 35 | end; 36 | --------------------------------------------------------------------------------