Editing Figure to Create Equilateral Triangle

Hi, I'm trying to make this figure an equilateral triangle but I'm not entirely sure how since I've already tried editing part of the code (specifically below the f1=figure lines) . The code is below:

%Input:
%sand: sand fraction [0..1], (nx1)
%clay: Clay fraction[0..1], (nx1)
%T: type of classification: 'usda'
%Varargin{1}: PLOT, BOOLEAN: 1: plots the usda texture triangle plus data
%points
%
%Output:
% SC:    CellArray of soil class strings, (nx1)
% silt:  Silt fraction [%], (nx1)
% SCINT: Array of soil class integers, (nx1)
% SC2:  CellArray of soil class strings in short notation, e.g. S for SAND (nx1)
%
%Example:
%soil_classification(sand,clay, 'usda')
%soil_classification([0.5;0.3;0.1;0],[0.1;0.2;0.4;0.8], 'usda',1)
%--------------------------------------------------------------------------
%disp('-------------------------------------------------------------------')
%disp('                       U S D A soil Classification                 ')
%disp('-------------------------------------------------------------------')
function [SC, silt, SCINT, SC2]=soil_classification(sand, clay, T,varargin)

   if strcmp(T,'usda')==0
      error('only usda defined so far...')
   end
   if isempty(sand)|isnan(sand)|min(sand)<0
       error('wrong input: sand')
   end
   if isempty(clay)|isnan(clay)|min(clay)<0
       error('wrong input: sand')
   end
   if max(sand)>1
       sand=sand/100;
       warning('sand is >1; ...divided by 100 to get fraction instead of %')
   end
   if max(clay)>1
       clay=clay/100;
       warning('clay is >1; ...divided by 100 to get fraction instead of %')
   end
   if max(sand+clay)>1
      error('data inconsisent: (Clay + Sand)>1')
   end
  %--------------------------------------------------------------------------
  %--------------------------------------------------------------------------
  %--------------------------------------------------------------------------
  silt=1-sand-clay;
  i=1;
   for i=1:length(clay)
       if (silt(i)+1.5*clay(i))<.15
           SC{i,:}='SAND';
       elseif ((silt(i)+1.5*clay(i))>=.15)&((silt(i)+2*clay(i))<.3)
           SC{i,:}='LOAMY SAND';
       elseif (clay(i)>=0.07) & (clay(i)<=0.2) & (sand(i)>0.52) & ((silt(i)+2*clay(i))>=0.3) 
           SC{i,:}='SANDY LOAM';
       elseif (clay(i)<0.07) & (silt(i) < 0.5) & ((silt(i)+2*clay(i))>=0.3)
           SC{i,:}='SANDY LOAM';
       elseif (clay(i)>=0.07) & (clay(i)<=0.27) & (silt(i)>=0.28) & (silt(i)<0.5) & (sand(i)<=0.52)
           SC{i,:}='LOAM';
       elseif ((silt(i)>=0.5) & clay(i)>=0.12 & clay(i)<0.27) | (silt(i)>=0.5 & silt(i)<0.8 & clay(i)<0.12)
           SC{i,:}='SILT LOAM';
       elseif silt(i)>=0.8 & clay(i)<0.12
           SC{i,:}='SILT';
       elseif clay(i)>=0.2 & clay(i)<0.35 & silt(i)<0.28 & sand(i)>0.45
           SC{i,:}='SANDY CLAY LOAM';
       elseif clay(i)>=0.27 & clay(i) <0.4 & sand(i)>0.2 & sand(i)<=0.45
           SC{i,:}='CLAY LOAM';
       elseif clay(i)>=0.27 & clay(i)<0.4 & sand(i)<=0.2
           SC{i,:}='SILTY CLAY LOAM';
       elseif clay(i)>=0.35 & sand(i)>=0.45
           SC{i,:}='SANDY CLAY';
       elseif clay(i)>=0.4 & silt(i)>=0.4
           SC{i,:}='SILTY CLAY';
       elseif clay(i)>= 0.4 & sand(i)<=0.45 & silt(i)<0.4
           SC{i,:}='CLAY';
       else
           warning('no soil class found')
       end
   end
   %------------------------------------------------------------------------
   if varargin{1}==1
       close
       f1=figure;
       %set(gcf,'Color','w','position',[2800 300 600 600])
       plot([0 100],[0 0],'k');hold on
       set(gca,'XDir','reverse')
       plot([0 50],[0 100],'k')
       plot([50 100],[100 0],'k')
       xlabel('Sand [%]')
       grin on
       text(95,60,'Clay [%]','FontSize',14)
       text(25,60,'Silt [%]','FontSize',14)
       text(55,-5,'Sand [%]','FontSize',14)

       pl=fill([100 85 95 100],[0 0 10 0],'w')
       text(97,3, 'Sand','color','k')

       p2= fill([85 70 92.4 95 85],[0 0 15 10 0],'w')
       text(87,3,{'Loamy';'   sand'})

       p3=fill([70 50 46.7 55 62 90 92.4 70],[0 0 7 7 20 20 15 0],'w')
       text(75,10,'Sandy Loam')    

       p4=fill([55 46.7 38 58.1 62 55],[7 7 27 27 20 7],'w')
       text(55,15,'Loam')

       p5=fill([50 20 13.5 6 13.2 38 50],[0 0 12 12 27 27 0],'w')
       text(35, 10, 'Silt Loam')
       p6=fill([20 0 6 13.5 20],[0 0 12 12 0],'w')
       text(12,5,'Silt')

       p7=fill([90 62 58.1 62.5 82.5 90],[20 20 27 35 35 20],'w')
       text(85,27,'Sandy Clay Loam')

       p8=fill([58.1 33 40 65 58],[27 27 40 40 27],'w')
       text(55,34,'Clay Loam','Color','k')

       p9=fill([33 13.5 20 40 33],[27 27 40 40 27],'w')
       text(33,33,{'Silty';'Clay Loam'})

       p10=fill([82.5 62.5 72.5 82.5],[35 35 55 35],'w')
       text(80,38,'Sandy Clay','Color','k')

       p11=fill([65 40 30 50 72.5 65],[40 40 60 100 55 40],'w')
       text(55,60,'Clay')

       p12=fill([40 20 30 40],[40 40 60 40],'w')
       text(35,45,'Silty Clay','Color','k')
       axis square
       axis off

       i=1;
       for i=1:length(sand)
           o=100-(1-clay(i))*100; %offset
           plot(sand(i)*100+o/2,clay(i)*100,'ok','MarkerFaceColor','k')
       end
   end

   %%get SCINT
   SCINT = nan(size(SC,1),1);
   SCINT(strcmp(SC,'SAND')) = 1;
   SCINT(strcmp(SC,'LOAMY SAND')) = 2;
   SCINT(strcmp(SC,'SANDY LOAM')) = 3;
   SCINT(strcmp(SC,'LOAM')) = 4;        
   SCINT(strcmp(SC,'SILT LOAM')) = 5;   
   SCINT(strcmp(SC,'SILT')) = 6;   
   SCINT(strcmp(SC,'SANDY CLAY LOAM')) = 7;   
   SCINT(strcmp(SC,'CLAY LOAM')) = 8;   
   SCINT(strcmp(SC,'SILTY CLAY LOAM')) = 9;   
   SCINT(strcmp(SC,'SANDY CLAY')) = 10;   
   SCINT(strcmp(SC,'SILTY CLAY')) = 11;   
   SCINT(strcmp(SC,'CLAY')) = 12;   

   %%get SC2:
   SC2 = SC;

   SC2 = strrep(SC2,'SAND','S');
   SC2 = strrep(SC2,'LOAMY SAND','LS');
   SC2 = strrep(SC2,'SANDY LOAM','SL');
   SC2 = strrep(SC2,'LOAM','L');
   SC2 = strrep(SC2,'SILT LOAM','SIL');
   SC2 = strrep(SC2,'SILT','SI');
   SC2 = strrep(SC2,'SANDY CLAY LOAM','SCL');
   SC2 = strrep(SC2,'CLAY LOAM','CL');
   SC2 = strrep(SC2,'SILTY CLAY LOAM','SICL');
   SC2 = strrep(SC2,'SANDY CLAY','SC');
   SC2 = strrep(SC2,'SILTY CLAY','SIC');
   SC2 = strrep(SC2,'CLAY','C');
   SC2 = strrep(SC2,' ','');
   SC2 = strrep(SC2,'Y','');
   %test: [SC,~,~,SC2] = soil_classification([0:0.1:1,0:0.1:0.5],[1:-0.1:0,0:0.1:0.5],'usda',0)
  end %of function

To create the figure, put the following into the command window:

soil_classification([0.6,0.2,.3,.4,.3,.1,.1,.8,.6,.9,.73,.6,.55,.64,.69,.1], [0.3,0.6,.3,.2,.1,.5,.3,.1,.1,.1,.1,.34,.11,.27,.13,.5], 'usda',1)

Let me know how to edit the figure to make it any equilateral traignle rather than an isosceles triangle. Thanks!

Answer 1

[Star Strider]

Your triangle should have a height of 50, not 100.

This will outline the triangle as equilateral:

         f1=figure;
         %set(gcf,'Color','w','position',[2800 300 600 600])
         plot([0 100],[0 0],'k');hold on
         set(gca,'XDir','reverse')
         plot([0 50],[0 50],'k')
         plot([50 100],[50 0],'k')

You need to go through and change the other relevant lines of your code to accommodate that.

Alternatively, there’s a simpler solution:

daspect([1  2/sqrt(3)  1])

That should go just before ‘%% get SCINT’ just after the last if-block. This takes advantage of the properties of equilateral triangles, adjusted for the way they are plotted in MATLAB.

Answer 2

[Roger Stafford]

If (x1,y1) and (x2,y2) are any two points, then a third point defined by:

(x1+x2-sqrt(3)*(y2-y1))/2,(y1+y2+sqrt(3)*(x2-x1))/2

together with these two points will always constitute the three vertices of an equilateral triangle.