# Beginning and end of the curve isn't linked with points

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Josef on 22 May 2023
Commented: Josef on 23 May 2023
Here is my MWE:
clc;
close all;
%There are input constants
cP=0.05;
cN=0.05;
cMg=0.005;
logb0=2.88;
logb1=1.17;
logb2=4.85;
logb3=2.58;
logKs1=-12.6;
pKa1=-2.143;
pKa2=-7.205;
pKa3=-12.34;
pKb1NH3=-4.753355133;
%there is a range of x-axis (0-14)
pH=0:0.01:14;
%There are calculations of cH2PO4 cHPO4 cPO4, they have to be calculated for black curve equation (they are variables of final curve equation and depend on pH value)
Ka1=power(10,pKa1);
Ka2=power(10,pKa2);
Ka3=power(10,pKa3);
cH2PO4=cP.*Ka1.*(power(10,-pH)).^(2)./((power(10,-pH).^(3))+Ka1.*(power(10,-pH).^(2))+Ka1.*Ka2.*(power(10,-pH).^(1))+Ka1.*Ka2.*Ka3);
cHPO4=cP.*Ka1.*Ka2.*power(10,-pH)./((power(10,-pH).^(3))+Ka1.*(power(10,-pH).^(2))+Ka1.*Ka2.*(power(10,-pH).^(1))+Ka1.*Ka2.*Ka3);
cPO4=cP.*Ka1.*Ka2.*Ka3./((power(10,-pH).^(3))+Ka1.*(power(10,-pH).^(2))+Ka1.*Ka2.*(power(10,-pH).^(1))+Ka1.*Ka2.*Ka3);
%There is calculations of cNH4, it has to be calculated for black curve equation (it is variable of final curve equation and depends on pH value also)
pOH=14-pH;
Kb1=power(10,pKb1NH3);
cNH4=cN.*Kb1./(power(10,-pOH)+Kb1);
%there are some partial calculations for the black curve equation
b0=power(10,logb0);
b1=power(10,logb1);
b2=power(10,logb2);
b3=power(10,logb3);
Ks1=power(10,logKs1);
cOH=power(10,pH-14);
%this is the black curve equation
logcNP=Ks1./(cPO4.*cNH4).*(1+b1.*cH2PO4+b0.*cHPO4+b2.*cPO4+b3*cOH);
%there are calculated a crosssections of the black curve with magenta dashed line (cMg value of 0.005 at the beginning of the code)
Index_NP = find(diff(sign(logcNP - cMg)));
for i = 1:numel(Index_NP);
IndexRange_NP = max(1,Index_NP(i)-1) : min(numel(pH),Index_NP(i)+1);
Crossection_NP(i) = interp1(logcNP(IndexRange_NP),pH(IndexRange_NP), cMg);
end
%Here are boundary consitions of magenta curve (not dashed)
pH_NP=(Crossection_NP(1)<=pH&pH<=Crossection_NP(2));
%This is plot of the final curve (black), crossections (cyan points), magenta dashed line and magenta curve
semilogy(pH,logcNP,'-', 'color', 'k', 'MarkerFaceColor','w', 'MarkerEdgeColor', 'm');
box off;
hold on;
semilogy(pH(pH_NP),logcNP(pH_NP),'-', 'color', 'm', 'MarkerFaceColor','w', 'MarkerEdgeColor', 'm');
box off;
hold on;
plot([0 Crossection_NP(1)],[cMg cMg],'--', 'color', 'm', 'LineWidth',0.5);
box off;
hold on;
plot(Crossection_NP(1), cMg, 'oc', 'MarkerFaceColor', 'w' ,'MarkerSize', 5);
box off;
hold on;
plot(Crossection_NP(2), cMg, 'oc', 'MarkerFaceColor', 'w' ,'MarkerSize', 5);
box off;
hold on;
axis([0 14 0.000000000000000001 1000000000000000000]);
xlabel('pH (-)');
ylabel('c {(mol/dm^{3})}');
axis square;
grid on;
axis on;
box off;
hold off;
the MWE leads to full scale plot:
if you zoom for more detailed view of magenta curve beginning and end It can be seen:
As it can be seen from zoomed pictures, the magenta curve is not joined with cyan points. How can It be done - magenta curve joined with cyan points? Seems like it is a problem of plotting accuracy.

Askic V on 22 May 2023
At the bottom of your script I have added the following code:
% Define number of digits
numDigits = 10;
% Enable data cursor mode
dcm = datacursormode(gcf);
set(dcm, 'DisplayStyle', 'datatip', 'SnapToDataVertex', 'on',...
'UpdateFcn', @(src, event) ...
{['X: ' num2str(event.Position(1), numDigits)],...
['Y: ' num2str(event.Position(2), numDigits)]});
And this is how it looks like:
This is done with the help of chatGPT.
##### 3 CommentsShow 1 older commentHide 1 older comment
Askic V on 23 May 2023
Edited: Askic V on 23 May 2023
I see, in that case, try to reduce the step (plot is drawing a diagram from discrete set of points, by connecting with lines.
Try this:
pH=0:0.001:14; % reduce step for example 10 times
Josef on 23 May 2023
Thank you, your solution works! :-)