smoothen curve plotted using discrete points

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flowrate = [ 0 93 100 120 140 160 172 180 200 220 232 ] ;
head = [ 9.51 8.76 8.68 8.41 8.01 7.45 7.03 6.70 5.73 4.49 3.61 ] ;
cv20 = [ 0.8 1.1 2.2 4.1 6.6 9.9 13.9 18.6 24.1 30.3 37.2] ;
cv20new = smooth(cv20);
cv30 = [ 0.8 1 1.5 2.4 3.7 5.3 7.3 9.6 12.3 15.3 18.7 ] ;
cv30new = smooth(cv30);
cv40 = [ 0.8 0.9 1.3 1.8 2.7 3.7 5 6.4 8.2 10.1 12.3 ] ;
cv40new = smooth(cv40);
cv50 = [ 0.8 0.9 1.1 1.6 2.2 2.9 3.9 5 6.3 7.7 9.3 ] ;
cv50new = smooth(cv50);
cv60 = [ 0.8 0.8 1.1 1.4 1.9 2.5 3.3 4.2 5.2 6.4 7.7 ] ;
cv60new = smooth(cv60);
cv70 = [ 0.8 0.8 1 1.3 1.8 2.3 2.9 3.7 4.6 5.6 6.7] ;
cv70new = smooth(cv70);
cv80 = [ 0.8 0.8 1 1.3 1.7 2.1 2.7 3.4 4.2 5.1 6.1 ] ;
cv80new = smooth(cv80);
plot(flowrate,head)
title('Pump Performance Curves Estimates')
hold on
plot(flowrate,cv20new)
hold on
plot(flowrate,cv30new)
hold on
plot(flowrate,cv40new)
hold on
plot(flowrate,cv50new)
hold on
plot(flowrate,cv60new)
hold on
plot(flowrate,cv70new)
hold on
plot(flowrate,cv80new)
hold off
ylim([0.0 10.0])
i want my curve to be smoothened into a parabola like the below graph:
The curves for cv20,cv30 .. are not smoothening even after i used the smooth curve command.

Accepted Answer

Mathieu NOE
Mathieu NOE on 8 Jan 2022
hello
this would be my suggestion - others methods I tried have not been successfull
flowrate = [ 0 93 100 120 140 160 172 180 200 220 232 ] ;
head = [ 9.51 8.76 8.68 8.41 8.01 7.45 7.03 6.70 5.73 4.49 3.61 ] ;
cv20 = [ 0.8 1.1 2.2 4.1 6.6 9.9 13.9 18.6 24.1 30.3 37.2] ;
cv30 = [ 0.8 1 1.5 2.4 3.7 5.3 7.3 9.6 12.3 15.3 18.7 ] ;
cv40 = [ 0.8 0.9 1.3 1.8 2.7 3.7 5 6.4 8.2 10.1 12.3 ] ;
cv50 = [ 0.8 0.9 1.1 1.6 2.2 2.9 3.9 5 6.3 7.7 9.3 ] ;
cv60 = [ 0.8 0.8 1.1 1.4 1.9 2.5 3.3 4.2 5.2 6.4 7.7 ] ;
cv70 = [ 0.8 0.8 1 1.3 1.8 2.3 2.9 3.7 4.6 5.6 6.7] ;
cv80 = [ 0.8 0.8 1 1.3 1.7 2.1 2.7 3.4 4.2 5.1 6.1 ] ;
% plot
figure(1)
plot(flowrate,head,flowrate,cv20,flowrate,cv30,...
flowrate,cv40,flowrate,cv50,flowrate,cv60,...
flowrate,cv70,flowrate,cv80);
title('Pump Performance Curves Estimates')
ylim([0.0 10.0])
% plot
flowrate2 = linspace(min(flowrate),max(flowrate),100);
[cv20new] = my_opti_fminsearch(flowrate,cv20,flowrate2);
[cv20new] = my_opti_fminsearch(flowrate,cv20,flowrate2);
[cv30new] = my_opti_fminsearch(flowrate,cv30,flowrate2);
[cv40new] = my_opti_fminsearch(flowrate,cv40,flowrate2);
[cv50new] = my_opti_fminsearch(flowrate,cv50,flowrate2);
[cv60new] = my_opti_fminsearch(flowrate,cv60,flowrate2);
[cv70new] = my_opti_fminsearch(flowrate,cv70,flowrate2);
[cv80new] = my_opti_fminsearch(flowrate,cv80,flowrate2);
figure(2)
plot(flowrate,head,flowrate2,cv20new,flowrate2,cv30new,...
flowrate2,cv40new,flowrate2,cv50new,flowrate2,cv60new,...
flowrate2,cv70new,flowrate2,cv80new);
title('Pump Performance Curves Estimates')
ylim([0.0 10.0])
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [cvnew] = my_opti_fminsearch(flowrate,cv,flowrate2)
cv = interp1(flowrate,cv,flowrate2);
% fminsearch method
x = flowrate2;
a = cv(1);
f = @(b,x) a + b.*(x.^2);
b_init = (cv(end) - a)./(flowrate(end).^2);
obj_fun = @(params) norm(f(params(1),flowrate2)-cv);
sol = fminsearch(obj_fun, [b_init]);
b_sol = sol(1);
cvnew = f(b_sol, flowrate2);
end
  2 Comments
Mathieu NOE
Mathieu NOE on 12 Jan 2022
here you want all curves to be a perfect parabola , so none of the "smoothing" functions can do an exact parabola
the trick is indeed to fit a parabola equation to your data with the constant term always the same (so all curves have same origin)
all the best

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