Bi-linear (piecewise) curve fitting
Can someone explain how to plot the two linear lines (Billinear curve fiiting) from the existing curve?
Neeta Dsouza answered .
2025-11-20
T1 = readtable('testdata.xlsx');
x = T1.Displacement;
y = T1.BaseForce;
% top flat curve (apex)
[m,idy] = max(y);
ym = m*ones(size(y));
plot(x,y,'*-',x,ym,'g','Linewidth',3);
hold on
% red curve ( "yellow" net area must be zero)
% origin = 0,0 (first data point)
x1 = x(1);
y1 = y(1);
% let's find out which second point of the curve let us find the min area
xx = x(1:idy);
yy = y(1:idy);
for ck = 2:idy
x2 = x(ck);
y2 = y(ck);
slope = (y2-y1)/(x2-x1);
yl = y1 + slope*(xx - x1);
% compute yellow area A
A(ck) = trapz(xx,(yy-yl));
end
% find zero crossing value for A (with linear interpolation)
threshold = 0;
xx_zc = find_zc(xx,A,threshold);
yy_zc = interp1(xx,yy,xx_zc);
slope = (yy_zc-y1)/(xx_zc-x1);
yl = y1 + slope*(xx - x1);
plot(xx,yl,'r','Linewidth',3);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [Zx] = find_zc(x,y,threshold)
% positive slope "zero" crossing detection, using linear interpolation
y = y - threshold;
zci = @(data) find(diff(sign(data))>0); %define function: returns indices of +ZCs
ix=zci(y); %find indices of + zero crossings of x
ZeroX = @(x0,y0,x1,y1) x0 - (y0.*(x0 - x1))./(y0 - y1); % Interpolated x value for Zero-Crossing
Zx = ZeroX(x(ix),y(ix),x(ix+1),y(ix+1));
end