How can I make curve form data?
6 views (last 30 days)
I would like to make a convex curve from this (x,y) data that I have. The curve must connect the first and last points of y.
The help would be apprecited,
Thanks in advance,
David Goodmanson on 8 Feb 2020
Edited: David Goodmanson on 8 Feb 2020
The differences from a straight line are small, so it make sense to look at that difference.
x = [7000,7050,7100,7150,7200]'
y = [-92.9,-125.6,-158.5,-190.9,-223.5]'
ylin = linspace(y(1),y(end),5)'
ydiff = y - ylin;
The three differences are all negative, so absent any other information it can just be fit with a parabola that is zero at the end points. This will lead to a curve that is convex downwards.
p = (x-x(1)).*(x-x(end)); % parabola, zero at end points
c = p\ydiff; % least squares fit
xnew = linspace(7000,7200,500); % grid with more points
ydiffnew = c*(xnew-x(1)).*(xnew-x(end)); % fitted parabola, zero at end points
Then the final result ynew is this plus the linear line
slope = (y(end)-y(1))/(x(end)-x(1));
ylinnew = y(1) + slope*(xnew-x(1));
ynew = ylinnew + ydiffnew;