# How can I make curve form data?

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Riyadh Muttaleb on 6 Feb 2020
Commented: Riyadh Muttaleb on 9 Feb 2020
Hi All,
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.
x= 7000,7050,7100,7150,7200
y= -92.9,-125.6,-158.5,-190.9,-223.5
The help would be apprecited,

Walter Roberson on 7 Feb 2020
After the polyfit,
xs = linspace(x(1), x(2));
ys = polyval(p, xs);
plot(xs, ys)
Riyadh Muttaleb on 7 Feb 2020
I got a straight line!
Walter Roberson on 7 Feb 2020
No you didn't -- you get a curved line that was sampled over a small enough region that it looked flat.
If you look at diff(y) you will see that the differences between adjacent y values is approximately constant, which is what you would expect for a straight line.
If you fit as a polynomial of degree 2, then the minimum of that polynomial is at 23425 and the zero crossings are at 6859 and 39990

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;
figure(1)
plot(x,ydiff,'o-');
grid on
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
figure(2)
plot(x,ydiff,'o-',xnew,ydiffnew)
grid on
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;
figure(3)
plot(x,y,'o-',xnew,ynew)
grid on

#### 1 Comment

Riyadh Muttaleb on 9 Feb 2020
Thank you so much for your great work, However, the seconed part the curve is very good while in the third part it looks like a straight line!