Curve fitting: general Parabola --> translated and rotated coordinate system
37 Ansichten (letzte 30 Tage)
Ältere Kommentare anzeigen
Hi guys, I have a set of points through which I need to fit a general parabola (to find out its vertex, angle of inclination of directrix from x-axis and parameter a). But problem is these points are not well conditioned and they are in a rotated and translated coordinate system, though not inclined set of axes(angle between axes ==90 degree). Does anyone how to do that in matlab?
Points are something like this:
x= [-5.2:.4:0,-5.2:.4:0]';
y=[4,3.6,5.2,6,6.4,6.8,6.8,7.2,7.6,10.4,10.4,11.2,11.6,11.2,3.6,3.2,2.8,2.4,2,1.6,1.2,0.4,0,-.4,-1.2,-1.2,-1.6,-1.6]';
Just do plot(x,y,'.') and you will see what I am talking about.
Any help would be much appreciated.
Thanks, Shubham
0 Kommentare
Akzeptierte Antwort
Matt J
am 28 Jun. 2013
Bearbeitet: Matt J
am 28 Jun. 2013
Something like this, maybe:
function [vertex,theta, a] = myfit(x,y)
xy=[x(:),y(:)].';
theta= fminsearch(@(theta) cost(theta,xy), 45);
[~,coeffs]=cost(theta,xy);
[a,b,c]=deal(coeffs(1),coeffs(2), coeffs(3));
xv=-b/2/a;
vertex=R(-theta)*[xv;polyval(coeffs,xv)];
function [Cost,coeffs,xx,yy] = cost(theta,xy)
Rxy=R(theta)*xy;
[xx,idx]=sort(Rxy(1,:));
yy=Rxy(2,idx);
[coeffs,S]=polyfit(xx,yy,2);
Cost=S.normr;
function Rmat=R(theta)
Rmat=[cosd(theta), -sind(theta); sind(theta), cosd(theta)];
5 Kommentare
Carl Witthoft
am 17 Okt. 2016
I think there's a bug in the proposed solution: if the original parabola is rotated in the opposite direction, the default starting value (+45) will find a local minimum at a value roughly 90 degrees off, and not very accurately there. Probably the initial value should be selected after determining in which quadrant(s) the majority of the input dataset reside(s). The reason for this problem is that the parabola x=y^2 will yield a minimum more or less for a degenerate parabola, i.e. straight line, along the axis of the parabola.
Christoph
am 3 Apr. 2017
Bearbeitet: Christoph
am 3 Apr. 2017
First let me thank you very much for your provided code, it helped me a lot. Second this would be an idea how to draw the ellipse afterwards,
a = coeffs(1);
b = coeffs(2);
c = coeffs(3);
t=-1000:1:+1000;
xEllipse = -(a.*t.^2 + b*t + c) * sin(-theta) + cos(-theta)*t;
yEllipse = +(a.*t.^2 + b*t + c) * cos(-theta) + sin(-theta)*t;
plot(xEllipse,yEllipse,'b.');
Example Image or curve fitting, red the original points fitted with a polynomial for each side, plotted in blue.
And my question would be: If I am skipping the fminsearch for minimizing the cost function and finding the best theta angle and just use the 45° theta angle for the coefficient calculation I can also achieve good, sometimes also better cost results as while using the fminseach function. I am not able to understand this at the moment, could you provide a clarification for me. Thank you very much, Christoph
Weitere Antworten (0)
Siehe auch
Kategorien
Mehr zu Least Squares finden Sie in Help Center und File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!