Projecting a dataset on an ellipse

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Salad Box
Salad Box 2022-12-8
评论： Matt J 2022-12-16
Hi,
I fit an ellipse (in green) to my dataset (white dots).
I'd like to project each data point on the ellipse (or shifting each data point onto the ellipse using the shortest distance). Those projections on the ellipse will form a new set of data. How can I achieve this?
  2 个评论
Jonas
Jonas 2022-12-8
if you have the ellipse and your x and y corrdinates, use the interp2() function with the 'nearest' interpolation method
Salad Box
Salad Box 2022-12-12
Thank you. I will give it a try.

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回答（1 个）

Matt J
Matt J 2022-12-12
This code requires the download of trustregprob from the file exchange
https://www.mathworks.com/matlabcentral/fileexchange/53191-quadratic-minimization-with-norm-constraint
function Xp=ellipseprj(Q,xc,X0)
%Projects given 2D points onto 2D ellipse
%
% Xp=ellipseprj(Q,xc,X0)
%
%IN:
%
% Q,xc: Ellipse equation matrices. Q is 2x2 and xc is 2x1 such that
% ellipse equation is (y-xc).'*Q*(y-xc)=1
% X0: 2xN matrix of points to be projected
%
%OUT:
%
% Xp: 2xN matrix of projected points
N=size(X0,2);
xc=xc(:);
[Rt,D]=eig(Q);
Rt=real(Rt); D=real(D);
iD=diag(1./diag(D));
iDsqrt=sqrt(iD);
b=-iDsqrt*Rt.'*bsxfun(@minus,xc,X0);
Yp=nan(size(X0));
for i=1:N
Yp(:,i)=trustregprob(iD,b(:,i),1);
end
Xp=bsxfun(@plus, Rt*iDsqrt*Yp,xc);
  2 个评论
Salad Box
Salad Box 2022-12-16
Thank you for your answer.
% Q,xc: Ellipse equation matrices. Q is 2x2 and xc is 2x1 such that
% ellipse equation is (y-xc).'*Q*(y-xc)=1
I still don't fully understand what Q and xc is.
What do you mean by ellipse equation (y-xc).'*Q*(y-xc)=1?

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