Surface data cloud fitting to even asphere model
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I've got a set of (r,z) data which represent a surface section. I would like to fit such data to the Even asphere expression:
Where 
is the surface sagita, r is the radial coordinate, R is the radius of curvatre at the vertex, κ is the conic constant and 
are the coefficients describing the deviation of the surface from a pure conic section. Can anyone help to address the problem?
is the surface sagita, r is the radial coordinate, R is the radius of curvatre at the vertex, κ is the conic constant and are the coefficients describing the deviation of the surface from a pure conic section. Can anyone help to address the problem?I have calculated the value of R by first fitting the data to a sphere with the code attached below, but I can't find a way to fit the data to the term 
once R has been calculated. Thank you, your help is very much appreciated!
once R has been calculated. Thank you, your help is very much appreciated!-----------------------------------------------------------------
Function to fit circle to data set:
function Par = CircleFitting(XY)
centroid = mean(XY); % the centroid of the data set
X = XY(:,1) - centroid(1); % centering data
Y = XY(:,2) - centroid(2); % centering data
Z = X.*X + Y.*Y;
Zmean = mean(Z);
Z0 = (Z-Zmean)/(2*sqrt(Zmean));
ZXY = [Z0 X Y];
[U,S,V]=svd(ZXY,0);
A = V(:,3);
A(1) = A(1)/(2*sqrt(Zmean));
A = [A ; -Zmean*A(1)];
Par = [-(A(2:3))'/A(1)/2+centroid , sqrt(A(2)*A(2)+A(3)*A(3)-4*A(1)*A(4))/abs(A(1))/2];
end
采纳的回答
Torsten
2022-9-7
% your data
x = ...;
y = ...;
z = ...;
p0 = [...]; % initial guess for R and kappa
p = lsqnonlin(@(p)fun(p,x,y,z),p0)
function res = fun(p,x,y,z)
rho = 1/p(1);
kappa = p(2);
r = sqrt(x.^2+y.^2);
res = z - r.^2*rho./(1+sqrt(1-(1+kappa)*(r*rho).^2));
end
9 个评论
Cl ES
2022-9-7
Cl ES
2022-9-7
Torsten
2022-9-7
Sorry, I cannot recognize "my" code from what you programmed.
I tried to fit both R and kappa simultaneously.
So in order to test my approach, I need to know what the 2 columns of your data file contain. Is it correct to assume that the first column is r and the second column is z ?
Cl ES
2022-9-8
Torsten
2022-9-8
And r can be negative ? I thought it is sqrt(x^2+y^2) ?
Bruno Luong
2022-9-8
it doesn't matter aspheric equation is even and depends on r^2 only
data = readmatrix('https://de.mathworks.com/matlabcentral/answers/uploaded_files/1119340/data.txt');
r = data(:,1);
z = data(:,2);
p0 = [50 0.01]; % initial guess for R and kappa
lb = [0 0];
ub = [Inf Inf];
format long
%p = lsqnonlin(@(p)fun(p,r,z),p0)
p = fmincon(@(p)fun(p,r,z),p0,[],[],[],[],lb,ub,@(p)nonlcon(p,r,z))
fun(p,r,z)
function res = fun(p,r,z)
rho = 1/p(1);
kappa = p(2);
%res = z - r.^2*rho./(1+sqrt(1-(1+kappa)*(r*rho).^2));
res = sum((z - r.^2*rho./(1+sqrt(1-(1+kappa)*(r*rho).^2))).^2);
end
function [c,ceq] = nonlcon(p,r,z)
rho = 1/p(1);
kappa = p(2);
c = -(1-(1+kappa)*(r*rho).^2);
ceq = [];
end
Cl ES
2022-9-8
Torsten
2022-9-8
So many brackets ... I corrected the code.
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