3D curve fitting

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tabf
tabf 2023-6-12
评论： tabf 2023-6-24
I am a beginner in MATLAB, and now I have obtained a point cloud data for 3D curve fitting relative to these points, not surface fitting. Is there any method that can achieve good 3D curve fitting? thanks
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显示 9更早的评论
Mathieu NOE
Mathieu NOE 2023-6-23
this is a code to find a polynomial fit for the S shaped groove (trajectory)
N = readmatrix('S.txt');
x = N(:, 1);
y = N(:, 2);
z = N(:, 3);
% detrend the Z data
order = 1;
p = polyfitn([x,y],z,order);
pC = p.Coefficients; % get the polynomial coefficients
pTerms = p.ModelTerms;
% create the polynomial model (z = f(x,y))
zt = 0;
for k = 1:numel(pC)
zt = zt + pC(k)*(x.^pTerms(k,1)).*(y.^pTerms(k,2)); %
end
figure(1),
plot3(x,y,z,'r.',x,y,zt,'.k','linewidth',2); %
xlabel('X');
ylabel('Y');
zlabel('Z');
legend('raw data','fitted plane');
axis tight square
% apply detrend to the Z data
zd = z - zt;
figure(2),
plot3(x,y,zd,'.','linewidth',2); %
xlabel('X');
ylabel('Y');
zlabel('Z');
axis tight square
% keep the highets z points to get the S shape of the groove
id = (zd>0.85*max(zd));
xx = x(id);
yy = y(id);
% make sure x data is unique and sorted
[xx,ia,ic] = unique(xx);
yy = yy(ia);
% Fit a polynomial p of degree "degree" to the (x,y) data:
degree = 5;
p = polyfit(xx,yy,degree);
% Evaluate the fitted polynomial p and plot:
yyf = polyval(p,xx);
eqn = poly_equation(flip(p)); % polynomial equation (string)
Rsquared = my_Rsquared_coeff(yy,yyf); % correlation coefficient
figure(3);plot(xx,yy,'*',xx,yyf,'-')
xlabel('X');
ylabel('Y');
legend('data',eqn)
title(['Data fit , R² = ' num2str(Rsquared)]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function Rsquared = my_Rsquared_coeff(data,data_fit)
% R² correlation coefficient computation
% The total sum of squares
sum_of_squares = sum((data-mean(data)).^2);
% The sum of squares of residuals, also called the residual sum of squares:
sum_of_squares_of_residuals = sum((data-data_fit).^2);
% definition of the coefficient of correlation is
Rsquared = 1 - sum_of_squares_of_residuals/sum_of_squares;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function eqn = poly_equation(a_hat)
eqn = " y = "+a_hat(1);
for i = 2:(length(a_hat))
if sign(a_hat(i))>0
str = " + ";
else
str = " ";
end
if i == 2
eqn = eqn+str+a_hat(i)+" * x";
else
eqn = eqn+str+a_hat(i)+" * x^"+(i-1)+" ";
end
end
eqn = eqn+" ";
end
tabf
tabf 2023-6-24
I tried to fit the 2D curves of XY and yz first, and then merge the two curves into one 3D curve, but the results I have obtained are not very good now

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采纳的回答

Mathieu NOE
Mathieu NOE 2023-6-15
hello again
I can make you this suggestion
I devised that your curve could be parametrized by these 2 equations :
z = a + b*y;
x = c + d*sin(w*y+e);
hope it helps
% ptCloud = pcread('quxiandian.pcd');
% N = ptCloud.Location;
N = readmatrix('QUXIANDIAN.txt');
x = N(:, 1);
y = N(:, 2);
z = N(:, 3);
%% model fit
% z = a + b*y;
% x = c + d*sin(w*y+e);
% initial values (for further optimisation - see below)
w = (2*pi)/(max(y)-min(y));
b = (max(z)-min(z))/(max(y)-min(y));
a = z(1) - b*y(1);
c = mean(x);
d = (max(x)-min(x))/2;
e = 4;
% create data for the fit model
yf = linspace(min(y),max(y),100);
zf = a + b*yf;
xf = c + d*sin(w*yf+e);
% Fit a polynomial p of degree "degree" to the (y,z) data:
degree = 1;
p = polyfit(y,z,degree);
a = p(2);
b = p(1);
% Fit custom equation to the (x,y) data:
% option 1 : with fminsearch
f = @(c,d,e,w,y) c + d*sin(w*y+e);
obj_fun = @(params) norm(f(params(1), params(2), params(3), params(4), y)-x);
C1_guess = [c d e w];
sol = fminsearch(obj_fun, C1_guess); %
% update c,d,e,w
c = sol(1);
d = sol(2);
e = sol(3);
w = sol(4);
zf = a + b*yf;
xf = c + d*sin(w*yf+e);
figure(1),plot3(x,y,z,'r.',xf,yf,zf,'k','linewidth',2)
axis tight square
  1 个评论
Mathieu NOE
Mathieu NOE 2023-6-16
hello again
FYI, you can also do a polynomial fit using this excellent FEX submission :
polyfitn - File Exchange - MATLAB Central (mathworks.com)
code :
N = readmatrix('QUXIANDIAN.txt');
x = N(:, 1);
y = N(:, 2);
z = N(:, 3);00;
p = polyfitn([x,y],z,3);
% % FEX : https://fr.mathworks.com/matlabcentral/fileexchange/34765-polyfitn?s_tid=ta_fx_results
% % The result can be converted into a symbolic form to view the model more simply.
% % Here I'll use the sympoly toolbox, but there is also a polyn2sym function provided.
% % FEX : https://fr.mathworks.com/matlabcentral/fileexchange/9577-symbolic-polynomial-manipulation?s_tid=srchtitle
% polyn2sympoly(p)
% % ans =
% % 0.0011322*X1^3 + 0.0010727*X1^2*X2 - 0.28262*X1^2 - 0.00058434*X1*X2^2 - 0.10892*X1*X2 + 20.7666*X1 - 0.00022656*X2^3 + 0.062697*X2^2 + 2.5926*X2 - 121.0331
p = p.Coefficients; % get the polynomial coefficients
% create clean smooth x,y data
yf = linspace(min(y),max(y),200);
xf = interp1(y,x,yf);
% smooth a bit xf
xf = smoothdata(xf,'gaussian',10);
% create the polynomial model (z = f(x,y))
zf = p(1)*xf.^3 + p(2)*xf.^2.*yf + p(3)*xf.^2 + p(4)*xf.*yf.^2 + p(5)*xf.*yf + p(6)*xf + p(7)*yf.^3 + p(8)*yf.^2 + p(9)*yf + p(10);
plot3(x,y,z,'r.',xf,yf,zf,'k','linewidth',2)
axis tight square

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