create a 3D smoothing with csaps (or similar)

To get a better set of nodes arranged in space as a ‘curve’, how can I improve this code? Could you suggest?

load curve_1

cc = curve_1;  %or curve_2
x = cc(:,1);
y = cc(:,2);
z_min = min(cc(:,3));
z_max = max(cc(:,3));
z = z_min:0.1:z_max;
z = z';

% code
[pp,p] = csaps(z,[x;y]);
val = fnval(pp,z);
figure
plot3(x,y,z);
hold on
plot3(val(1,:),val(2,:),z,'r-')
grid on

Answer 1

[Mathieu NOE]

hello again !

as your post title is about smoothing, this is what I propose , based on the fex submission :

smoothn - File Exchange - MATLAB Central (mathworks.com)

I attached the function in my answer if it makes your life simpler

now, maybe we should also create some intermediate points with interpolation (will be done just after this first answer)

so the starter :

load curve_1
cc = curve_1;  %or curve_2
% load curve_2
% cc = curve_2;  %or curve_2

x = cc(:,1);
y = cc(:,2);
z = cc(:,3);

% smoothing (if needed)
[zz,s,exitflag] = smoothn({x,y,z},1); 
xn = zz{1};
yn = zz{2};
zn = zz{3};

plot3(x,y,z,'*');
hold on 
plot3(xn,yn,zn);

[Mathieu NOE]

now with interpolation (to generate more points ) before smoothing

now you can play with interpolation number of points , method (here spline to already bring some smoothness) and last stage is smoothn itself (with optionnal smoothing factor S)

hope it helps !

% load curve_1
% cc = curve_1;  %or curve_2
load curve_2
cc = curve_2;  %or curve_2

x = cc(:,1);
y = cc(:,2);
z = cc(:,3);

% unique & sort z ascending (for interpolation purposes)
[z,ia,ic] = unique(z);
x = x(ia);
y = y(ia);

% interpolation first 
z_min = min(z);
z_max = max(z);
zi = linspace(z_min,z_max,100);
xi = interp1(z,x,zi,'spline');
yi = interp1(z,y,zi,'spline');

% smoothing (if needed)
[zzz,s,exitflag] = smoothn({xi,yi,zi},1); 
xn = zzz{1};
yn = zzz{2};
zn = zzz{3};

plot3(x,y,z,'dr');
hold on 
plot3(xi,yi,zi,'*g');
plot3(xn,yn,zn,'b');
hold off

[Mathieu NOE]

yet another alternative, uing interpolation and polynomial fitting with polyfitn

polyfitn - File Exchange - MATLAB Central (mathworks.com)

load curve_1
cc = curve_1;  %or curve_2
% load curve_2
% cc = curve_2;  %or curve_2

x = cc(:,1);
y = cc(:,2);
z = cc(:,3);

% unique & sort z ascending (for interpolation purposes)
[z,ia,ic] = unique(z);
x = x(ia);
y = y(ia);

% interpolation first 
z_min = min(z);
z_max = max(z);
zi = linspace(z_min,z_max,100)';
xi = interp1(z,x,zi,'spline');
yi = interp1(z,y,zi,'spline');

% polynomial fit
% % FEX : https://fr.mathworks.com/matlabcentral/fileexchange/34765-polyfitn?s_tid=ta_fx_results
order = 1;
p = polyfitn([xi,yi],zi,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)*(xi.^pTerms(k,1)).*(yi.^pTerms(k,2)); %
end

figure(1),
  plot3(x,y,z,'r*',xi,yi,zt,'k','linewidth',2);  % 
  xlabel('X');
  ylabel('Y');
  zlabel('Z');
  legend('raw data','fitted curve');
  axis tight square

[Alberto Acri]

Thank you @Mathieu NOE! You always surprise me!

[Mathieu NOE]

My pleasure , and thanks again for accepting my answer

you can also reward other contributors by voting

Answer 2

[Matt J]

load curve_1

cc = curve_1;  %or curve_2
x = cc(:,1);
y = cc(:,2);
z = cc(:,3);
t=linspace(0,1,height(cc));
tu=linspace(0,1,5*height(cc));

% code
[pp,p] = csaps(t,cc',0.995);
val = fnval(pp,tu);
figure
plot3(x,y,z,'o');
hold on
plot3(val(1,:),val(2,:),val(3,:),'r-')
grid on

[Alberto Acri]

Thank you! I accepted Mathieu's answer because it gave me more solutions. However, your answer is well accepted and I cannot accept both!