Avoid nans in 2D cubic spline interpolation

I have XYZ data (X and Y are the coordinates of Z values). Intermintently, the Z values have NaNs.The data is a radar line with gaps in the data (hence the NaNs) and uneven spacing between each points (see figure, blue is the existing values, orange is the NaN values). What I would like is to interpolate the non-nan values on a regular spacing and leave the nans as they are. My XYZ array is +40k rows and contains approximately +5k of NaNs, sometimes consecutive and sometimes spread out.

I am using the interparc function from John (https://uk.mathworks.com/matlabcentral/fileexchange/34874-interparc) to interpolate my points as I am working with a curved line and do not want to create a meshgrid, but I get an error message every time:

Warning: All data points with NaN as their site will be ignored.

> In chckxy (line 37)

In spline (line 53)

In interparc (line 316)

Error using chckxy (line 42)

There should be at least two data points.

I have tried to replace the NaNs by an arbitrary value (999) and make each value unique, as per (https://uk.mathworks.com/matlabcentral/answers/344604-how-to-change-duplicate-values-so-that-every-value-is-unique)

% replace nans by value
new2_dpth(isnan(new2_dpth)) = 999;
% create unique values for NaNs
a = new2_dpth;
[uvals, ~, uidx] = unique(a, 'stable');
b = a;   
for K = 1 : length(uvals)
  mask = uidx == K;
  b(mask) = uvals(K) + (0 : nnz(mask) - 1) * 0.01;
end

I can then interpolate this and remove any value above a certain threshold, but get very strange results (see second figure).

I have also tried to remove the nan's from the interpolation using a for and if loop, but this is time consuming and does not seem to work either (see below)

f=[];
for i = 1:length(b)
    if b (i) ~= -999
        f = interparc (100,new2_x,new2_y,b);
    else
        continue
    end
end

Any help would be really appreciated! Thanks.

[darova]

Is this correct?

[icylab]

Hi Darova,

Thanks for your help. Yes I guess this is similar to what I need. However, I already know how to interpolate data on a regular grid. I just need this interpolation to stop before and start after the nans (and not interpolate them). I'm not sure your figure does that?

Answer 1

[darova]

Here is what i tried: Created new mesh and place there NaN (red points_

clc,clear

    % generate random data
x = sort(rand(1,20)*5);
y = sin(x);
z = x.^2;
ix = [2 7 12 18];               % indices of NaN's
plot3(x,y,z,'.-b')
hold on
plot3(x(ix),y(ix),z(ix),'ok')
hold off

t = [0 cumsum(sqrt(diff(x).^2+diff(y).^2+diff(z).^2))];
ti = linspace(0,t(end),15);     % new mesh
[tt,in] = sort([t(ix) ti]);     % sort new mesh and NaN points
[~,ii] = sort(in);              % sort indices to get places of NaN

    % interpolate data with mesh
xx = spline(t,x,tt);
yy = spline(t,y,tt);
zz = spline(t,z,tt);
i1 = ii(1:length(ix));          % first indices are NaN

hold on
plot3(xx,yy,zz+3,'.:r')
plot3(xx(i1),yy(i1),zz(i1)+3,'ok')
zz(i1) = nan;                   % place NaN in data to create breaks
plot3(xx,yy,zz+3,'-r','linewidth',2)
hold off

axis vis3d

[darova]

I get general idea of interpolation from HERE

[icylab]

Thanks Darova!

I have tried your solution but keep getting the error message:

Error using chckxy (line 51)
The data sites should be distinct.

Error in spline (line 53)
[x,y,sizey,endslopes] = chckxy(x,y);

Here is the code I adapted:

ix = isnan(new2_dpth); % get logical (1 = nan values)
ix_dpth = new2_dpth(~ix); % take nans out

new2_xx = reshape(new2_x,[1,43885]); % reshape arrays in horizontal direction (previously [43885,1])
new2_yy = reshape(new2_y,[1,43885]); % reshape arrays in horizontal direction (previously [43885,1])
new2_dd = reshape(new2_dpth,[1,43885]); % reshape arrays in horizontal direction (previously [43885,1])

t = [0 cumsum(sqrt(diff(new2_xx).^2+diff(new2_yy).^2))];
ti = linspace(0,t(end),43885);     % new mesh
[tt,in] = sort([t(ix) ti]);     % sort new mesh and NaN points
[~,ii] = sort(in);              % sort indices to get places of NaN

xx = spline(t,new2_xx,tt);
yy = spline(t,new2_yy,tt);
zz = spline(t,new2_dd,tt);

[icylab]

Also, second figure in my initial example was simply connecting each point in the figure with a line, hence the weird blue filled sections in the figure. Just replace '-o' by 'o' when calling plot and this fixes it. Sorry about that.

[darova]

You have NaN only in new2_dd? Or x and y?

[icylab]

Only in new2dd

[darova]

Try this

zz = spline(t(~ix),new2_dd(~ix),tt);            % take only number (without NaN)

I gave you incorrect example above

t = [0 cumsum(sqrt(diff(x).^2+diff(y).^2+diff(z).^2))];

Because z in your case have NaN's. You can't use it