Why does MATLAB piecewise cubic interpolation give diagonalized plot data in 2-D surface plot fits?

Question

Does anyone know why does MATLAB 'piecewise cubic interpolation' gives diagonalized plot data in a 2-D surface plot fit? Attached is a 2-D surface plot (below the code & data) from the code using this cubic fit. As can be seen, peaks in the image/plot are diagonalized at five isolated data points (pointing upper left to lower right). Instead of being a symmetric Gaussian spread that was expected. Why does the cubic interpolation do this?

The cubic fit is shown at: http://www.mathworks.co.uk/help/curvefit/fit.html

Below is the matlab code with 'piecewise cubic interpolation' to fit data from:

'helm2Coils126.txt' & 'positionsData2_20x20_2.txt'.

Any help with this would much appreciated.

Thanking you in advance,

Brendan Darrer

================================CODE=====================================

% 2D MIT surface plots of p.d. phase-difference against x y coordinates 
% Written by Brendan Darrer
% Date 20th September 2013.
% oscillator = 2.6V at f = 500Hz, lock-in amplifier: sensitivity = 50mV, time constant = 500ms.
% background phase: ---- degrees.

A = load('helm2Coils126.txt')
B = load('positionsData2_20x20_2.txt')

% correcting phase offset
for i=1:10   % columns
    for j=1:40 % rows
        if (A(j,i) < 0) % correct offset, if e.g. phase = -179 when it should be 181.
            A(j,i) = 360 + A(j,i);
        end
    end
end

p = A';
A2 = p(:)'

A = A2'
B = [B A]

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

Fig2Handle = figure('Position', [100, 100, 1049, 895]);

xlin=linspace(min(x),max(x),100);  % was 50
ylin=linspace(min(y),max(y),100); % was 50
[X,Y]=meshgrid(xlin,ylin); 

% cubic piecewise interpolation:
Z=griddata(x,y,z,X,Y,'cubic');

surf(X,Y,Z) % interpolated

axis tight; hold on

view(0,90);

plot3(x,y,z,'.','MarkerSize',10)

colormap hsv
colorbar

xlabel('x axis / mm')
ylabel('y axis / mm')
zlabel('phase \Delta\phi / degrees')

====================== END OF CODE =============================

%====== helm2Coils126.txt ==== copy & paste into .txt file ========
%====================(10 COLUMNS, 40 ROWS)=====================

-14.690 -144.460 -173.610 -177.820 -179.260 -179.930 179.690 179.580 179.340 179.360
-128.020 -175.360 -177.990 -179.420 179.680 179.420 179.330 179.170 179.160 179.120
-175.050 -178.450 -179.890 179.770 179.350 179.140 179.070 179.070 178.990 178.960
-178.060 -179.590 179.550 179.290 179.070 179.040 178.940 178.870 178.890 178.900
-179.270 179.780 179.360 179.130 178.990 178.910 178.880 178.940 178.730 178.470
-178.900 179.730 179.160 179.000 179.000 178.860 178.900 179.080 178.760 179.450
179.430 -179.870 179.350 179.220 178.910 178.980 178.950 178.990 178.870 178.520
-179.930 179.220 179.040 179.070 178.940 178.840 178.840 178.810 178.810 178.880
179.430 179.130 179.000 179.000 178.850 178.840 178.820 178.800 178.860 178.840
179.370 179.070 178.930 178.880 178.860 178.810 178.880 178.830 178.810 178.790
179.320 179.120 179.000 178.900 178.860 178.840 178.830 178.870 178.860 178.800
179.360 179.140 178.990 178.920 178.880 178.840 178.890 178.860 178.840 178.900
179.470 179.170 178.950 178.960 178.950 178.860 178.840 178.850 178.860 178.830
179.700 179.190 179.060 -2.820  178.860 178.910 178.850 178.840 178.790 178.840
179.870 179.440 179.250 179.020 179.000 178.970 178.870 178.850 178.820 178.850
-179.450 179.690 179.290 179.030 178.920 178.900 178.890 178.870 178.840 178.850
-177.830 -179.580 179.600 179.270 179.090 178.980 178.950 178.880 178.860 178.890
-175.210 -178.450 -179.850 179.560 179.200 179.080 178.960 178.990 178.930 178.910
-129.050 -175.360 -178.460 -179.730 179.650 179.370 179.250 179.120 179.100 179.040
-16.750 -121.430 -175.270 -178.000 -179.460 179.230 179.330 179.400 179.580 -179.960
179.260 179.350 179.520 179.600 179.900 -179.300 -177.900 -174.010 -107.820 -15.650
179.050 179.090 179.140 179.240 179.440 179.650 -179.680 -174.620 -175.350 -107.820
178.920 178.910 178.940 179.050 179.140 179.260 179.550 -179.970 -178.710 -174.930
178.810 178.870 178.870 178.930 178.990 179.040 179.180 179.470 -179.810 -178.250
178.740 178.850 178.840 178.870 178.910 179.030 179.130 179.380 179.840 -178.840
178.460 178.720 178.760 178.760 178.820 178.870 179.040 178.980 179.430 179.750
178.730 178.770 178.790 178.790 178.840 178.810 178.920 179.060 179.220 179.620
178.780 178.840 178.810 178.780 178.820 178.810 178.870 178.950 179.170 179.360
178.910 178.820 178.910 -2.710  178.830 178.830 178.870 178.900 -2.900  179.240
178.840 178.840 178.870 178.840 178.820 178.840 178.810 178.920 179.020 179.300
178.870 178.870 178.870 178.800 178.800 178.700 178.760 178.840 179.040 179.300
178.890 178.840 178.790 178.690 178.480 177.550 178.480 178.860 179.080 179.250
178.740 178.840 178.820 178.760 177.590 -93.940 177.420 178.890 179.120 179.340
178.970 178.840 178.770 178.740 178.520 177.530 178.700 178.990 179.090 179.570
178.830 178.800 178.800 178.760 178.760 178.780 178.830 179.000 179.290 179.810
178.820 178.900 178.840 178.940 178.940 178.920 178.960 179.130 179.410 -179.960
178.970 178.990 178.900 178.960 178.910 179.040 179.190 179.540 -179.930 -178.180
-2.790  179.060 179.040 179.050 179.110 179.320 179.710 -179.720 -178.270 -174.540
179.000 179.140 179.210 179.440 179.410 179.750 -179.470 -177.830 -167.850 -20.630
179.220 179.290 179.400 179.780 179.900 -179.470 -178.300 -171.660 -168.110 -22.730

=========================end 1st text file============================

======= positionsData2_20x20_2.txt ======== copy & paste into .txt file =========

===================(2 COLUMNS, 400 ROWS)==============================

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0 0
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130 0
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234 0
247 0

===================end 2nd text file==============================

Answer 1

Are you sure of the plot you are showing? Below is the result obtained by your code on your data. I'm using Matlab 2012a.

Answer 2

The cubic piecewise interpolation of the data produces a 2D surface plot (as shown in the original question), in MATLAB 2012b and MATLAB 2013a. However I found other Interpolations for scattered data at matlab Interpolations, that include: 'linear' --> Linear interpolation; 'cubic' --> Cubic piecewise interpolation; 'natural' --> Natural neighbour interpolation; 'nearest' --> Nearest neighbour interpolation.

'Natural neighbour' gave the closest to smoothed Gaussian like edges of the data in x and y. However I have stayed with the cubic interpolation, as it gave the a rounded curve in the z component of the image. Whereas, 'natural neighbour' interpolation gives sharp spikes in the z component, which was unrealistic for my data.

Below are 2 surface plots showing the difference between 'natural neighbour' and 'cubic piecewise' interpolation, for an example image of a copper disk in a metallic container, taken from eddy current imaging.