Scatteredinterpolant (linear) from symmetric data does not produce symmetric isolines

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ES_Thorny
ES_Thorny 2024-7-17
编辑： Bruno Luong 2024-7-26
I utilised the scatteredinterpolant function to generate an interpolation from which I derived isolines. My data are situated on a non-equispaced grid of points that are symmetric with respect to the midline. In fact, I only have data on one side, so I placed data on the other side by copying the values from the original data set, exploiting the symmetry.
When I generate iso-lines using the NATURAL method, the isolines have a symmetric trend. If I use the simplest method, i.e. LINEAR, the iso-lines are not symmetric, which does not make sense.
Do you know what may cause this issue and how to sort it out?

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回答（1 个）

Bruno Luong
Bruno Luong 2024-7-17
scatteredinterpolant all methods is based on triangulation of the data points. Even the data points are symmetric, the triangulation migh not.
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Bruno Luong
Bruno Luong 2024-7-26
x_PP_sym=x_PP;
y_PP_sym=-y_PP;
PP_i_sym=PP_i;
% Adding other points symmetrically with respect to y=0
x_PP_sym=x_PP;
y_PP_sym=-y_PP;
PP_i_sym=PP_i;
You create twice the variable and do not use it anywhere later. Clearly Your code is NOT correct.
Bruno Luong
Bruno Luong 2024-7-26
编辑：Bruno Luong 2024-7-26
Ran in:
This demo shows how to enforce the interpolation output to be symmetric, as it is an a priori expectation characteristic, whatever the input might be and or breaking symmetric due to scattering interpolation algorithm.
[x_PP,y_PP,PP_i] = peaks(20);
x_PP=x_PP(:);
y_PP=y_PP(:);
P_v=PP_i(:);
% ---------------
% Scattered Interpolant
% ---------------
% Grid
x0=min(x_PP);
x1=max(x_PP);
y0=min(y_PP);
y1=-y0; %max(y_PP); % Change by Bruno
N=50;
xll=linspace(x0,x1,N) ;
yll=linspace(y0,y1,N) ;
[X,Y] = meshgrid(xll,yll) ;
P=[x_PP,y_PP];
V=PP_i;
F = scatteredInterpolant(x_PP,y_PP,P_v);
F.Method ='linear';
F.ExtrapolationMethod ='none';
Z=F(X,Y);
Z=(Z+flip(Z,1))/2; % Add by Bruno, symmetrize the Z with to Y
% Contour plot
clevels=linspace(-4,4,10)
clevels = 1x10
-4.0000 -3.1111 -2.2222 -1.3333 -0.4444 0.4444 1.3333 2.2222 3.1111 4.0000
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
[ch0,ch]=contour(X,Y,Z,10);
ch.LineWidth = 2;
axis equal
xlabel('x (mm)')
ylabel('y (mm)');
colormap(jet)
Cbar=colorbar;
Cbar.Label.String = 'Pressure (kPa)';
caxis([clevels(1) clevels(end)])
yline(0)

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