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Griddata doesn't reach sample points

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Hello, I have 3 vectors I am using griddata to interpolate. The problem is that the sample points are not included in the griddata output as seen in the sample red dots in the image '20'; 20 corresponds to the amount of space between the points of linspace. If I increase this to 100 the sample points are eventually reached, but the resulting image is very crowded.
Any advice on how to get griddata to reach the sample points for a lower amount of linspace points?
Thanks
N = 20; %vs e.g.100
x = [8.53315129274914,9.30925339785209,8.53315129274914,9.30925339785209,9.30925339785209,9.30925339785209,9.30925339785209,4.45216152440796,3.79261956232135,3.79261956232135,17.0677590031963,17.0677590031963,4.09601048577567,5.68892934348203];
y = [1.32520094900129,1.32154631465502,1.19462692171560,1.24730173230503,1.10676794920524,1.09225969341119,0.815136578214699,0.757268342808360,1.01606958162158,0.942815599343300,0.675121536953220,0.693923408467932,1.15323471371613,1.62262286756171];
xvec = linspace(min(x), max(x), N);
yvec = linspace(min(y), max(y), N);
[X, Y] = meshgrid(xvec, yvec);
data = [53.3523658491640,73.0221175190515,66.4448159677658,53.0481929355336,34.9019870840489,27.0340993276701,388.109339785705,341.752595986306,561.738449969976,481.741285644030,93.8209397136714,36.7262731504483,538.496713957595,820.698548835111];
Z = griddata(x,y,data,X,Y);
figure
surf(X,Y,Z)
view(2)
hold on
plot3(x,y,data,'r.','MarkerSize',20)

Accepted Answer

the cyclist
the cyclist on 11 Jul 2023
Here is the relevant line of the documentation for griddata that explains what is happening:
"For all interpolation methods other than "v4", the output vq contains NaN values for query points outside the convex hull of the sample data. The "v4" method performs the same calculation for all points regardless of location."
Using "v4", you will see points where you expected to originally:
N = 20; %vs e.g.100
x = [8.53315129274914,9.30925339785209,8.53315129274914,9.30925339785209,9.30925339785209,9.30925339785209,9.30925339785209,4.45216152440796,3.79261956232135,3.79261956232135,17.0677590031963,17.0677590031963,4.09601048577567,5.68892934348203];
y = [1.32520094900129,1.32154631465502,1.19462692171560,1.24730173230503,1.10676794920524,1.09225969341119,0.815136578214699,0.757268342808360,1.01606958162158,0.942815599343300,0.675121536953220,0.693923408467932,1.15323471371613,1.62262286756171];
xvec = linspace(min(x), max(x), N);
yvec = linspace(min(y), max(y), N);
[X, Y] = meshgrid(xvec, yvec);
data = [53.3523658491640,73.0221175190515,66.4448159677658,53.0481929355336,34.9019870840489,27.0340993276701,388.109339785705,341.752595986306,561.738449969976,481.741285644030,93.8209397136714,36.7262731504483,538.496713957595,820.698548835111];
Z = griddata(x,y,data,X,Y,"v4");
figure
surf(X,Y,Z)
view(2)
hold on
plot3(x,y,data,'r.','MarkerSize',20)

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