Dear all
I am attaching a dataset, called "Points.txt", where the first and second columns represent the spatial coordinates along the x- and y-th directions, respectively, and the third column the value of a variable at each listed pair of points (x,y). I was wondering which could be a good way to increase the number of points mainly inside the hexagonal shape within the current listed points are restricted to:

I have tried the following:
pgon=nsidedpoly(6,’Center’,[0 0],’SideLength’,1);
%% Let’s rearrange the data associated to the interlayer isotropic exchange, Jinter
% Let’s load the preliminar data
Jinter=cell2mat(struct2cell(load(strcat(pwd,’Preliminar-DataJinter.mat’))));
% Let’s construct the unit vectors of the in-plane unit cell
x=unique(Jinter(:,1));
y=unique(Jinter(:,2));
a1_points=[max(x) 0];
a2_points=[-0.5 max(y)];
a1_modulus=sqrt(dot(a1_points,a1_points));
a2_modulus=sqrt(dot(a2_points,a2_points));
a1=a1_points./a1_modulus;
a2=a2_points./a2_modulus;
% Let’s construct the supercell for Jinter
diff_y=max(y)-min(y);
counter=0;
for dy=[-1 0 1]
for i=1:length(Jinter(:,1))
if (Jinter(i,1:2)++dy*[0 1]*diff_y)~=any(Jinter(:,1:2))
counter=counter+1;
Jinter_extended(counter,1:2)=Jinter(i,1:2)+dy*[0 1]*diff_y;
Jinter_extended(counter,3)=Jinter(i,3);
end
end
end
counter=length(Jinter_extended(:,1));
for i=1:length(Jinter(:,1))
if (Jinter(i,1:2)+[a1(1)+abs(a2(1)) abs(a2(2))])~=any(Jinter_extended(:,1:2))
counter=counter+1;
Jinter_extended(counter,1:2)=Jinter(i,1:2)+[a1(1)+abs(a2(1)) abs(a2(2))];
Jinter_extended(counter,3)=Jinter(i,3);
end
end
counter=length(Jinter_extended(:,1));
for i=1:length(Jinter(:,1))
if (Jinter(i,1:2)+[a1(1)+abs(a2(1)) -abs(a2(2))])~=any(Jinter_extended(:,1:2))
counter=counter+1;
Jinter_extended(counter,1:2)=Jinter(i,1:2)+[a1(1)+abs(a2(1)) -abs(a2(2))];
Jinter_extended(counter,3)=Jinter(i,3);
end
end
counter=length(Jinter_extended(:,1));
for i=1:length(Jinter(:,1))
if (Jinter(i,1:2)+[-(a1(1)+abs(a2(1))) abs(a2(2))])~=any(Jinter_extended(:,1:2))
counter=counter+1;
Jinter_extended(counter,1:2)=Jinter(i,1:2)+[-(a1(1)+abs(a2(1))) abs(a2(2))];
Jinter_extended(counter,3)=Jinter(i,3);
end
end
counter=length(Jinter_extended(:,1));
for i=1:length(Jinter(:,1))
if (Jinter(i,1:2)+[-(a1(1)+abs(a2(1))) -abs(a2(2))])~=any(Jinter_extended(:,1:2))
counter=counter+1;
Jinter_extended(counter,1:2)=Jinter(i,1:2)+[-(a1(1)+abs(a2(1))) -abs(a2(2))];
Jinter_extended(counter,3)=Jinter(i,3);
end
end
clear a1 a2 a1_modulus a2_modulus a1_points a2_points Jinter diff_y x y dy
% Let’s plot it
u17=figure(17)
scatter(Jinter_extended(:,1),Jinter_extended(:,2),[],Jinter_extended(:,3),’o’,’filled’);
colormap(gca,bluewhitered(256));
clim([min(Jinter_extended(:,3)) max(Jinter_extended(:,3))]);
clr17=colorbar;
box on;
pbaspect([1 6/4 1]);
clear u17 clr17
% Now, let’s interpolate data
x_extended=linspace(min(Jinter_extended(:,1)),max(Jinter_extended(:,1)));
y_extended=linspace(min(Jinter_extended(:,2)),max(Jinter_extended(:,2)));
Jinter_interpolated=RegularizeData3D(Jinter_extended(:,1),Jinter_extended(:,2),Jinter_extended(:,3),x_extended,y_extended,’interp’,’bicubic’,’smoothness’,1e-4);
x_interpolation=linspace(-1,1,201);
y_interpolation=linspace(-sqrt(3)/2,sqrt(3)/2,201);
[X,Y]=meshgrid(x_interpolation,y_interpolation);
interpolated_Jinter=interp2(x_extended,y_extended,Jinter_interpolated,X,Y,’cubic’);
clear X Y Jinter_interpolated x_extended y_extended Jinter_extended
% Let’s plot it
u18=figure(18)
uimagesc(x_interpolation,y_interpolation,interpolated_Jinter);
colormap(gca,bluewhitered(256));
% hold on
axis xy;
% plot(pgon);
clim([min(min(interpolated_Jinter)) max(max(interpolated_Jinter))]);
clr18=colorbar;
box on;
pbaspect([1 sqrt(3)/2 1]);
clear u18 clr18
% Now, let’s rearrange and save the data
x_intermediate=linspace(-100,100,201);
y_intermediate=linspace(-100,100,201);
counter=0;
for i=1:length(x_interpolation)
for j=1:length(y_interpolation)
counter=counter+1;
Jinter_save(counter,1)=x_intermediate(i);
Jinter_save(counter,2)=y_intermediate(j);
Jinter_save(counter,3)=interpolated_Jinter(i,j);
end
end
writematrix(Jinter_save,strcat(pwd,’Interpolated-DataInterpolated_J_Inter.txt’),’Delimiter’,’space’);
clear interpolated_Jinter Jinter_save x_interpolation y_interpolation counter i j x_intermediate y_intermediate
where the "Jinter.mat" is exactly the same dataset as in "Points.txt". The problem with this is that, for example, if I take a look at the generated "Interpolated_J_Inter.txt", the value for (0,0) differs notably.
Any ideas?Dear all
I am attaching a dataset, called "Points.txt", where the first and second columns represent the spatial coordinates along the x- and y-th directions, respectively, and the third column the value of a variable at each listed pair of points (x,y). I was wondering which could be a good way to increase the number of points mainly inside the hexagonal shape within the current listed points are restricted to:

I have tried the following:
pgon=nsidedpoly(6,’Center’,[0 0],’SideLength’,1);
%% Let’s rearrange the data associated to the interlayer isotropic exchange, Jinter
% Let’s load the preliminar data
Jinter=cell2mat(struct2cell(load(strcat(pwd,’Preliminar-DataJinter.mat’))));
% Let’s construct the unit vectors of the in-plane unit cell
x=unique(Jinter(:,1));
y=unique(Jinter(:,2));
a1_points=[max(x) 0];
a2_points=[-0.5 max(y)];
a1_modulus=sqrt(dot(a1_points,a1_points));
a2_modulus=sqrt(dot(a2_points,a2_points));
a1=a1_points./a1_modulus;
a2=a2_points./a2_modulus;
% Let’s construct the supercell for Jinter
diff_y=max(y)-min(y);
counter=0;
for dy=[-1 0 1]
for i=1:length(Jinter(:,1))
if (Jinter(i,1:2)++dy*[0 1]*diff_y)~=any(Jinter(:,1:2))
counter=counter+1;
Jinter_extended(counter,1:2)=Jinter(i,1:2)+dy*[0 1]*diff_y;
Jinter_extended(counter,3)=Jinter(i,3);
end
end
end
counter=length(Jinter_extended(:,1));
for i=1:length(Jinter(:,1))
if (Jinter(i,1:2)+[a1(1)+abs(a2(1)) abs(a2(2))])~=any(Jinter_extended(:,1:2))
counter=counter+1;
Jinter_extended(counter,1:2)=Jinter(i,1:2)+[a1(1)+abs(a2(1)) abs(a2(2))];
Jinter_extended(counter,3)=Jinter(i,3);
end
end
counter=length(Jinter_extended(:,1));
for i=1:length(Jinter(:,1))
if (Jinter(i,1:2)+[a1(1)+abs(a2(1)) -abs(a2(2))])~=any(Jinter_extended(:,1:2))
counter=counter+1;
Jinter_extended(counter,1:2)=Jinter(i,1:2)+[a1(1)+abs(a2(1)) -abs(a2(2))];
Jinter_extended(counter,3)=Jinter(i,3);
end
end
counter=length(Jinter_extended(:,1));
for i=1:length(Jinter(:,1))
if (Jinter(i,1:2)+[-(a1(1)+abs(a2(1))) abs(a2(2))])~=any(Jinter_extended(:,1:2))
counter=counter+1;
Jinter_extended(counter,1:2)=Jinter(i,1:2)+[-(a1(1)+abs(a2(1))) abs(a2(2))];
Jinter_extended(counter,3)=Jinter(i,3);
end
end
counter=length(Jinter_extended(:,1));
for i=1:length(Jinter(:,1))
if (Jinter(i,1:2)+[-(a1(1)+abs(a2(1))) -abs(a2(2))])~=any(Jinter_extended(:,1:2))
counter=counter+1;
Jinter_extended(counter,1:2)=Jinter(i,1:2)+[-(a1(1)+abs(a2(1))) -abs(a2(2))];
Jinter_extended(counter,3)=Jinter(i,3);
end
end
clear a1 a2 a1_modulus a2_modulus a1_points a2_points Jinter diff_y x y dy
% Let’s plot it
u17=figure(17)
scatter(Jinter_extended(:,1),Jinter_extended(:,2),[],Jinter_extended(:,3),’o’,’filled’);
colormap(gca,bluewhitered(256));
clim([min(Jinter_extended(:,3)) max(Jinter_extended(:,3))]);
clr17=colorbar;
box on;
pbaspect([1 6/4 1]);
clear u17 clr17
% Now, let’s interpolate data
x_extended=linspace(min(Jinter_extended(:,1)),max(Jinter_extended(:,1)));
y_extended=linspace(min(Jinter_extended(:,2)),max(Jinter_extended(:,2)));
Jinter_interpolated=RegularizeData3D(Jinter_extended(:,1),Jinter_extended(:,2),Jinter_extended(:,3),x_extended,y_extended,’interp’,’bicubic’,’smoothness’,1e-4);
x_interpolation=linspace(-1,1,201);
y_interpolation=linspace(-sqrt(3)/2,sqrt(3)/2,201);
[X,Y]=meshgrid(x_interpolation,y_interpolation);
interpolated_Jinter=interp2(x_extended,y_extended,Jinter_interpolated,X,Y,’cubic’);
clear X Y Jinter_interpolated x_extended y_extended Jinter_extended
% Let’s plot it
u18=figure(18)
uimagesc(x_interpolation,y_interpolation,interpolated_Jinter);
colormap(gca,bluewhitered(256));
% hold on
axis xy;
% plot(pgon);
clim([min(min(interpolated_Jinter)) max(max(interpolated_Jinter))]);
clr18=colorbar;
box on;
pbaspect([1 sqrt(3)/2 1]);
clear u18 clr18
% Now, let’s rearrange and save the data
x_intermediate=linspace(-100,100,201);
y_intermediate=linspace(-100,100,201);
counter=0;
for i=1:length(x_interpolation)
for j=1:length(y_interpolation)
counter=counter+1;
Jinter_save(counter,1)=x_intermediate(i);
Jinter_save(counter,2)=y_intermediate(j);
Jinter_save(counter,3)=interpolated_Jinter(i,j);
end
end
writematrix(Jinter_save,strcat(pwd,’Interpolated-DataInterpolated_J_Inter.txt’),’Delimiter’,’space’);
clear interpolated_Jinter Jinter_save x_interpolation y_interpolation counter i j x_intermediate y_intermediate
where the "Jinter.mat" is exactly the same dataset as in "Points.txt". The problem with this is that, for example, if I take a look at the generated "Interpolated_J_Inter.txt", the value for (0,0) differs notably.
Any ideas? Dear all
I am attaching a dataset, called "Points.txt", where the first and second columns represent the spatial coordinates along the x- and y-th directions, respectively, and the third column the value of a variable at each listed pair of points (x,y). I was wondering which could be a good way to increase the number of points mainly inside the hexagonal shape within the current listed points are restricted to:

I have tried the following:
pgon=nsidedpoly(6,’Center’,[0 0],’SideLength’,1);
%% Let’s rearrange the data associated to the interlayer isotropic exchange, Jinter
% Let’s load the preliminar data
Jinter=cell2mat(struct2cell(load(strcat(pwd,’Preliminar-DataJinter.mat’))));
% Let’s construct the unit vectors of the in-plane unit cell
x=unique(Jinter(:,1));
y=unique(Jinter(:,2));
a1_points=[max(x) 0];
a2_points=[-0.5 max(y)];
a1_modulus=sqrt(dot(a1_points,a1_points));
a2_modulus=sqrt(dot(a2_points,a2_points));
a1=a1_points./a1_modulus;
a2=a2_points./a2_modulus;
% Let’s construct the supercell for Jinter
diff_y=max(y)-min(y);
counter=0;
for dy=[-1 0 1]
for i=1:length(Jinter(:,1))
if (Jinter(i,1:2)++dy*[0 1]*diff_y)~=any(Jinter(:,1:2))
counter=counter+1;
Jinter_extended(counter,1:2)=Jinter(i,1:2)+dy*[0 1]*diff_y;
Jinter_extended(counter,3)=Jinter(i,3);
end
end
end
counter=length(Jinter_extended(:,1));
for i=1:length(Jinter(:,1))
if (Jinter(i,1:2)+[a1(1)+abs(a2(1)) abs(a2(2))])~=any(Jinter_extended(:,1:2))
counter=counter+1;
Jinter_extended(counter,1:2)=Jinter(i,1:2)+[a1(1)+abs(a2(1)) abs(a2(2))];
Jinter_extended(counter,3)=Jinter(i,3);
end
end
counter=length(Jinter_extended(:,1));
for i=1:length(Jinter(:,1))
if (Jinter(i,1:2)+[a1(1)+abs(a2(1)) -abs(a2(2))])~=any(Jinter_extended(:,1:2))
counter=counter+1;
Jinter_extended(counter,1:2)=Jinter(i,1:2)+[a1(1)+abs(a2(1)) -abs(a2(2))];
Jinter_extended(counter,3)=Jinter(i,3);
end
end
counter=length(Jinter_extended(:,1));
for i=1:length(Jinter(:,1))
if (Jinter(i,1:2)+[-(a1(1)+abs(a2(1))) abs(a2(2))])~=any(Jinter_extended(:,1:2))
counter=counter+1;
Jinter_extended(counter,1:2)=Jinter(i,1:2)+[-(a1(1)+abs(a2(1))) abs(a2(2))];
Jinter_extended(counter,3)=Jinter(i,3);
end
end
counter=length(Jinter_extended(:,1));
for i=1:length(Jinter(:,1))
if (Jinter(i,1:2)+[-(a1(1)+abs(a2(1))) -abs(a2(2))])~=any(Jinter_extended(:,1:2))
counter=counter+1;
Jinter_extended(counter,1:2)=Jinter(i,1:2)+[-(a1(1)+abs(a2(1))) -abs(a2(2))];
Jinter_extended(counter,3)=Jinter(i,3);
end
end
clear a1 a2 a1_modulus a2_modulus a1_points a2_points Jinter diff_y x y dy
% Let’s plot it
u17=figure(17)
scatter(Jinter_extended(:,1),Jinter_extended(:,2),[],Jinter_extended(:,3),’o’,’filled’);
colormap(gca,bluewhitered(256));
clim([min(Jinter_extended(:,3)) max(Jinter_extended(:,3))]);
clr17=colorbar;
box on;
pbaspect([1 6/4 1]);
clear u17 clr17
% Now, let’s interpolate data
x_extended=linspace(min(Jinter_extended(:,1)),max(Jinter_extended(:,1)));
y_extended=linspace(min(Jinter_extended(:,2)),max(Jinter_extended(:,2)));
Jinter_interpolated=RegularizeData3D(Jinter_extended(:,1),Jinter_extended(:,2),Jinter_extended(:,3),x_extended,y_extended,’interp’,’bicubic’,’smoothness’,1e-4);
x_interpolation=linspace(-1,1,201);
y_interpolation=linspace(-sqrt(3)/2,sqrt(3)/2,201);
[X,Y]=meshgrid(x_interpolation,y_interpolation);
interpolated_Jinter=interp2(x_extended,y_extended,Jinter_interpolated,X,Y,’cubic’);
clear X Y Jinter_interpolated x_extended y_extended Jinter_extended
% Let’s plot it
u18=figure(18)
uimagesc(x_interpolation,y_interpolation,interpolated_Jinter);
colormap(gca,bluewhitered(256));
% hold on
axis xy;
% plot(pgon);
clim([min(min(interpolated_Jinter)) max(max(interpolated_Jinter))]);
clr18=colorbar;
box on;
pbaspect([1 sqrt(3)/2 1]);
clear u18 clr18
% Now, let’s rearrange and save the data
x_intermediate=linspace(-100,100,201);
y_intermediate=linspace(-100,100,201);
counter=0;
for i=1:length(x_interpolation)
for j=1:length(y_interpolation)
counter=counter+1;
Jinter_save(counter,1)=x_intermediate(i);
Jinter_save(counter,2)=y_intermediate(j);
Jinter_save(counter,3)=interpolated_Jinter(i,j);
end
end
writematrix(Jinter_save,strcat(pwd,’Interpolated-DataInterpolated_J_Inter.txt’),’Delimiter’,’space’);
clear interpolated_Jinter Jinter_save x_interpolation y_interpolation counter i j x_intermediate y_intermediate
where the "Jinter.mat" is exactly the same dataset as in "Points.txt". The problem with this is that, for example, if I take a look at the generated "Interpolated_J_Inter.txt", the value for (0,0) differs notably.
Any ideas? interpolate two-dimensional data MATLAB Answers — New Questions

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