Interpolation to arbitrary points on a patch plot

Hi,

My question is, if I have all my points on the plane and each point is assigned a specific value, how can I retrieve the values interpolated to an arbitrary point in the colored figure below?

(Perhaps better understood by running the program below after the problem I posed.)

A practical concrete example of this is shown in the PATCH figure below. If I select 2 vertical lines and enter the coordinates of 5 points equally spaced on the lines, how can I retrieve the interpolated values at those purple points?

THE PROGRAM:

%Values of points
q = [0;2.00997512422418;2.11482859825566;0;...
    1.50960259671213;1.00498756211209;1.47648230602334];
RGB = [0 0 1
          0 0.5 1
          0 1 1
          0 1 0.5
          0 1 0
          0.5 1 0
          1 1 0
          1 0.5 0
          1 0 0];
% data for patch (connectivity matrices)
msh_1.nn_tria = [3,2,7;2,6,7;5,3,7;6,5,7];
msh_1.nn_quad = [5,4,1,6];
msh_1.xy = [0,0;2,0;2,1;0,1;1,1;1,0;1.5,0.5];
%% Visualisation with patch
figure (8)
set(gcf, 'color', 'w')
colormap(RGB);
colorbar('EastOutside')
patch('Faces',msh_1.nn_tria,'Vertices', msh_1.xy,'FaceVertexCData',q,'FaceColor','interp')
patch('Faces',msh_1.nn_quad,'Vertices', msh_1.xy,'FaceVertexCData',q,'FaceColor','interp')
axis equal

FIGURE:

Do you have any idea how can I solve this problem?

Thank you so much for your helpful comments!

Answer 1

[Voss]

%Values of points
q = [0;2.00997512422418;2.11482859825566;0;...
    1.50960259671213;1.00498756211209;1.47648230602334];
RGB = [0 0 1
          0 0.5 1
          0 1 1
          0 1 0.5
          0 1 0
          0.5 1 0
          1 1 0
          1 0.5 0
          1 0 0];
% data for patch (connectivity matrices)
msh_1.nn_tria = [3,2,7;2,6,7;5,3,7;6,5,7];
msh_1.nn_quad = [5,4,1,6];
msh_1.xy = [0,0;2,0;2,1;0,1;1,1;1,0;1.5,0.5];
%% Visualisation with patch
figure()
set(gcf, 'color', 'w')
colormap(RGB);
colorbar('EastOutside')
patch('Faces',msh_1.nn_tria,'Vertices', msh_1.xy,'FaceVertexCData',q,'FaceColor','interp')
patch('Faces',msh_1.nn_quad,'Vertices', msh_1.xy,'FaceVertexCData',q,'FaceColor','interp')
axis equal

% interpolate q at msh_1.xy to the required points
I = scatteredInterpolant(msh_1.xy,q);
[x,y] = meshgrid([0.68; 1.87],linspace(0,1,5));
v = I(x,y)

v = 5×2

0.6834 1.8793 0.6834 1.8838 0.7742 1.9101 0.9004 1.9363 1.0265 2.0361

% visualization of interpolated values
str = compose('%.3f  ',v);
text(x(:),y(:),str(:),'HorizontalAlignment','right','BackgroundColor','w')
line(x(:),y(:),'LineStyle','none','Marker','o','Color',[0.75 0 0.75],'MarkerFaceColor',[0.75 0 0.75])

% visualization of original (q) values, for comparison
figure()
set(gcf, 'color', 'w')
colormap(RGB);
colorbar('EastOutside')
patch('Faces',msh_1.nn_tria,'Vertices', msh_1.xy,'FaceVertexCData',q,'FaceColor','interp')
patch('Faces',msh_1.nn_quad,'Vertices', msh_1.xy,'FaceVertexCData',q,'FaceColor','interp')
axis equal

str = compose('%.3f  ',q);
text(msh_1.xy(:,1),msh_1.xy(:,2),str(:),'HorizontalAlignment','right','BackgroundColor','w')
line(msh_1.xy(:,1),msh_1.xy(:,2),'LineStyle','none','Marker','x','Color','k')

[Kovacs Mario]

but the other respondent's method is similar to yours, but his gave slightly different numbers.

These were his lines:

F=scatteredInterpolant(msh_1.xy, q);

interpolatedValues = F({[0.68,1.87],0:0.2:1})

What do you think is the reason for this difference?

[Voss]

linspace(0,1,5)

ans = 1x5

0 0.2500 0.5000 0.7500 1.0000

0:0.2:1

ans = 1x6

0 0.2000 0.4000 0.6000 0.8000 1.0000

[Kovacs Mario]

Thank you!

[Voss]

You're welcome!

Answer 2

[Matt J]

For example,

F=scatteredInterpolant(msh_1.xy, q);

interpolatedValues = F({[0.68,1.87],0:0.2:1})

[Kovacs Mario]

Thank you so much for your answer! :)

It was helpful too!