Filtering data from interpolated points on patch

Hi,

The problem would be:

In the figure below, there are 6 points (xy) and the values (q) are assigned to these points. From these points, 3 triangles, colored by value, are drawn using the PATCH command.

By interpolating along two vertical lines I have determined 10-10 values. However, my problem is that it also interpolates values to places where there is no colored triangle (only white background).

Is there any way to zero out all the interpolated values that do not fall on the colored areas?

(This just demonstrates a simpler scenario, there are where I need to filter out these points for a model with many more triangles and white areas.)

The programme can be found below.

FIGURE:

PROGRAM:

xy = [1 3.1
    2.6 2.8
    1.3 1.9
    2.8 1.5
    3.7 2.1
    2 0.9];
Connectivity_matrix = [3 2 1
    5 2 4
    6 4 3];
q = [1 2 3 1 2 3]';
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];
I = scatteredInterpolant(xy,q);
[x,y] = meshgrid([1.7; 2.4],linspace(0.8,3.2,10));
v = I(x,y)
figure ()
set(gcf, 'color', 'w')
colormap(RGB);
colorbar('EastOutside')
patch('Faces',Connectivity_matrix,'Vertices', xy,'FaceVertexCData',q,'FaceColor','interp')
axis equal
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])

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

Thank you so much for your helpful comments!

Answer 1

[Voss]

xy = [1 3.1
      2.6 2.8
      1.3 1.9
      2.8 1.5
      3.7 2.1
      2 0.9];
Connectivity_matrix = [3 2 1
                       5 2 4
                       6 4 3];
q = [1 2 3 1 2 3]';
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];
I = scatteredInterpolant(xy,q);
[x,y] = meshgrid([1.7; 2.4],linspace(0.8,3.2,10));
v = I(x,y)

v = 10×2

3.5931 2.8530 3.2777 2.7888 2.9945 1.8470 2.6885 1.5410 2.5098 1.6863 2.6667 1.8431 2.3388 2.0000 1.9162 2.1457 1.4936 1.8717 1.2417 1.8429

% use inpolygon to say which points are in each triangle:
N_triangles = size(Connectivity_matrix,1);
in_triangle = false(numel(x),N_triangles);
for ii = 1:N_triangles
    tri_xy = xy(Connectivity_matrix(ii,:),:);
    in_triangle(:,ii) = inpolygon(x(:),y(:),tri_xy(:,1),tri_xy(:,2));
end
% a point is in a triangle if it is in any triangle:
in_triangle = any(in_triangle,2);
% zero out the interpolated values of points not in a triangle:
v(~in_triangle) = 0

v = 10×2

0 0 0 0 2.9945 1.8470 2.6885 1.5410 0 0 0 0 2.3388 0 1.9162 2.1457 1.4936 0 0 0

figure ()
set(gcf, 'color', 'w')
colormap(RGB);
colorbar('EastOutside')
patch('Faces',Connectivity_matrix,'Vertices', xy,'FaceVertexCData',q,'FaceColor','interp')
axis equal
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])

% make texts and dots only at points in a triangle:
text(x(in_triangle),y(in_triangle),str(in_triangle),'HorizontalAlignment','right','BackgroundColor','w')
line(x(in_triangle),y(in_triangle),'LineStyle','none','Marker','o','Color',[0.75 0 0.75],'MarkerFaceColor',[0.75 0 0.75])

[Kovacs Mario]

Thank you so much for your answer!

Maybe you can help me, if there are not only triangles but also quadrilaterals in the model, how should I modify your program?

You can see the program for that below:

xy = [1 3.1
    2.6 2.8
    1.3 1.9
    2.8 1.5
    3.7 2.1
    2 0.9
    3 4];
Connectivity_matrix_tria = [5 2 4
    6 4 3];
Connectivity_matrix_quad = [3 2 7 1];
q = [1 2 3 1 2 3 3]';
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];
I = scatteredInterpolant(xy,q);
[x,y] = meshgrid([1.7; 2.4],linspace(0.8,4,10));
v = I(x,y)
figure ()
set(gcf, 'color', 'w')
colormap(RGB);
colorbar('EastOutside')
patch('Faces',Connectivity_matrix_tria,'Vertices', xy,'FaceVertexCData',q,'FaceColor','interp')
patch('Faces',Connectivity_matrix_quad,'Vertices', xy,'FaceVertexCData',q,'FaceColor','interp')
axis equal
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])

Thank you so much for your help! :)

[Voss]

You're welcome!

It works pretty much the same way, since inpolygon will work for any polygon.

xy = [1 3.1
      2.6 2.8
      1.3 1.9
      2.8 1.5
      3.7 2.1
      2 0.9
      3 4];
Connectivity_matrix_tria = [5 2 4
                            6 4 3];
Connectivity_matrix_quad = [3 2 7 1];
q = [1 2 3 1 2 3 3]';
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];
I = scatteredInterpolant(xy,q);
[x,y] = meshgrid([1.7; 2.4],linspace(0.8,4,10));
v = I(x,y)

v = 10×2

3.5931 2.8539 3.1799 2.7702 2.7905 1.6430 2.5098 1.6863 2.6205 1.8954 2.0571 2.1046 1.4936 1.9314 1.6258 2.1405 1.6156 2.3497 1.5517 2.4667

% use inpolygon to say which points are in each polygon:
C = {Connectivity_matrix_tria; Connectivity_matrix_quad};
NC = numel(C);
N_poly = cellfun(@(x)size(x,1),C);
in_poly = cell(1,NC);
NX = numel(x);
for ii = 1:NC
    in_poly{ii} = false(NX,N_poly(ii));
    for jj = 1:N_poly(ii)
        poly_xy = xy(C{ii}(jj,:),:);
        in_poly{ii}(:,jj) = inpolygon(x(:),y(:),poly_xy(:,1),poly_xy(:,2));
    end
end
% a point is in a polygon if it is in any polygon:
in_poly = any([in_poly{:}],2);
% zero out the interpolated values of points not in a triangle:
v(~in_poly) = 0

v = 10×2

0 0 0 0 2.7905 1.6430 0 0 2.6205 0 2.0571 0 1.4936 1.9314 1.6258 2.1405 0 2.3497 0 0

figure ()
set(gcf, 'color', 'w')
colormap(RGB);
colorbar('EastOutside')
patch('Faces',Connectivity_matrix_tria,'Vertices', xy,'FaceVertexCData',q,'FaceColor','interp')
patch('Faces',Connectivity_matrix_quad,'Vertices', xy,'FaceVertexCData',q,'FaceColor','interp')
axis equal
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])
text(x(in_poly),y(in_poly),str(in_poly),'HorizontalAlignment','right','BackgroundColor','w')
line(x(in_poly),y(in_poly),'LineStyle','none','Marker','o','Color',[0.75 0 0.75],'MarkerFaceColor',[0.75 0 0.75])

[Kovacs Mario]

Thank you!

[Voss]

You're welcome!