How to find angle between a fixed point to multiple point ??

I would like to calculate the angle ABC which is shown in the figure. I have fixed line AB and multiple point on the boundary-1 (in red colour). I want to calculate a array of angle between line AB and BC (C is a moving point is on the boundary-1) and also corresponding distance from point C to nearest point on the boundary-2(in green colour). I attached a figure for clearification and boundaries mat file.

Thank you for your help

Answer 1

[Star Strider]

Perhaps this —

M = load('M.mat');
M = M.M;
N = load('N.mat');
N = N.N;

xv = 506;                                               % Determined Manually
yv = 119;                                               % Determined Manually
a = atan2d(M(:,2)-yv, M(:,1)-xv);                       % Angles (°)
d = hypot(yv-M(:,2), xv-M(:,1));                        % Distances
v = (1:210:size(M,1)).';                                % Selection Vector For Plot

figure
plot(N(:,1), N(:,2),'g')
hold on
plot(M(:,1), M(:,2),'r')
plot([xv*ones(size(v)) M(v,1)].', [yv*ones(size(v)) M(v,2)].', '--m')
plot(506, 119,'k+')
yl = ylim;
plot([1 1]*506, [yl(1) 119], '-k')
hold off
grid
Ax = gca;
% Ax.YDir = 'reverse';
axis('equal')
text(M(v,1), M(v,2), compose('\\leftarrow r = %.2f, \\theta = %.2f\\circ', [d(v) a(v)]), 'Rotation',0) 

The angles make more sense with a normal y-axis direction. Un-comment the ‘YDir’ assignment to show it as in the original image.

.

[Surendra Ratnu]

Thank you for your reply. It is also worked well for my case. But I have some other measurement. I attached a image (Which is the cropped image). In this image, C is the moving point(indicated by black circle) and supposed E is the point normal to line BC which lies on the boundary-2. The distance between point E and C is the d (which is indicated in the image). Can you give provide the any solution to calculate the distance d??

Again thank you for your contribution.

[Star Strider]

This was interesting!

There are 1367 data pairs in ‘M’ and 3266 in ‘N’ and the approsimate coordinating pairs do not strictly coincide. Since any sort of direct comparison is not likely to be efficient because of that, I decided to use hypot again, this time searching for the minimum distance between the ‘M’ coordinates (looping on them) and the ‘N’ coordinates, returning that distance and the associated index. of the matching ‘N’ pair. This sort of ‘exhaustive search’ is generally not efficient, however it works here because of the way the data are arranged.

That approach seems to have worked —

M = load('M.mat');
M = M.M;
N = load('N.mat');
N = N.N;

xv = 506;                                               % Determined Manually
yv = 119;                                               % Determined Manually
a = atan2d(M(:,2)-yv, M(:,1)-xv);                       % Angles (°)
d = hypot(yv-M(:,2), xv-M(:,1));                        % Distances
v = (1:210:size(M,1)).';                                % Selection Vector For Plot

figure
plot(N(:,1), N(:,2),'g')
hold on
plot(M(:,1), M(:,2),'r')
plot([xv*ones(size(v)) M(v,1)].', [yv*ones(size(v)) M(v,2)].', '--m')
plot(506, 119,'k+')
yl = ylim;
plot([1 1]*506, [yl(1) 119], '-k')
hold off
grid
Ax = gca;
% Ax.YDir = 'reverse';
axis('equal')
text(M(v,1), M(v,2), compose('\\leftarrow r = %.2f, \\theta = %.2f\\circ', [d(v) a(v)]), 'Rotation',0) 

for k = 1:size(M,1)
    [dh,ix] = min(hypot(M(k,2)-N(:,2), M(k,1)-N(:,1)));
    dv(k,:) = dh;
    ixv(k,:) = ix;
end

dist_table = table(dv, ixv, M, N(ixv,:), 'VariableNames',{'Distance','M(index)','M','N(M(index),:)'}) 

dist_table = 1367×4 table
    Distance    M(index)        M         N(M(index),:)
    ________    ________    __________    _____________

     58.464       3239      507    133     520     76  
     58.189       3232      508    133     527     78  
     58.822       3232      509    134     527     78  
     57.567       3232      510    133     527     78  
     57.245       3229      511    133     530     79  
     55.973       3229      512    132     530     79  
      55.66       3229      513    132     530     79  
     55.362       3226      514    132     533     80  
     55.027       3226      515    132     533     80  
     53.759       3226      516    131     533     80  
     52.811       3226      516    130     533     80  
     52.498       3226      517    130     533     80  
     51.245       3226      518    129     533     80  
      49.98       3223      519    128     536     81  
     48.703       3223      520    127     536     81  
      47.76       3223      520    126     536     81  

select = M(:,1)>369 & M(:,1)<386 & M(:,2)>250 & M(:,2)<350;
dist_table_matching_detail_plot = dist_table(select,:)

dist_table_matching_detail_plot = 99×4 table
    Distance    M(index)        M         N(M(index),:)
    ________    ________    __________    _____________

      5.831       406       385    349     380    352  
          6       402       385    348     379    348  
     6.0828       402       385    347     379    348  
     6.3246       402       385    346     379    348  
      5.831       402       384    345     379    348  
     6.0828       399       384    344     378    345  
     6.3246       399       384    343     378    345  
     6.7082       399       384    342     378    345  
          6       395       383    341     377    341  
     6.0828       395       383    340     377    341  
     6.3246       395       383    339     377    341  
     6.7082       395       383    338     377    341  
          7       391       383    337     376    337  
          7       390       383    336     376    336  
          6       389       382    335     376    335  
     6.0828       389       382    334     376    335  

figure
plot(N(ixv,1), N(ixv,2),'.g')
hold on
plot(M(:,1), M(:,2),'.r')
plot([M(:,1) N(ixv,1)].', [M(:,2) N(ixv,2)].','k')
hold off
axis equal
grid
axis([369  386    250 350])
xlabel('X [M(:,1), N(:,1)]')
ylabel('Y [M(:,2), N(:,2)]')
title('Enlarged Section (Detail)')

The distance appear to be appropriate with respect to the plot. Sinc the earlier distances and radii are from the central reference to the red ‘M’ curve, the earlier distances can be indexed to the distances between the curves.

Distance_Angle_Summary = table(M, d, a, dv, 'VariableNames',{'M','Reference Distance','Reference Angle(°)','Radial Distance (M-N)'})

Distance_Angle_Summary = 1367×4 table
        M         Reference Distance    Reference Angle(°)    Radial Distance (M-N)
    __________    __________________    __________________    _____________________

    507    133          14.036                85.914                 58.464        
    508    133          14.142                 81.87                 58.189        
    509    134          15.297                 78.69                 58.822        
    510    133           14.56                74.055                 57.567        
    511    133          14.866                70.346                 57.245        
    512    132          14.318                65.225                 55.973        
    513    132          14.765                61.699                  55.66        
    514    132          15.264                58.392                 55.362        
    515    132          15.811                55.305                 55.027        
    516    131           15.62                50.194                 53.759        
    516    130          14.866                47.726                 52.811        
    517    130          15.556                    45                 52.498        
    518    129           15.62                39.806                 51.245        
    519    128          15.811                34.695                  49.98        
    520    127          16.125                29.745                 48.703        
    520    126          15.652                26.565                  47.76        

If you want to compute the angle of the radial distances (distances between the two curves), that would be simply:

av = atan2d(M(:,2)-N(ixv,2), M(k,1)-N(ixv,1));

I checked that, and specifically on the ‘select’ subset. It works.

.

[Surendra Ratnu]

Thank you for your help. It works for me. Can you tell me how will i seperate the extruded part from the boundary-2 (which is shows in the image matlab.png in green circle). I want to seperate the green circle portion from the green line (boundary-2). I also mention the extruded part in the attached figure). Can you give me some hint on it ??

Thank you for time.

[Star Strider]

This is a challenging project. (There might be a more efficient way to do this with image processing functions, however none of the ones I looked at aeemed to provide a solution to this.)

Th code works by first creating a polyshape from the ‘N’ coordinates (this considerably reduces the number of data points), then calculates the centroid coordinates of the polyshape and uses hypot and atan2 to generate the radii (‘r’) and angles (‘th’) from it to the rest of the polyshape. The angles (‘th’) are made consistent and increasing using the unwrap function, creating ‘uth’. After some editing to get rid of unnecessary data (with ‘qix’), it then creates a vector of srtictly increasing angles in ‘uthq’ and then interpolates them to create ‘rq’. This creates the desired result that can be further used to process to remove the extrusions, done with the movmin to essentially ‘filter out’ the extrusions. That result is plotted as the magneta lline in the figure.

M = load('M.mat');
M = M.M;
N = load('N.mat');
N = N.N;

pgn = polyshape(N(:,1), N(:,2), 'Simplify',1, 'KeepCollinearPoints',0);

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

[cx,cy] = centroid(pgn);
vtcs = pgn.Vertices;

vx = pgn.Vertices(:,1);
vy = pgn.Vertices(:,2);
th = atan2(vy-cy, vx-cx);
r = hypot(vy-cy, vx-cx);
uth = unwrap(th);
ixv = 1:numel(r);

uth = uth(~isnan(uth));
qix = find(diff([uth(1); uth])<-2,1,'first');
uthidx = 1:qix-1;

uth = uth(uthidx);
r = r(uthidx);

uthq = linspace(min(uth), max(uth), numel(uth));
rq = interp1(uth, r, uthq);
rqmin = movmin(rq, 29);

% figure
% plot(uth,r)
% hold on
% plot(uthq, rqmin)
% hold off
% grid

xs = r.*cos(uth)+cx;
ys = r.*sin(uth)+cy;
xsq = rqmin.*cos(uthq)+cx;
ysq = rqmin.*sin(uthq)+cy;

figure
plot(xs,ys)
hold on
plot(xsq, ysq, '-m')
hold off
grid
axis('equal')

I cannot claim that this is robust to even similar data sets. It seems to work reasonably well here.

.

[Surendra Ratnu]

ok thank you for your help

[Star Strider]

As always, my pleasure!