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

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Surendra Ratnu 2023-4-30

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https://ww2.mathworks.cn/matlabcentral/answers/1955384-how-to-find-angle-between-a-fixed-point-to-multiple-point

评论： Star Strider 2023-5-3

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

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Answer 1

Star Strider 2023-4-30

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1955384-how-to-find-angle-between-a-fixed-point-to-multiple-point#answer_1226134

在 MATLAB Online 中打开

M.mat
N.mat

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.

.

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Star Strider 2023-5-1

在 MATLAB Online 中打开

M.mat
N.mat

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
MReference DistanceReference Angle(°)Radial Distance (M-N)___________________________________________________________________

  133          14.036                85.914                 58.464        
  133          14.142                 81.87                 58.189        
  134          15.297                 78.69                 58.822        
  133           14.56                74.055                 57.567        
  133          14.866                70.346                 57.245        
  132          14.318                65.225                 55.973        
  132          14.765                61.699                  55.66        
  132          15.264                58.392                 55.362        
  132          15.811                55.305                 55.027        
  131           15.62                50.194                 53.759        
  130          14.866                47.726                 52.811        
  130          15.556                    45                 52.498        
  129           15.62                39.806                 51.245        
  128          15.811                34.695                  49.98        
  127          16.125                29.745                 48.703        
  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.

.

Star Strider 2023-5-2

在 MATLAB Online 中打开

M.mat
N.mat

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 2023-5-3

ok thank you for your help

Star Strider 2023-5-3

As always, my pleasure!

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