Select only those nodes of an rx3 matrix placed at a distance 'd' from a node P (1x3)

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Alberto Acri 2023-9-27

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https://ww2.mathworks.cn/matlabcentral/answers/2026412-select-only-those-nodes-of-an-rx3-matrix-placed-at-a-distance-d-from-a-node-p-1x3

评论： Voss 2023-9-28

采纳的回答： Voss

M.mat

在 MATLAB Online 中打开

Hi! Is there any way to extract the coordinates of the nodes of the similar circle on the left?

I had thought of something related to the distance 'd' between one node and another of the similar circle but there are nodes that may be at a greater distance from the set 'd' (see nodes A and B). So, using this procedure, it would be necessary first to add nodes between A and B for example. Any methods that could be used?

load M
P = [25.9349 -15.0445 77.3427];
figure
plot3(P(:,1),P(:,2),P(:,3),'k.','Markersize',20);
hold on
plot3(M(:,1),M(:,2),M(:,3),'r.','Markersize',10);
hold off
axis equal

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Answer 1

Voss 2023-9-27

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https://ww2.mathworks.cn/matlabcentral/answers/2026412-select-only-those-nodes-of-an-rx3-matrix-placed-at-a-distance-d-from-a-node-p-1x3#answer_1320137

在 MATLAB Online 中打开

M.mat

load M

figure

plot3(M(:,1),M(:,2),M(:,3),'r.')

view(2)

% keep only points whose x-coordinate is less than 28:

idx = M(:,1) < 28;

M = M(idx,:);

figure

plot3(M(:,1),M(:,2),M(:,3),'r.')

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Voss 2023-9-27

编辑：Voss 2023-9-27

在 MATLAB Online 中打开

M1.mat

Use a different distance threshold for this data set.

load M1

P = [28.73645 -15.2786 69.24005];

figure

plot3(P(:,1),P(:,2),P(:,3),'k.','Markersize',20);

hold on

plot3(M1(:,1),M1(:,2),M1(:,3),'r.','Markersize',10);

hold off

axis equal

view(2)

d = sum((M1-P).^2,2); % (squared) distance to point P

hist(d,100) % histogram (w/ 100 bins) to help pick distance threshold

d_thresh = 5; % distance threshold

idx = d < d_thresh;

M1 = M1(idx,:);

plot3(M1(:,1),M1(:,2),M1(:,3),'r.')

hold on

plot3(P(1),P(2),P(3),'ko')

view(2)

You could try to write a general algorithm - maybe find the lowest-valued histogram bin whose count is zero and use that as the (squared) distance threshold - but that would depend on the width of the bins and I don't think it would be a good enough approach to work in every possible case. And, obviously if your data represents two rings/circles that overlap, then the distance-thresholding approach won't work at all in that case. Maybe someone else has a better idea.

Voss 2023-9-27

编辑：Voss 2023-9-27

在 MATLAB Online 中打开

To illustrate the problem with a simple example. Let's say the P and M are these:

P = [28.73645 -15.2786 69];
M = [ ...
5  -15    69; ...
3  -14.8  69; ...
  -14.6  69; ...
75 -14.75 69; ...
5  -15    69; ...
25 -15.2  69; ...
  -15.5  69; ...
25 -15.65 69; ...
5  -15.7  69; ...
75 -15.6  69; ...
  -15.5  69; ...
25 -15.25 69; ...
25 -14.75 69; ...
3  -14.7 69; ...
2  -14.8 69];

And the last three rows of M are the ones you want to discard.

plot3(M(:,1),M(:,2),M(:,3),'r.')

hold on

plot3(M(end-2:end,1),M(end-2:end,2),M(end-2:end,3),'kx')

plot3(P(1),P(2),P(3),'ko')

view(2)

The distance-threshold approach won't work because those three points are closer to P than some points you want to keep

d = sum((M-P).^2,2); % (squared) distance to point P
disp(d)
6606
5466
5300
2796
1335
2428
5914
3746
2335
1035
1185
2646
5161
5253
5168

Notice that the last three elements (the squared distances to the points to discard) are less than the first element (squared distance to a point to keep).

Therefore, there is no distance threshold you can apply that will keep the first point and discard the last three.

You'll potentially have this problem any time the ring is elongated (more like an ellipse with high eccentricity than a circle).

Voss 2023-9-28

编辑：Voss 2023-9-28

在 MATLAB Online 中打开

M.mat
M1.mat

Actually, the rings don't have to be very elliptical for that method not to work; if there is any part of another ring near enough to a 'flat' side of the ring you want, then those points would incorrectly be included as well. (And, even if there is a distance threshold that would work in a given case, I don't know if there's a very reliable way to find it.)

So here's an alternate method that I think will work better - and it's more in line with the approach you initially conceived of. The idea is to find points that are close to each other (not to find points that are close to P, which was the previous approach I suggested).

% (squared) distance threshold used to determine whether two points are

% 'connected', i.e., close enough to each other to be considered part of

% the same ring:

d_thresh = 0.25;

% note that the same d_thresh is used in both cases here, so maybe (?) the

% same value will work in all cases you have

load M1

P = [28.73645 -15.2786 69.24005];

M_original = M1;

% start with the point in M1 closest to P,

[~,min_idx] = min(sum((M1-P).^2,2));

% and find which points in M1 are "connected" to that point:

is_connected = get_connected_points(M1,M1(min_idx,:),d_thresh);

% matrix of connected points:

M_final = M1(is_connected,:);

% plot results:

figure

plot3(P(1),P(2),P(3),'ok')

hold on

plot3(M_original(:,1),M_original(:,2),M_original(:,3),'r.')

plot3(M_final(:,1),M_final(:,2),M_final(:,3),'g.')

load M

P = [25.9349 -15.0445 77.3427];

M_original = M;

% start with the point in M closest to P,

[~,min_idx] = min(sum((M-P).^2,2));

% and find which points in M are "connected" to that point:

is_connected = get_connected_points(M,M(min_idx,:),d_thresh);

% matrix of connected points:

M_final = M(is_connected,:);

% plot results:

figure

plot3(P(1),P(2),P(3),'ok')

hold on

plot3(M_original(:,1),M_original(:,2),M_original(:,3),'r.')

plot3(M_final(:,1),M_final(:,2),M_final(:,3),'g.')

function is_connected = get_connected_points(M,P,d_thresh,is_connected)

% inputs:

% M: Nx3 matrix of points

% P: reference point

% thresh: squared distance threshold

% is_connected: Nx1 logical vector saying whether each point has been found

% to be connected (i.e., closer than thresh) to some point in M so far;

% this is not given initially but is used in recursive calls

% output:

% is_connected: (updated) is_connected vector

if nargin < 4

% if no is_connected vector is given, initialize to all false

% (no points have been found to be connected yet at the beginning)

is_connected = false(size(M,1),1);

elseif all(is_connected)

% if all points have been found to be connected, nothing left to do

return

end

% d: squared distance between each point in M and reference point P

% d is Inf for points already found to be connected so that they are not "found" again

d = Inf(size(M,1),1);

% for those points still in play (i.e., not found to be connected to any

% other point (yet)), calculate their squared distance from reference point P

d(~is_connected) = sum((M(~is_connected,:)-P).^2,2);

% find the indices of points closer than d_thresh to the reference point P

idx = find(d < d_thresh);

% mark those points as connected

is_connected(idx) = true;

% for each of those newly-found connected points,

for ii = 1:numel(idx)

% find the points connected to them, i.e., run this function again,

% with each newly-found point as the reference point P, updating and

% returning the is_connected vector each time

is_connected = get_connected_points(M,M(idx(ii),:),d_thresh,is_connected);

end

Alberto Acri 2023-9-28

Ok thanks for the help @Voss! This solution might be the most useful.

Voss 2023-9-28

You're welcome!

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Select only those nodes of an rx3 matrix placed at a distance 'd' from a node P (1x3)

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Select only those nodes of an rx3 matrix placed at a distance 'd' from a node P (1x3)

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