MATLAB: Sort coordinates based on closest connectivity

3d linesconnectivitycoordinatessorttraveling salesman problem

Hello,

I have an nx3 array representing x,y,z coordinates in space. These coordinates are all connected and represent a tortuous line. I would like to calculate the length of this line, however the coordinates I have are not in order of connectivity. Is it possible to reorder them such that I can simply calculate the length by doing a for loop like:

length = 0;
for i = 1:length(array)-1
    length = norm([coords(i,1)-coords(i+1,1),coords(i,2)-coords(i+1,2),coords(i,3)-coords(i+1,3)]);
end

I have tried just finding the neighbours of each coordinate and reordering that way, but this gets very convoluted quickly and requires that I "walk" through the line. For the total dataset I am trying to analyze I will literally have millions of these lines, so I am trying to avoid slow solutions like that.

Edit: The lines I'm working with are in an image, and the points on the line must have a max distance from each consecutive point of (1,1,1). That is, 1 pixel in x,y, and z.

Best Answer

Try https://www.mathworks.com/matlabcentral/answers/?term=tag%3A%22traveling+salesman+problem%22

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MATLAB: How do we calculate Euclidean Distance Matrix in Matlab

You probably want pdist: https://fr.mathworks.com/help/stats/pdist.html

MATLAB: Joining a set of points inside a buffer to get a polygon.

[s,t] = boundary(polyout);  %%this is the boundary polygon of the buffer 
numPoints = length(clustersCentroids);
x = X;  %points to be joined
y = Y;
x([1 2],:)=x([2 1],:);
y([1 2],:)=y([2 1],:);
figure
plot(x, y, 'bo', 'LineWidth', 2, 'MarkerSize', 17);
grid on;
 imshow(I2);
xlabel('X', 'FontSize', 10);
ylabel('Y', 'FontSize', 10);
% Make a list of which points have been visited
beenVisited = false(1, numPoints);
% Make an array to store the order in which we visit the points.
visitationOrder = ones(1, numPoints);
% Define a filasafe
maxIterations = numPoints + 1;
iterationCount = 1;
% Define a current index.  currentIndex will be 1 to start and then will vary.
currentIndex = 1;
while sum(beenVisited) < numPoints
    visitationOrder(iterationCount) = currentIndex; 
  beenVisited(currentIndex) = true; 
  % Get the x and y of the current point.
  thisX = x(currentIndex);
  thisY = y(currentIndex);
  %text(thisX + 0.01, thisY, num2str(currentIndex), 'FontSize', 35, 'Color', 'r');
  % Compute distances to all other points
  distances = sqrt((thisX - x) .^ 2 + (thisY - y) .^ 2);
  distances(beenVisited)=inf;
   distances(currentIndex) = inf;
  % Don't consider visited points by setting their distance to infinity.
  [out,idx] = sort(distances);
  xx=[x(currentIndex) x(idx(1))]
   yy=[y(currentIndex) y(idx(1))]
  if isempty(polyxpoly(xx,yy,s,t))
   iterationCount = iterationCount + 1;
   currentIndex =idx(1);
  else 
     xx=[x(currentIndex) x(idx(2))]
   yy=[y(currentIndex) y(idx(2))]  
  if isempty(polyxpoly(xx,yy,s,t))
   iterationCount = iterationCount + 1;
   currentIndex =idx(2);
   else 
     xx=[x(currentIndex) x(idx(3))]
   yy=[y(currentIndex) y(idx(3))]  
  if isempty(polyxpoly(xx,yy,s,t))
   iterationCount = iterationCount + 1;
   currentIndex =idx(3);
   else 
     xx=[x(currentIndex) x(idx(4))]
   yy=[y(currentIndex) y(idx(4))]  
  if isempty(polyxpoly(xx,yy,s,t))
   iterationCount = iterationCount + 1;
   currentIndex =idx(4);
  end
  end
  end
  end
end
% Plot lines in that order.
hold on;
orderedX = [x(visitationOrder); x(1)];
orderedY = [y(visitationOrder) ;y(1)];
plot(orderedX,orderedY, 'm-', 'LineWidth', 2);
title('Result', 'FontSize', 10);

The method used here was a modified form of 'travelling salesman problem'. The condition of the buffer is included into this concept.

Best Answer

Related Solutions

MATLAB: How do we calculate Euclidean Distance Matrix in Matlab

MATLAB: Joining a set of points inside a buffer to get a polygon.

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