MATLAB: Sorting of points in 2D

aerofoilairfoilalphashapeboundarycentroidconvmmpolyfitmovmeanpolyfitpolyvalsorting in 2d

Dear All,

I face issue in arranging the airfoil coordinates coming from a CAD program. The coordinates are arranged from minumum x value to maximum x value. But I require to arrange the points starting from Trailing Edge ( Max X coordinate) and then proceed on top side all the way to Leading Edge ( Minimum X coordinate) and then again proceed in the bottom side and terminate in the Trailing Edge.

The input.txt ( required input file to be sorted)

Output.txt (the coordinates sorted manually).

I have several airfoil coordinates of similar nature, so a matlab function could help me out doing the job manually everytime.

Any help is really appreciated.

Thanks in Advance,

K Vijay Anand

Best Answer

Here is some simple code that that works quite nicely for your aerofoil. The code assumes that the top and bottom are both functions of x (i.e. no implicit curves in some other variable) and that they are both sampled with approximately the same step size (like your data). A convolution is used to smooth the data to create a moving average over 3 data points. The y-data are compared against this moving average to decide if the data point belongs to the top or bottom of the aerofoil, and then those two sets of points are sorted separately.

Inp = readtable('Input.txt','Delimiter','\t');
tmp = conv(Inp.y([1,1:end,end]),ones(1,3)/3,'valid'); % smoothed data
idx = Inp.y >= tmp; % true/false == top/bottom
idx(end) = true; % trailing edge -> top
Out = [sortrows(Inp(idx,:),-1);sortrows(Inp(~idx,:),+1)];
writetable(Out,'Out.txt','Delimiter','\t')

Checking against your original "Output.txt" and plotting the data:

>> Chk = readtable('Output.txt','Delimiter','\t');
>> isequal(Chk,Out)
ans =
     1
>> plot(Inp.x,Inp.y,'-*', Inp.x,tmp,'-+', Out.x,Out.y,'-x')
>> legend('original','moving average','sorted')

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MATLAB: How to sort an array to follow a path

I don't know much about reading in stl files but you might want to look into options that would read in the points in different ways to them them in sequential order, if it's possible.

Here are two methods that each produce the same figure shown at the bottom.

Method 1 shows a solution using k = convhull(x,y)

% Create coordinates that form a circle

th = linspace(0,2*pi,60); 
x = sin(th); 
y = cos(th); 
% Scatter the order of the coordinates so they

% are no longer sequential

idx =  randsample(numel(x), numel(x)); 
x = x(idx);   
y = y(idx);
% Compute 2D convext hull
idx = convhull(x,y);
% Plot before and after sort

figure()
subplot(1,2,1)
plot(x,y,'r-o')
axis square
grid on
title('Original scattered coordinates')
subplot(1,2,2)
plot(x(idx), y(idx), 'r-o')
axis square
grid on
title('Sorted coordinates')

Method 2 shows a solution using proximity. This method relies on the following assumptions:

The perimeter line does not cross over itself.
The distance between coordinate A and it's neightboring coordinate B is the minimum distance between coordinate A and any other coordinate in the perimeter execept, perhaps the coordinate that come sequentially before A. In other words, if parts of the parimeter come very close to eachother such that their distance is closer than the interval of coordinates, this will fail.

See inline comments for details.

% Create coordinates that form a circle
th = linspace(0,2*pi,60); 
x = sin(th); 
y = cos(th); 
% Scatter the order of the coordinates so they
% are no longer sequential
idx =  randsample(numel(x), numel(x)); 
x = x(idx);   
y = y(idx); 
% Set up loop variables.  The first coordinate
% will be the first coordinate in the new, sorted order.
yIdx = [1,nan(size(y)-1)]; 
xyTemp = [x(:), y(:)]; 
xyTemp(1,:) = NaN; 
idx = [1, nan(1, numel(x)-1)]; 
counter = 0; 
% Loop through each coordinate and find its nearest neightbor,
% Then eliminate that coordinate from being chosen again, and
% then start the loop again finding the nearest neighbor to 
% the pointe we just located.
while any(isnan(idx))
    counter = counter+1; 
    % find closest coordinate to (x(i),y(i)) that isn't already taken
    [~, idx(counter+1)] = min(pdist2(xyTemp,[x(idx(counter)), y(idx(counter))])); 
    % Eliminate that from the pool
    xyTemp(idx(counter+1),:) = NaN; 
end
% Plot before and after sort
figure()
subplot(1,2,1)
plot(x,y,'r-o')
axis square
grid on
title('Original scattered coordinates')
subplot(1,2,2)
plot(x(idx), y(idx), 'r-o')
axis square
grid on
title('Sorted coordinates')

MATLAB: How to move points in a curve in the normal direction

Try to reverse the sign before tol

x_n(2, 1) = x_airfoil(i, 1) + +1*tol*(y_airfoil(i+1, 1)-y_airfoil(i, 1))/sqrt(((x_airfoil(i+1, 1)-x_airfoil(i, 1))^2+(y_airfoil(i+1, 1)-y_airfoil(i, 1))^2));
y_n(2, 1) = y_airfoil(i, 1) + -1*tol*(x_airfoil(i+1, 1)-x_airfoil(i, 1))/sqrt(((x_airfoil(i+1, 1)-x_airfoil(i, 1))^2+(y_airfoil(i+1, 1)-y_airfoil(i, 1))^2));

Or the opposite

x_n(2, 1) = x_airfoil(i, 1) + -1*tol*(y_airfoil(i+1, 1)-y_airfoil(i, 1))/sqrt(((x_airfoil(i+1, 1)-x_airfoil(i, 1))^2+(y_airfoil(i+1, 1)-y_airfoil(i, 1))^2));
y_n(2, 1) = y_airfoil(i, 1) + +1*tol*(x_airfoil(i+1, 1)-x_airfoil(i, 1))/sqrt(((x_airfoil(i+1, 1)-x_airfoil(i, 1))^2+(y_airfoil(i+1, 1)-y_airfoil(i, 1))^2));

Best Answer

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MATLAB: How to sort an array to follow a path

MATLAB: How to move points in a curve in the normal direction

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