Order Points for plotting

I have the coordinates of the above two shapes imported from a CAD software, however when I plot the shape the points are not in order. Is there a method to order the coordinates so that points on the perimeter of the shape that are side by side are next to each other in the matrix.

If there is any mathematical method that would help me, I am willing to understand it and code it myself. Thank you

[KSSV]

When you extract it from CAD, you can extract into a stl file right?

Attach your data, there are some methods which can be tried. Read about boundary

[Ahmed Abdulla]

I attached the sample data for the anchor shape, i tried boundary but for some reason it skips some points ans changes the shape :(

[Ahmed Abdulla]

Thanks @KSSV, This is the result of using boundary with a shrink factor of 1, however a few points get ignored. Is there a way of using all points?

[Walter Roberson]

use a different shrink factor?

[Ahmed Abdulla]

@Walter Roberson Here I am using a shrink factor of 1 which is the highest I can go :(

Answer 1

[KSSV]

load('A.mat') ;
x = A(:,1) ; y = A(:,2) ;
n = length(x) ; 

iwant = zeros(n,2) ; 
i = 1 ; 
iwant(i,:) = [x(i) y(i)] ; 
x(i) = [] ; y(i) = [] ; 
while ~isempty(x)
    i = i+1;  
    idx = knnsearch([x y],iwant(i-1,:));
    iwant(i,:) = [x(idx) y(idx)] ; 
    x(idx) = [] ; y(idx)= []; 
end
iwant(end+1,:) = iwant(1,:) ; 
plot(iwant(:,1),iwant(:,2))

[Ahmed Abdulla]

Thank you @KSSV for your amazing effort. If you notice in the bottom left there is distorion where the code miss chose the points. I tried with several of my shapes and the problem persists :(

[KSSV]

Lets randomize the points and run the code.

load('A.mat') ;
x = A(:,1) ; y = A(:,2) ;

n = length(x) ; 
idx = randperm(n,n) ; 
x = x(idx) ; y = y(idx) ;

iwant = zeros(n,2) ; 
i = 1 ; 
iwant(i,:) = [x(i) y(i)] ; 
x(i) = [] ; y(i) = [] ; 
while ~isempty(x)
    i = i+1;  
    idx = knnsearch([x y],iwant(i-1,:));
    iwant(i,:) = [x(idx) y(idx)] ; 
    x(idx) = [] ; y(idx)= []; 
end
iwant(end+1,:) = iwant(1,:) ; 
plot(iwant(:,1),iwant(:,2))

[Ahmed Abdulla]

Thank you @KSSV for your efforts I really appreciate it. Unfortunately this doesnt work every time and I am trying to make a generalised function that will work for any shape and at all times