Creating points inside polygon boundary?

Hello. I am trying to create a set number of points inside the boundary of an input polygon. i want to add it as a condition to my while loop to check if each point is within the polygon, if not then it should continues until it finds a point that is within, till i get my (n) desired number of points. My polygon is composed of (xb) vector contains x coordinates and and (yb) containts y coordinates which serve as vectors of the polygon points. Can anyone help me and suggest a solution to generate these points only inside this following polygon? Here is the script which i work on it

w=14.7 ; h=12.5 ; ds=0.3 ; n=500 ; THT=240;
  % Biomimetic pattern parameters
  a=3.7; b=0.67; phi = (sqrt(5)+1)/2;
  % Constraints
  Dm=(sqrt(w^2 + h^2)) + ds ; D1 = 0.75*THT;
  xb=[-1186.53,1245.2,1232.51,1237.01,1002.74,946.118,954.654,1039.93,1047.05,901.728,905.519,873.292,700.736,464.325,380.736,334.014,258.286,199.453,-20.7446,-352.379,-587.244,-715.189,-867.852,-991.447,-1024.5,-930.733,-994.878,-1092.17,-1141.61,-1101.29,-1123.56,-1219.41,-1186.53];  
  yb=[-1085.44,-1056.98,-404.032,-76.0963,133.888,217.392,395.52,579.397,640.168,815.22,1270.41,1397.06,1539.57,1531.35,1522.04,1540.16,1562.23,1573.83,1571.67,1529.67,1488.86,1413.44,1320.06,1223.01,533.811,357.565,126.811,-11.116,-103.213,-288.39,-347.769,-435.997,-1085.44];
  % Generation of points coordinates
  r = zeros(1, n);
  teta = zeros(1, n);
  x = zeros(1, n);
  y = zeros(1, n);
  k = 1; 
  curpoint = 1;
  while curpoint <= n
      r(curpoint) = a*k^b;
      %Minimum radial distance
      if  r(curpoint) > D1   
         teta(curpoint) = 2*pi*(phi^-2)*k; 
         [x(curpoint), y(curpoint)] = pol2cart(teta(curpoint), r(curpoint));
         %Only add this point if it is far enough away from all others
         if curpoint == 1 || all(hypot(x(curpoint) - x(1:curpoint-1), y(curpoint) - y(1:curpoint-1)) >= Dm)
             curpoint = curpoint + 1; 
         end
      end
      k = k + 1;
  end

[Ameer Hamza]

Your dataset looks like this (except red dot).

How do you decide which point is inside or outside? Is red marker inside?

[zouhir zeroual]

I want that generated points by (r) and (teta) equations should be created inside the above polygon defined by xb and yb vectors not outside thanks

Answer 1

[the cyclist]

I would use the rejection method. Define a square that encloses the entire polygon (e.g. by using the largest/smallest x & y values). Then generate random points inside that square. To see if each point lies within your polygon, use the built-in inpolygon function. Reject those points that are not within the polygon, and use what is left.

[zouhir zeroual]

But i am generating points according to fermat spiral equations (r and teta) instead of random.point, could you add this to my previous code ?

[Walter Roberson]

Then when you do your spiral equations, before accepting a point, check to see if inpolygon() considers it to be inside the object.

[zouhir zeroual]

Yes exactly, before add a point i want to check if it's inside my polygon, if it is add it, if not ignore it till i get the (n) points i want

[Walter Roberson]

inpolygon(x(curpoint), y(curpoint), xb, yb)

[zouhir zeroual]

Could you please sir Roberson modify my code and add this statement in order to accept only points inside the polygon and thanks. Alot

[Walter Roberson]

           if curpoint == 1 || (all(hypot(x(curpoint) - x(1:curpoint-1), y(curpoint) - y(1:curpoint-1)) >= Dm) && inpolygon(x(curpoint), y(curpoint), xb, yb))

[zouhir zeroual]

thanks for you help