Extract a set of polygons

Based of a concave polygon witch has as input his vertices , I obstain the sectors that partition that poligon in convex pieces, so after that i have the coodinates of start and end points of the segment lines that do the partition.

My problem is that I need to identify each of this pieces and store them based of their vertices

This is the plot , Vx=[210 450 390 300 360 270 270 360 285 225 285 240 195 90 120 15 60 120 90 45 45 15 120 150 150];

Vy=[90 195 240 195 180 180 195 255 360 300 315 180 300 240 315 225 120 195 90 90 45 15 60 30 225]; are the vertices of the main polygon, and those are stard and end point coordinates of those segments

ex = 120.0000 395.4545 240.0000 270.0000 312.2727 210.0000 24.5902 197.8723 45.0000 150.0000

ey = 60.0000 171.1364 180.0000 270.0000 321.8182 90.0000 202.6230 292.3404 27.8571 232.5000

sx = 90 360 270 270 285 240 90 120 45 150

sy = 90 180 180 195 315 180 240 195 45 225

[Johan]

You could try to do it with polyshape by giving a finite width to your segment. Here is an example below, still need a bit of work though.

Vx=[210 450 390 300 360 270 270 360 285 225 285 240 195 90 120 15 60 120 90 45 45 15 120 150 150];
Vy=[90 195 240 195 180 180 195 255 360 300 315 180 300 240 315 225 120 195 90 90 45 15 60 30 225];

ex =  [120.0000  395.4545  240.0000  270.0000  312.2727  210.0000   24.5902  197.8723   45.0000  150.0000];
ey =  [60.0000  171.1364  180.0000  270.0000  321.8182   90.0000  202.6230  292.3404   27.8571  232.5000];
sx =  [90   360   270   270   285   240    90   120    45   150];
sy =  [90   180   180   195   315   180   240   195    45   225];

%Convert vertices to polyshape
myshape = polyshape(Vx,Vy);
%Initialize arrays for the loop 
mysubshape = myshape;
mypieces = polyshape();
for i_seg = 1:length(sx)
    mysegment = [sx(i_seg),ex(i_seg);sy(i_seg),ey(i_seg)];
    %Create segment of 0.1 width
    mypolysegement = polyshape([mysegment(1,:),mysegment(1,:)+0.1],[mysegment(2,:),mysegment(2,:)+0.1]);
    %subtract segment from mysubshape, this should lead to at least 2
    %polygon. The polygons are individualised by the regions() function
    temp = regions(subtract(mysubshape,mypolysegement));
    %The largest polygon is the remaining shape the other are the pieces
    %exept for the last segment
    Area_pieces = area(temp);
    mysubshape = temp(Area_pieces == max(Area_pieces));
    if i_seg < length(sx)
        mypieces = [mypieces; temp(Area_pieces < max(Area_pieces))];
    else
        mypieces = [mypieces; temp];
    end
        
end

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

%Result is not perfect, some pieces are not separated properly
figure(1)
clf
hold on
plot(myshape)    
plot(mypieces) 
hold off 
axis equal