Separate multiple triangulat​ion.Connec​tivityList based on connectivity

Hello, I have a triangulation object which when plotted using the patch command produces multiple non-enclosed faceted surfaces.

I would like to find a way to separate out all discrete surfaces into distinct triangulation.ConnectivityList or triangulation objects. I started implementing this using the triangulation function isConnected(), which only considers connectivity along a single edge and ultimately begs for a recursive solution. I wondered if there was a simpler or already implemented solution to accomplish this task.

I've extended the example in triangulation doc to include two distinct faceted surfaces. Thanks in advance for your help!

P = [ 2.5    8.0    1
    6.5    8.0    1
    2.5    5.0    1
    6.5    5.0    1
    1.0    6.5    1
    8.0    6.5    1];
P = [ P;
    2.5    8.0    3
    6.5    8.0    3
    2.5    5.0    3
    6.5    5.0    3
    1.0    6.5    3
    8.0    6.5    3]

P = 12×3

2.5000 8.0000 1.0000 6.5000 8.0000 1.0000 2.5000 5.0000 1.0000 6.5000 5.0000 1.0000 1.0000 6.5000 1.0000 8.0000 6.5000 1.0000 2.5000 8.0000 3.0000 6.5000 8.0000 3.0000 2.5000 5.0000 3.0000 6.5000 5.0000 3.0000

T = [5  3  1;
    3  2  1;
    3  4  2;
    4  6  2];
T = [T;
    11  9  7;
    9   8  7;
    9  10  8;
    10  12  8]

T = 8×3

5 3 1 3 2 1 3 4 2 4 6 2 11 9 7 9 8 7 9 10 8 10 12 8

TR = triangulation(T,P)

TR = 
  triangulation with properties:

              Points: [12×3 double]
    ConnectivityList: [8×3 double]

h1 = patch('faces',TR.ConnectivityList,'vertices',TR.Points);
set(h1,'FaceColor',[.89 .855 .788], 'FaceLighting','gouraud','EdgeColor','none','FaceAlpha',0.5,'SpecularStrength',.1);
lighting phong;
axis equal
xlabel('x');ylabel('y');zlabel('z')
view([0 40])

Answer 1

[Donald Hume]

I spent a good deal of time searching the internet for an answer to this problem, however it's never enough.

@Sven has a great solution described on File Exchange: SplitFV. Thanks, Sven!