How can we increase/decrease the number of triangles in a triangulation that is created from a polyshape object?

I wrote the following code:

C1 = polyshape(X1,Y1);

C2 = polyshape(X2,Y2);

C = subtract(C1,C2);

T = triangulate(C);

where X1, X2, Y1 & Y2 are column vectors of x- & y-coordinates of points that define the outer and inner boundaries of a region. The last command breaks the region C into triangles. My question is: How can we increase or decrease the numbr of triangles in the triangualtion or is it fixed?

Answer 1

[Matt J]

To increase the number of triangles, you would have to add vertices along the edges, like in the following:

p1= polyshape([0,0; 1 0; 0 1]);
p2=polyshape([0,0,; 1 0; 0.5,0.5,;0,1],'Simplify',0);

doPlot(p1)

doPlot(p2)

function doPlot(p)
 figure
 plot(p,'FaceColor','g'); hold on
 triplot(triangulation(p),'r'); hold off
 axis equal
end

[Saad Mansoor]

Thank you Matt for your answer. Actually I already tried increasing the vertices but it didn't work. The polyshape function automatically deleted vertices that lie on a straight line except the two extreme ones. But I'm using ver2018. Maybe in the latest version this may not be the case.

[Matt J]

I don't think it's any different in 2018. You need to set 'Simplify'='off' like in my posted code.

[Image Analyst]

Add a very tiny bit of noise to the coordinates so they're no longer on a perfectly straight line.

[Saad Mansoor]

Thank you Matt & Image Analyst for your valuable inputs. Yes, when I use 'Simplify',0) in the polyshape command it starts working. So I get the two figures shown below. The traingles span the whole width of the hexagonal ring. Any idea how to have smaller triangles?

Answer 2

[Image Analyst]

To decrease the number of vertex points that describe a polygon while still somewhat resembling the original shape, see the algorithm in the attached paper.

Answer 3

[Matt J]

Another way:

p1=nsidedpoly(6);
p2=p1.scale(0.5);
P=subtract(p1,p2);


P=subTri(P);
for i=1:3
P=splitTri(P);
end

plot(P); axis equal

function p=subTri(P)
%Sub-divide a scalar polyshape P into a vector of triangular sub-polyshapes

 T=triangulation(P);
 V=T.Points;

 for i=height(T):-1:1
  p(i)=polyshape(V(T(i,:),:));
 end

 p=p(:)';

end

function pnew=splitTri(p)
%Given a vector of triangular polyshapes, p, split each p(i) into smaller
%triangular polyshapes.

    if isscalar(p)
     V=interp1( p.Vertices([1,2,3,1],:) , 1:0.5:3.5);
    
     pnew=subTri(polyshape(V,'Simplify',0));
    else
    
      C=arrayfun(@splitTri,p,'uni',0);
      pnew=[C{:}];
    end
end