Note:

XC = baryToCart(TR, SI, B)
XC = baryToCart(TR, SI, B)
returns the
Cartesian coordinates XC
of each point in B
that
represents the barycentric coordinates with respect to its associated
simplex SI
.
TR  Triangulation representation. 
SI  Column vector of simplex indices that index into the triangulation
matrix TR.Triangulation 
B  B is a matrix that represents the barycentric
coordinates of the points to convert with respect to the simplices SI . B is
of size m byk , where m = length(SI) ,
the number of points to convert, and k is the number
of vertices per simplex. 
XC  Matrix of Cartesian coordinates of the converted points. XC is
of size m byn , where n is
the dimension of the space where the triangulation resides. That is,
the Cartesian coordinates of the point B(j) with
respect to simplex SI(j) is XC(j) . 
A simplex is a triangle/tetrahedron or higherdimensional equivalent.
Compute the Delaunay triangulation of a set of points.
x = [0 4 8 12 0 4 8 12]'; y = [0 0 0 0 8 8 8 8]'; dt = DelaunayTri(x,y)
Compute the barycentric coordinates of the incenters.
cc = incenters(dt); tri = dt(:,:);
Plot the original triangulation and reference points.
figure subplot(1,2,1); triplot(dt); hold on; plot(cc(:,1), cc(:,2), '*r'); hold off; axis equal;
Stretch the triangulation and compute the mapped locations of the incenters on the deformed triangulation.
b = cartToBary(dt,[1:length(tri)]',cc); y = [0 0 0 0 16 16 16 16]'; tr = TriRep(tri,x,y) xc = baryToCart(tr, [1:length(tri)]', b);
Plot the deformed triangulation and mapped locations of the reference points.
subplot(1,2,2); triplot(tr); hold on; plot(xc(:,1), xc(:,2), '*r'); hold off; axis equal;