I would like to have more information of the theory behind this. What it means that it is "quadratic"? Should it be exact for 2nd. degree functions? I tried this
X=[1:10 1:10];Y=[zeros(1,10) ones(1,10)];%Data points
f=100*(X').^2; %data points
tri=delaunay(X,Y);%Triangulation
triplot(tri,X,Y) %to interpret the case
x=linspace(0,11,300);y=repmat(0.5,1,300);
fC=tinterp([X' Y'],tri,f,x,y,'quadratic');
plot(diff(fC));%should be linear if the interpolant is exact for 2nd degree
Apparently from this example the interpolant is C0 (i.e. continuous but not differentiable), but it is a little bit misleading what is meant by "quadratic".
I tried to contact the author before posting, but apparently changed addres. Thank you anyway for his contribution.