% mythreecorners
I=0;
p = size(T,1)
for i = 1:p
    x1 = x(T(i,1));
    x2 = x(T(i,2));
    x3 = x(T(i,3));
    y1 = y(T(i,1));
    y2 = y(T(i,2));
    y3 = y(T(i,3));
    z1 = z(T(i,1));
    z2 = z(T(i,2));
    z3 = z(T(i,3));
    A = .5*abs(det([x1, x2, x3; y1, y2, y3; 1, 1, 1]));
    zavg = (z1 + z2 + z3)/3
    I = I + zavg*A
end
I