Work wonderfully. One question. Not quite understand the Gauss Quadrature, but I noticed that the code by default outputs 64 note points. Can I increase the number of note points in order to improve the integration results?

Wait until Greg fixes this. The following code fragment should compute the volume of a simple tetrahedron.
At the very least, since the function is constant over the
simplex domain, its integral should be positive.

V = [0 0 0;0 0 1;0 1 0;1 0 0];
[X,Y,Z,W]=tetraquad(4,V);
F = ones(size(X));
Q = W'*F

Q =
-0.1667

The magnitude is correct, just the sign is wrong. Q should be 1/6.