Gauss Quadrature for Tetrahedra

Compute Gauss weights and nodes for a specied tetrahedron

Description

This script computes the (x,y,z) Gauss quadrature nodes and weights for a tetrahedron with user-specied vertices.

• Acknowledgements: This submission has inspired the following:; Homogen Integrate on Triangular Area and Tetrahedral Volume
• MATLAB release: MATLAB 7 (R14)

[John D'Errico]

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.

[John D'Errico]

Its fixed. Thanks Greg.