/*!
\page barycoords Barycentric coordinates algorithm

Computation of barycentric coordinates is used to fill interpolation
matrix in case of P1 an P1d types of interpolation. Computation of
barycentric coordinates consists in finding weights of vertices
bearing values within the cell. The cell is triangle in 2D space and
tetrahedron in 3D space.

Input of the algorithm includes
- coordinates of cell vertices (p1...pn),
- coordinates of a barycentre of cells intersection (b),
<br>where n is number of vertices which is either 3 or 4.

Purpose is to find coefficients a1...an so that 
- (a1*p1+...+an*pn)=b and
- (a1+...+an)=1.0

Combining the last two expressions we get an equation in matrix form
a * T = ( b - pn )
where
- a is a vector of coefficients a1...an
- b is a vector of cartesian coordinates of barycentre
- T is a matrix expressed via cartesian coordinates of vertices as
<br>in 2D case <pre>
| x1-x3 x2-x3 |
| y1-y3 y2-y3 |</pre>
in 3D case <pre>
| x1-x4 x2-x4 x3-x4 |
| y1-y4 y2-y4 y3-y4 |
| z1-z4 z2-z4 z3-z4 |</pre>

In 2D case solution is found by inversing T which is trivial: a = T^(-1) * ( b - pn ) 

In 3D case we use Gaussian elimination algorithm. First we use elementary
row operations to transform T into upper triangular form and
then perform back substitution to find coeficients a.

*/