Interpolation on a Triangular/Quad Facet

The coordinates of a triangular facet can be determined from the use of interpolation (shape) functions. Let

These can be rewritten as

and then

Then

On a quadrilateral facet using the interpolation functions gives

these can be rewritten

Using the first of these gives

which can be substituted into the second to give

This can then be solved for & and then the interpolation function used as for the triangular facet.