Class E_face

This is a table indexed by some points in the 2-simplex $\Delta_2$. The entries are instances of the class E_sample_point. Typically we will fix a triangle quadrature rule Q, with points $t_i$ say. The samples table will have indices $t_i$, and the corresponding entry will represent a point $u_i\in EX^*$ with barycentric coordinates $t_i$ with respect to this face. This is set up by the create_samples method.

This contains the same E_sample_point objects as the samples table, but organised as a list. This is set up by the create_samples method.

The area of this face, with respect to the metric on $EX^*$ inherited from the standard metric on $S^3$. This is calculated by the create_samples method.

The integral of the Gaussian curvature function over this face. This is calculated by the create_samples method.

obsolete

This method sets up the fields samples, samples_list, total_area and total_curvature, as described above.

This checks the correctness of the sample points. It returns an offset error (which measures the failure of the points to lie exactly on $EX^*$) and a barycentric error (which measures the failure of the barycentric coordinates to be equal to the indices in the samples table).