gistfile1.py

from firedrake import *


m = PeriodicUnitIntervalMesh(4)

V = FunctionSpace(m, 'CG', 1)

print m.coordinates.dat.data

u = Function(V)


# Interpolate does this:
to_element = V.fiat_element

to_pts = []
for dual in to_element.dual_basis():
    to_pts.append(dual.pt_dict.keys()[0])

coords = m.coordinates
coords_space = coords.function_space()
coords_element = coords_space.fiat_element
X = coords_element.tabulate(0, to_pts).values()[0]

for cell in range(4):
    for k in range(2):
        print cell, u.cell_node_map().values[cell][k], sum([X.T[k][i] * coords.dat.data[coords.cell_node_map().values[cell]][i] for i in range(2)])
        u.dat.data[u.cell_node_map().values[cell][k]] = sum([X.T[k][i] * coords.dat.data[coords.cell_node_map().values[cell]][i] for i in range(2)])

print u.dat.data