"""
Notes
-----

Important attributes of continuous (order > 0) :class:`Field` and
:class:`SurfaceField` instances:

- `vertex_remap` : `econn[:, :n_vertex] = vertex_remap[conn]`
- `vertex_remap_i` : `conn = vertex_remap_i[econn[:, :n_vertex]]`

where `conn` is the mesh vertex connectivity, `econn` is the
region-local field connectivity.
"""
import time
import numpy as nm

from sfepy.base.base import output, assert_
import fea
from sfepy.discrete.fem.utils import prepare_remap
from sfepy.discrete.common.dof_info import expand_nodes_to_dofs
from sfepy.discrete.fem.global_interp import get_ref_coors
from sfepy.discrete.fem.facets import get_facet_dof_permutations
from sfepy.discrete.fem.fields_base import (FEField, VolumeField, SurfaceField,
                                            H1Mixin)
from sfepy.discrete.fem.extmods.bases import evaluate_in_rc

class H1NodalMixin(H1Mixin):

    def _setup_facet_orientations(self):
        order = self.approx_order
        self.node_desc = self.interp.describe_nodes()

        edge_nodes = self.node_desc.edge_nodes
        if edge_nodes is not None:
            n_fp = self.gel.edges.shape[1]
            self.edge_dof_perms = get_facet_dof_permutations(n_fp, self.igs,
                                                             order)

        face_nodes = self.node_desc.face_nodes
        if face_nodes is not None:
            n_fp = self.gel.faces.shape[1]
            self.face_dof_perms = get_facet_dof_permutations(n_fp, self.igs,
                                                             order)

    def _setup_edge_dofs(self):
        """
        Setup edge DOF connectivity.
        """
        if self.node_desc.edge is None:
            return 0, None, None

        return self._setup_facet_dofs(1, self.node_desc.edge,
                                      self.edge_dof_perms,
                                      self.n_vertex_dof)

    def _setup_face_dofs(self):
        """
        Setup face DOF connectivity.
        """
        if self.node_desc.face is None:
            return 0, None, None

        return self._setup_facet_dofs(self.domain.shape.tdim - 1,
                                      self.node_desc.face,
                                      self.face_dof_perms,
                                      self.n_vertex_dof + self.n_edge_dof)

    def _setup_facet_dofs(self, dim, facet_desc, facet_perms, offset):
        """
        Helper function to setup facet DOF connectivity, works for both
        edges and faces.
        """
        facet_desc = nm.array(facet_desc)
        n_dof_per_facet = facet_desc.shape[1]

        cmesh = self.domain.cmesh

        facets = self.region.entities[dim]
        ii = nm.arange(facets.shape[0], dtype=nm.int32)
        all_dofs = offset + expand_nodes_to_dofs(ii, n_dof_per_facet)

        # Prepare global facet id remapping to field-local numbering.
        remap = 
prepare_remap(facets, cmesh.num[dim])