[field] Fix Mesh padding with Field as boundary

phi/field/_embed.py

@@ -3,7 +3,8 @@
 from phi.geom import UniformGrid, Box
 from phi.math import Tensor, spatial, Extrapolation, Shape, stack
 from phi.math.extrapolation import Undefined, ConstantExtrapolation, ZERO
-from phiml.math import unstack
+from phiml import math
+from phiml.math import unstack, rename_dims, instance, dual
 from ._field import Field
 from ._resample import sample
 
@@ -76,7 +77,14 @@ def is_flexible(self) -> bool:
         return False
 
     def sparse_pad_values(self, value: Tensor, connectivity: Tensor, dim: str, **kwargs) -> Tensor:
-        raise NotImplementedError
+        assert 'mesh' in kwargs, f"sparse padding with Field as boundary only supported for meshes"
+        from ..geom import Mesh
+        mesh: Mesh = kwargs['mesh']
+        boundary_slice = mesh.boundary_faces[dim]
+        face_pos = mesh.face_centers[boundary_slice]
+        face_pos = math.stored_values(face_pos)  # does this always preserve the order?
+        sampled = sample(self.field, face_pos)
+        return rename_dims(sampled, instance, dual(value))
 
     def __eq__(self, other):
         if not isinstance(other, FieldEmbedding):

phi/geom/_mesh.py

@@ -141,7 +141,7 @@ def pad_boundary(self, value: Tensor, widths: Dict[str, Dict[str, slice]] = None
         for name, b_slice in widths.items():
             if b_slice[dim].stop - b_slice[dim].start > 0:
                 slices.append(b_slice[dim])
-                values.append(mode.sparse_pad_values(value, connectivity[b_slice], name, **kwargs))
+                values.append(mode.sparse_pad_values(value, connectivity[b_slice], name, mesh=self, **kwargs))
         perm = np.argsort([s.start for s in slices])
         ordered_pieces = [values[i] for i in perm]
         return concat(ordered_pieces, dim, expand_values=True)