def test_lookup_tree(do_plot=False):
from meshmode.mesh.generation import make_curve_mesh, cloverleaf
mesh = make_curve_mesh(cloverleaf, np.linspace(0, 1, 1000), order=3)
from meshmode.mesh.tools import make_element_lookup_tree
tree = make_element_lookup_tree(mesh)
from meshmode.mesh.processing import find_bounding_box
bbox_min, bbox_max = find_bounding_box(mesh)
extent = bbox_max-bbox_min
for i in range(20):
pt = bbox_min + np.random.rand(2) * extent
print(pt)
for igrp, iel in tree.generate_matches(pt):
print(igrp, iel)
if do_plot:
with open("tree.dat", "w") as outf:
tree.visualize(outf)
def test_lookup_tree(do_plot=False):
from meshmode.mesh.generation import make_curve_mesh, cloverleaf
mesh = make_curve_mesh(cloverleaf, np.linspace(0, 1, 1000), order=3)
from meshmode.mesh.tools import make_element_lookup_tree
tree = make_element_lookup_tree(mesh)
from meshmode.mesh.processing import find_bounding_box
bbox_min, bbox_max = find_bounding_box(mesh)
extent = bbox_max - bbox_min
for i in range(20):
pt = bbox_min + np.random.rand(2) * extent
print(pt)
for igrp, iel in tree.generate_matches(pt):
print(igrp, iel)
if do_plot:
with open("tree.dat", "w") as outf:
tree.visualize(outf)
def check_nodal_adj_against_geometry(mesh, tol=1e-12):
def group_and_iel_to_global_iel(igrp, iel):
return mesh.groups[igrp].element_nr_base + iel
logger.debug("nodal adj test: tree build")
from meshmode.mesh.tools import make_element_lookup_tree
tree = make_element_lookup_tree(mesh, eps=tol)
logger.debug("nodal adj test: tree build done")
from meshmode.mesh.processing import find_bounding_box
bbox_min, bbox_max = find_bounding_box(mesh)
nadj = mesh.nodal_adjacency
nvertices_per_element = len(mesh.groups[0].vertex_indices[0])
connected_to_element_geometry = [set() for i in range(mesh.nelements)]
connected_to_element_connectivity = [set() for i in range(mesh.nelements)]
for igrp, grp in enumerate(mesh.groups):
for iel_grp in range(grp.nelements):
iel_g = group_and_iel_to_global_iel(igrp, iel_grp)
nb_starts = nadj.neighbors_starts
for nb_iel_g in nadj.neighbors[nb_starts[iel_g]:nb_starts[iel_g +
1]]:
connected_to_element_connectivity[iel_g].add(nb_iel_g)
for vertex_index in grp.vertex_indices[iel_grp]:
vertex = mesh.vertices[:, vertex_index]
# check which elements touch this vertex
for nearby_igrp, nearby_iel in tree.generate_matches(vertex):
if nearby_igrp == igrp and nearby_iel == iel_grp:
continue
nearby_grp = mesh.groups[nearby_igrp]
nearby_origin_vertex = mesh.vertices[:, nearby_grp.
vertex_indices[
nearby_iel]
[0]] # noqa
transformation = np.empty(
(len(mesh.vertices), nvertices_per_element - 1))
vertex_transformed = vertex - nearby_origin_vertex
for inearby_vertex_index, nearby_vertex_index in enumerate(
nearby_grp.vertex_indices[nearby_iel][1:]):
nearby_vertex = mesh.vertices[:, nearby_vertex_index]
transformation[:, inearby_vertex_index] = \
nearby_vertex - nearby_origin_vertex
bary_coord, residual = \
np.linalg.lstsq(transformation, vertex_transformed)[0:2]
is_in_element_span = (
residual.size == 0
or np.linalg.norm(vertex_transformed) == 0
or (np.linalg.norm(residual) /
np.linalg.norm(vertex_transformed)) <= tol)
is_connected = (is_in_element_span
and np.sum(bary_coord) <= 1 + tol
and (bary_coord >= -tol).all())
el1 = group_and_iel_to_global_iel(nearby_igrp, nearby_iel)
el2 = group_and_iel_to_global_iel(igrp, iel_grp)
if is_connected:
connected_to_element_geometry[el1].add(el2)
connected_to_element_geometry[el2].add(el1)
assert is_symmetric(connected_to_element_connectivity, debug=True)
# The geometric adjacency relation isn't necessary symmetric:
#
# /|
# / |
# / |\
# B \ |/ A
# \ |
# \|
#
# Element A will see element B (its vertices are near B) but not the other
# way around.
assert connected_to_element_geometry == connected_to_element_connectivity
def check_nodal_adj_against_geometry(mesh, tol=1e-12):
def group_and_iel_to_global_iel(igrp, iel):
return mesh.groups[igrp].element_nr_base + iel
logger.debug("nodal adj test: tree build")
from meshmode.mesh.tools import make_element_lookup_tree
tree = make_element_lookup_tree(mesh, eps=tol)
logger.debug("nodal adj test: tree build done")
from meshmode.mesh.processing import find_bounding_box
bbox_min, bbox_max = find_bounding_box(mesh)
nadj = mesh.nodal_adjacency
nvertices_per_element = len(mesh.groups[0].vertex_indices[0])
connected_to_element_geometry = [set() for i in range(mesh.nelements)]
connected_to_element_connectivity = [set() for i in range(mesh.nelements)]
for igrp, grp in enumerate(mesh.groups):
for iel_grp in range(grp.nelements):
iel_g = group_and_iel_to_global_iel(igrp, iel_grp)
nb_starts = nadj.neighbors_starts
for nb_iel_g in nadj.neighbors[nb_starts[iel_g]:nb_starts[iel_g+1]]:
connected_to_element_connectivity[iel_g].add(nb_iel_g)
for vertex_index in grp.vertex_indices[iel_grp]:
vertex = mesh.vertices[:, vertex_index]
# check which elements touch this vertex
for nearby_igrp, nearby_iel in tree.generate_matches(vertex):
if nearby_igrp == igrp and nearby_iel == iel_grp:
continue
nearby_grp = mesh.groups[nearby_igrp]
nearby_origin_vertex = mesh.vertices[
:, nearby_grp.vertex_indices[nearby_iel][0]] # noqa
transformation = np.empty(
(len(mesh.vertices), nvertices_per_element-1))
vertex_transformed = vertex - nearby_origin_vertex
for inearby_vertex_index, nearby_vertex_index in enumerate(
nearby_grp.vertex_indices[nearby_iel][1:]):
nearby_vertex = mesh.vertices[:, nearby_vertex_index]
transformation[:, inearby_vertex_index] = \
nearby_vertex - nearby_origin_vertex
bary_coord, residual = \
np.linalg.lstsq(transformation, vertex_transformed)[0:2]
is_in_element_span = (
residual.size == 0
or np.linalg.norm(vertex_transformed) == 0
or (np.linalg.norm(residual)
/ np.linalg.norm(vertex_transformed)) <= tol)
is_connected = (
is_in_element_span
and np.sum(bary_coord) <= 1+tol
and (bary_coord >= -tol).all())
el1 = group_and_iel_to_global_iel(nearby_igrp, nearby_iel)
el2 = group_and_iel_to_global_iel(igrp, iel_grp)
if is_connected:
connected_to_element_geometry[el1].add(el2)
connected_to_element_geometry[el2].add(el1)
assert is_symmetric(connected_to_element_connectivity, debug=True)
# The geometric adjacency relation isn't necessary symmetric:
#
# /|
# / |
# / |\
# B \ |/ A
# \ |
# \|
#
# Element A will see element B (its vertices are near B) but not the other
# way around.
assert connected_to_element_geometry == connected_to_element_connectivity