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# Copyright (c) 2021-2025 Matthew Scroggs, Jørgen S. Dokken
# FEniCS Project
# SPDX-License-Identifier: MIT
import numpy as np
import pytest
import basix
cells = ["triangle", "quadrilateral", "tetrahedron", "hexahedron", "pyramid", "prism"]
@pytest.mark.parametrize("cell", cells)
def test_volume(cell):
cell_type = getattr(basix.CellType, cell)
volumes = {
"triangle": 1 / 2,
"quadrilateral": 1,
"tetrahedron": 1 / 6,
"hexahedron": 1,
"pyramid": 1 / 3,
"prism": 1 / 2,
}
assert np.isclose(basix.cell.volume(cell_type), volumes[cell])
@pytest.mark.parametrize("cell", cells)
def test_normals(cell):
cell_type = getattr(basix.CellType, cell)
normals = basix.cell.facet_normals(cell_type)
facets = basix.topology(cell_type)[-2]
geometry = basix.geometry(cell_type)
for normal, facet in zip(normals, facets):
assert np.isclose(np.linalg.norm(normal), 1)
for v in facet[1:]:
tangent = geometry[v] - geometry[facet[0]]
assert np.isclose(np.dot(tangent, normal), 0)
@pytest.mark.parametrize("cell", cells)
def test_outward_normals(cell):
cell_type = getattr(basix.CellType, cell)
normals = basix.cell.facet_outward_normals(cell_type)
facets = basix.topology(cell_type)[-2]
geometry = basix.geometry(cell_type)
midpoint = sum(geometry) / len(geometry)
for normal, facet in zip(normals, facets):
assert np.dot(geometry[facet[0]] - midpoint, normal) > 0
@pytest.mark.parametrize("cell", cells)
def test_facet_orientations(cell):
cell_type = getattr(basix.CellType, cell)
normals = basix.cell.facet_normals(cell_type)
outward_normals = basix.cell.facet_outward_normals(cell_type)
orientations = basix.cell.facet_orientations(cell_type)
for n1, n2, orient in zip(normals, outward_normals, orientations):
if orient:
assert np.allclose(n1, -n2)
else:
assert np.allclose(n1, n2)
@pytest.mark.parametrize("cell", cells)
def test_sub_entity_connectivity(cell):
cell_type = getattr(basix.CellType, cell)
connectivity = basix.cell.sub_entity_connectivity(cell_type)
topology = basix.topology(cell_type)
assert len(connectivity) == len(topology)
for dim, entities in enumerate(connectivity):
assert len(entities) == len(topology[dim])
for n, entity in enumerate(entities):
for dim2, connected_entities in enumerate(entity):
for n2 in connected_entities:
if dim > dim2:
for i in topology[dim2][n2]:
assert i in topology[dim][n]
else:
for i in topology[dim][n]:
assert i in topology[dim2][n2]
def test_sub_entity_type():
cell_type = basix.CellType.tetrahedron
for i in range(4):
assert basix.cell.sub_entity_type(cell_type, 0, i) == basix.CellType.point
for i in range(6):
assert basix.cell.sub_entity_type(cell_type, 1, i) == basix.CellType.interval
for i in range(4):
assert basix.cell.sub_entity_type(cell_type, 2, i) == basix.CellType.triangle
assert basix.cell.sub_entity_type(cell_type, 3, 0) == basix.CellType.tetrahedron
def test_facet_jacobians_2D_simplex():
cell = basix.cell.CellType.triangle
facet_jacobian = basix.cell.facet_jacobians(cell)
reference_vertices = np.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]])
mask = np.zeros(3, dtype=np.bool_)
for i in range(3):
mask[:] = True
mask[i] = False
facet = reference_vertices[mask]
reference_facet_jacobian = -facet[0:1, :].T + facet[1:2, :].T
np.testing.assert_allclose(reference_facet_jacobian, facet_jacobian[i])
def test_facet_jacobians_3D_simplex():
cell = basix.cell.CellType.tetrahedron
facet_jacobian = basix.cell.facet_jacobians(cell)
reference_vertices = np.array(
[[0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]
)
mask = np.zeros(4, dtype=np.bool_)
for i in range(4):
mask[:] = True
mask[i] = False
facet = reference_vertices[mask]
reference_facet_jacobian = np.array([-facet[0] + facet[1], -facet[0] + facet[2]]).T
np.testing.assert_allclose(reference_facet_jacobian, facet_jacobian[i])
@pytest.mark.parametrize(
"cell",
[
basix.cell.CellType.hexahedron,
basix.cell.CellType.tetrahedron,
basix.cell.CellType.prism,
basix.cell.CellType.pyramid,
],
)
def test_edge_jacobian_3D_simplex(cell):
edge_jacobian = basix.cell.edge_jacobians(cell)
geom = basix.geometry(cell)
topology = basix.topology(cell)
edges = topology[1]
for i, edge in enumerate(edges):
points = geom[edge]
reference_edge_jacobian = (points[1:2, :] - points[0:1, :]).T
np.testing.assert_allclose(reference_edge_jacobian, edge_jacobian[i])
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