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import numpy as np
import pytest
import meshzoo
from .helpers import is_near_equal
def _compute_cells_normals_dir(points, cells):
pc = points[cells]
midpoints = np.sum(pc, axis=1) / 3.0
nrm = np.sqrt(np.einsum("ij,ij->i", midpoints, midpoints))
normals = (midpoints.T / nrm).T
cross = np.cross(
pc[:, 1, :] - pc[:, 0, :],
pc[:, 2, :] - pc[:, 0, :],
)
return np.einsum("ij,ij->i", normals, cross)
def test_uv_sphere(num_points_per_circle=20, num_circles=10):
points, cells = meshzoo.uv_sphere(num_points_per_circle, num_circles)
assert len(points) == 162
assert is_near_equal(np.sum(points, axis=0), [0.0, 0.0, 0.0])
assert len(cells) == 320
assert (_compute_cells_normals_dir(points, cells) > 0.0).all()
assert np.all(np.abs(np.einsum("ij,ij->i", points, points) - 1.0) < 1.0e-10)
def test_geo_sphere(num_points_per_circle=20, num_circles=10):
points, tri, quad = meshzoo.geo_sphere(num_points_per_circle, num_circles)
# import meshio
# meshio.write_points_cells("geo-sphere.vtk", points, {"triangle": tri, "quad": quad})
assert len(points) == 162
assert is_near_equal(np.sum(points, axis=0), [0.0, 0.0, 0.0])
assert len(tri) == 40
assert len(quad) == 140
# assert (_compute_cells_normals_dir(points, cells) > 0.0).all()
assert np.all(np.abs(np.einsum("ij,ij->i", points, points) - 1.0) < 1.0e-10)
def test_tetra_sphere(n=16):
points, cells = meshzoo.tetra_sphere(n)
# import meshio
# meshio.write_points_cells("out.vtk", points, {"triangle": cells})
assert len(points) == 514
assert is_near_equal(np.sum(points, axis=0), [0.0, 0.0, 0.0])
assert len(cells) == 1024
assert (_compute_cells_normals_dir(points, cells) > 0.0).all()
assert np.all(np.abs(np.einsum("ij,ij->i", points, points) - 1.0) < 1.0e-10)
def test_octa_sphere(n=16):
points, cells = meshzoo.octa_sphere(n)
assert len(points) == 1026
assert is_near_equal(np.sum(points, axis=0), [0.0, 0.0, 0.0])
assert len(cells) == 2048
assert (_compute_cells_normals_dir(points, cells) > 0.0).all()
assert np.all(np.abs(np.einsum("ij,ij->i", points, points) - 1.0) < 1.0e-10)
@pytest.mark.parametrize("flat_top", [True, False])
def test_icosa_sphere(flat_top, n=16):
points, cells = meshzoo.icosa_sphere(n, flat_top)
# import meshio
# meshio.write_points_cells("out.vtk", points, {"triangle": cells})
assert len(points) == 2562
assert is_near_equal(np.sum(points, axis=0), [0.0, 0.0, 0.0])
assert len(cells) == 5120
assert (_compute_cells_normals_dir(points, cells) > 0.0).all()
assert np.all(np.abs(np.einsum("ij,ij->i", points, points) - 1.0) < 1.0e-10)
if __name__ == "__main__":
test_geo_sphere()
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