def test_surface():
"""test whether the surface is calculated correctly"""
for dim in [1, 2, 3]:
radius = 1 + random.random()
eps = 1e-10
vol1 = spherical.volume_from_radius(radius + eps, dim=dim)
vol0 = spherical.volume_from_radius(radius, dim=dim)
surface_approx = (vol1 - vol0) / eps
surface = spherical.surface_from_radius(radius, dim=dim)
assert surface == pytest.approx(surface_approx, rel=1e-3)
r2s = spherical.make_surface_from_radius_compiled(dim)
assert surface == pytest.approx(r2s(radius))
if dim == 1:
with pytest.raises(RuntimeError):
spherical.radius_from_surface(surface, dim=dim)
else:
assert spherical.radius_from_surface(
surface, dim=dim) == pytest.approx(radius)
def get_triangulation(self, resolution: float = 1) -> Dict[str, Any]:
"""obtain a triangulated shape of the droplet surface
Args:
resolution (float):
The length of a typical triangulation element. This affects the
resolution of the triangulation.
Returns:
dict: A dictionary containing information about the triangulation. The exact
details depend on the dimension of the problem.
"""
if self.dim == 2:
num = max(3, int(np.ceil(self.surface_area / resolution)))
angles = np.linspace(0, 2 * np.pi, num + 1, endpoint=True)
vertices = self.interface_position(angles)
lines = np.c_[np.arange(num), np.arange(1, num + 1) % num]
return {"vertices": vertices, "lines": lines}
elif self.dim == 3:
# estimate the number of triangles covering the surface
try:
surface_area = self.surface_area
except (NotImplementedError, AttributeError):
# estimate surface area from 3d spherical droplet
surface_area = spherical.surface_from_radius(self.radius,
dim=3)
num_est = (4 * surface_area) / (np.sqrt(3) * resolution**2)
tri = triangulated_spheres.get_triangulation(num_est)
φ, θ = tri["angles"][:, 0], tri["angles"][:, 1]
return {
"vertices": self.interface_position(θ, φ),
"triangles": tri["cells"],
}
else:
raise NotImplementedError(
f"Triangulation not implemented for {self.dim}d")
def surface_area(self) -> float:
"""float: surface area of the droplet"""
return spherical.surface_from_radius(self.radius, self.dim)