def points(field: PointCloud, velocity: Field, dt: float, integrator=euler):
"""
Advects the sample points of a point cloud using a simple Euler step.
Each point moves by an amount equal to the local velocity times `dt`.
Args:
field: point cloud to be advected
velocity: velocity sampled at the same points as the point cloud
dt: Euler step time increment
integrator: ODE integrator for solving the movement.
Returns:
Advected point cloud
"""
new_elements = integrator(field.elements, velocity, dt)
return field.with_elements(new_elements)
def respect_boundaries(particles: PointCloud, domain: Domain, not_accessible: list, offset: float = 0.5) -> PointCloud:
"""
Enforces boundary conditions by correcting possible errors of the advection step and shifting particles out of
obstacles or back into the domain.
Args:
particles: PointCloud holding particle positions as elements
domain: Domain for which any particles outside should get shifted inwards
not_accessible: List of Obstacle or Geometry objects where any particles inside should get shifted outwards
offset: Minimum distance between particles and domain boundary / obstacle surface after particles have been shifted.
Returns:
PointCloud where all particles are inside the domain / outside of obstacles.
"""
new_positions = particles.elements.center
for obj in not_accessible:
if isinstance(obj, Obstacle):
obj = obj.geometry
new_positions = obj.push(new_positions, shift_amount=offset)
new_positions = (~domain.bounds).push(new_positions, shift_amount=offset)
return particles.with_elements(Sphere(new_positions, math.mean(particles.bounds.size) * 0.005))
