Parallel mesh collision detection in python

.gitignore

*.xdmf
*.h5

README.md

Collision detection between two meshes

• Supports parallel (MPI) distributed meshes in DOLFINx

LICENSE

Copyright 2024 Jørgen S. Dokken

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

script.py

from mpi4py import MPI

from pathlib import Path
import numpy as np
from dolfinx import io, mesh, geometry, cpp


def mark_cells(msh, cell_index):
    num_cells = msh.topology.index_map(
        msh.topology.dim).size_local + msh.topology.index_map(
        msh.topology.dim).num_ghosts
    cells = np.arange(0, num_cells, dtype=np.int32)
    values = np.full(cells.shape, 0, dtype=np.int32)
    values[cell_index] = np.full(len(cell_index), 1, dtype=np.int32)
    cell_tag = mesh.meshtags(msh, msh.topology.dim, cells, values)
    return cell_tag


mesh_big = mesh.create_unit_square(
    MPI.COMM_WORLD, 32, 32, ghost_mode=mesh.GhostMode.none)
mesh_big.geometry.x[:, :2] -= 0.51
mesh_big.geometry.x[:, :2] *= 4
num_big_cells = mesh_big.topology.index_map(mesh_big.topology.dim).size_local + \
    mesh_big.topology.index_map(mesh_big.topology.dim).num_ghosts


mesh_small = mesh.create_unit_square(
    MPI.COMM_WORLD, 9, 7, ghost_mode=mesh.GhostMode.none)
mesh_small.geometry.x[:, :2] -= 2.45
num_small_cells = mesh_small.topology.index_map(mesh_small.topology.dim).size_local + \
    mesh_small.topology.index_map(mesh_small.topology.dim).num_ghosts

bb_tree = geometry.bb_tree(
    mesh_big, mesh_big.topology.dim, np.arange(num_big_cells, dtype=np.int32))
big_process = bb_tree.create_global_tree(mesh_big.comm)
bb_small = geometry.bb_tree(
    mesh_small, mesh_small.topology.dim, np.arange(num_small_cells, dtype=np.int32))

process_collisions = geometry.compute_collisions_trees(
    bb_small, big_process)
outgoing_edges = set()
num_outgoing_cells = np.zeros(mesh_big.comm.size, dtype=np.int32)
cell_indices = []
for cell_idx, process_idx in process_collisions:
    num_outgoing_cells[process_idx] += 1
    outgoing_edges = set.union(outgoing_edges, (process_idx,))
outgoing_edges = np.asarray(np.unique(list(outgoing_edges)), dtype=np.int32)
small_to_big_comm = mesh_small.comm.Create_dist_graph(
    list([mesh_small.comm.rank]), [len(np.unique(outgoing_edges))], outgoing_edges, reorder=False)

num_cells = num_small_cells
source, dest, _ = small_to_big_comm.Get_dist_neighbors()

num_vertices_per_cell_small = cpp.mesh.cell_num_vertices(
    mesh_small.topology.cell_types[0])

# Extract all mesh nodes per process
process_offsets = np.zeros(len(dest)+1, dtype=np.int32)
np.cumsum(num_outgoing_cells[dest], out=process_offsets[1:])
sending_cells = np.full(process_offsets[-1], 10, dtype=np.int32)
insert_counter = np.zeros_like(dest, dtype=np.int32)
for cell_idx, process_idx in process_collisions:
    local_idx = np.flatnonzero(dest == process_idx)
    assert len(local_idx) == 1
    idx = local_idx[0]
    sending_cells[process_offsets[idx]+insert_counter[idx]] = cell_idx
    insert_counter[idx] += 1


node_counter = np.zeros(mesh_small.geometry.index_map().size_local +
                        mesh_small.geometry.index_map().num_ghosts+1, dtype=np.int32)
local_pos = np.zeros_like(node_counter, dtype=np.int32)
send_geom = []
send_top = []
send_top_size = np.zeros_like(dest, dtype=np.int32)
send_geom_size = np.zeros_like(dest, dtype=np.int32)

for i in range(len(dest)):
    # Get nodes of all cells sent to a given process
    org_nodes = cpp.mesh.entities_to_geometry(
        mesh_small._cpp_object, mesh_small.topology.dim, sending_cells[process_offsets[i]:process_offsets[i+1]], False).reshape(-1)

    # Get the unique set of nodes sent to this process
    unique_nodes = np.unique(org_nodes)

    # Compute remapping of nodes
    node_counter[:] = 0
    node_counter[unique_nodes] = 1
    np.cumsum(node_counter, out=local_pos)
    local_pos -= 1  # Map to 0 index system
    send_geom.append(
        mesh_small.geometry.x[unique_nodes][:, :mesh_small.geometry.dim])
    send_geom_size[i] = np.size(send_geom[-1])
    send_top.append(local_pos[org_nodes])
    send_top_size[i] = np.size(send_top[-1])

# Compute send and receive offsets for geometry and topology
geom_offset = np.zeros(len(dest)+1, dtype=np.int32)
top_offset = np.zeros(len(dest)+1, dtype=np.int32)
np.cumsum(send_geom_size, out=geom_offset[1:])
np.cumsum(send_top_size, out=top_offset[1:])

if len(send_geom) == 0:
    send_geom = np.array([], dtype=mesh_small.geometry.x.dtype)
else:
    send_geom = np.vstack(send_geom).reshape(-1)
if len(send_top) == 0:
    send_top = np.array([], dtype=np.int32)
else:
    send_top = np.hstack(send_top)
if len(send_geom_size) == 0:
    send_geom_size = np.zeros(1, dtype=np.int32)
if len(send_top_size) == 0:
    send_top_size = np.zeros(1, dtype=np.int32)

recv_geom_size = np.zeros(max(len(source), 1), dtype=np.int32)
small_to_big_comm.Neighbor_alltoall(send_geom_size, recv_geom_size)
recv_geom_size = recv_geom_size[:len(source)]
send_geom_size = send_geom_size[:len(dest)]
recv_geom_offsets = np.zeros(len(recv_geom_size)+1, dtype=np.int32)
np.cumsum(recv_geom_size, out=recv_geom_offsets[1:])


recv_top_size = np.zeros(max(len(source), 1), dtype=np.int32)
small_to_big_comm.Neighbor_alltoall(send_top_size, recv_top_size)
recv_top_size = recv_top_size[:len(source)]
send_top_size = send_top_size[:len(dest)]

recv_top_offsets = np.zeros(len(recv_top_size)+1, dtype=np.int32)
np.cumsum(recv_top_size, out=recv_top_offsets[1:])

numpy_to_mpi = {np.float64: MPI.DOUBLE,
                np.float32: MPI.FLOAT, np.int8: MPI.INT8_T, np.int32: MPI.INT32_T}
# Communicate data
recv_geom = np.zeros(recv_geom_offsets[-1], dtype=mesh_small.geometry.x.dtype)
s_geom_msg = [send_geom, send_geom_size, numpy_to_mpi[send_geom.dtype.type]]
r_geom_msg = [recv_geom, recv_geom_size, numpy_to_mpi[recv_geom.dtype.type]]
small_to_big_comm.Neighbor_alltoallv(s_geom_msg, r_geom_msg)

recv_top = np.zeros(recv_top_offsets[-1], dtype=np.int32)
s_top_msg = [send_top, send_top_size, numpy_to_mpi[send_top.dtype.type]]
r_top_msg = [recv_top, recv_top_size, numpy_to_mpi[recv_top.dtype.type]]
small_to_big_comm.Neighbor_alltoallv(s_top_msg, r_top_msg)

# For each received geometry, create a mesh
local_meshes = []
for i in range(len(source)):
    local_meshes.append(mesh.create_mesh(
        MPI.COMM_SELF,
        recv_top[recv_top_offsets[i]:recv_top_offsets[i+1]
                 ].reshape(-1, num_vertices_per_cell_small),
        recv_geom[recv_geom_offsets[i]:recv_geom_offsets[i+1]
                  ].reshape(-1, mesh_small.geometry.dim),
        mesh_small.ufl_domain()))


def extract_cell_geometry(input_mesh, cell: int):
    mesh_nodes = cpp.mesh.entities_to_geometry(
        input_mesh._cpp_object, input_mesh.topology.dim, np.array([cell], dtype=np.int32), False)[0]

    return input_mesh.geometry.x[mesh_nodes]


# For each local mesh, compute the bounding box, compute colliding cells
tol = 1e-13
big_cells = []
local_cells = []
num_local_cells = np.zeros(max(len(source), 1), dtype=np.int32)
for i in range(len(source)):
    local_cells_i = set()
    o_cell_idx = local_meshes[i].topology.original_cell_index
    local_tree = geometry.bb_tree(
        local_meshes[i], local_meshes[i].topology.dim)
    cell_cell_collisions = geometry.compute_collisions_trees(
        local_tree, bb_tree)
    for local_cell, big_cell in cell_cell_collisions:

        geom_small = extract_cell_geometry(local_meshes[i], local_cell)
        geom_big = extract_cell_geometry(mesh_big, big_cell)
        distance = geometry.compute_distance_gjk(geom_big, geom_small)
        if np.linalg.norm(distance) <= tol:
            big_cells.append(big_cell)
            local_cells_i = local_cells_i.union([o_cell_idx[local_cell]])
    num_local_cells[i] = len(local_cells_i)
    local_cells.append(np.asarray(list(local_cells_i), dtype=np.int32))

# Create reverse communicator
big_to_small_comm = mesh_small.comm.Create_dist_graph_adjacent(
    dest, source, reorder=False
)
# Send incoming cell sizes
recv_cell_sizes = np.zeros(max(len(dest), 1), dtype=np.int32)
big_to_small_comm.Neighbor_alltoall(num_local_cells, recv_cell_sizes)
recv_cell_sizes = recv_cell_sizes[:len(dest)]
num_local_cells = num_local_cells[:len(source)]

recv_cell_offsets = np.zeros(len(recv_cell_sizes)+1, dtype=np.int32)
np.cumsum(recv_cell_sizes, out=recv_cell_offsets[1:])
recv_cells = np.zeros(recv_cell_offsets[-1], np.int32)
if len(source) == 0:
    send_cells = np.array([], dtype=np.int32)
else:
    send_cells = np.hstack(local_cells).astype(np.int32).reshape(-1)
s_cell_msg = [send_cells, num_local_cells, numpy_to_mpi[send_cells.dtype.type]]
r_cell_msg = [recv_cells, recv_cell_sizes, numpy_to_mpi[recv_cells.dtype.type]]
big_to_small_comm.Neighbor_alltoallv(s_cell_msg, r_cell_msg)

small_mesh_colliding_cells = []
for i in range(len(dest)):
    local_cells = sending_cells[process_offsets[i]:process_offsets[i+1]]
    recv_data = recv_cells[recv_cell_offsets[i]:recv_cell_offsets[i+1]]
    small_mesh_colliding_cells.append(local_cells[recv_data])
if len(small_mesh_colliding_cells) == 0:
    small_mesh_colliding_cells = np.array([], dtype=np.int32)
else:
    small_mesh_colliding_cells = np.hstack(small_mesh_colliding_cells)


sorted_unique_small_cells = np.unique(
    small_mesh_colliding_cells).astype(dtype=np.int32)
colliding_small_marker = mark_cells(mesh_small, sorted_unique_small_cells)
colliding_small_marker.name = "colliding cells small"


sorted_unique_big_cells = np.unique(big_cells).astype(dtype=np.int32)
colliding_big_marker = mark_cells(mesh_big, sorted_unique_big_cells)
colliding_big_marker.name = "colliding cells"


def create_partition_tag(domain: mesh.Mesh) -> mesh.MeshTags:
    """
    Create a cell marker with all cells owned by the process tagged with the process rank
    """
    tdim = domain.topology.dim
    num_cells_local = domain.topology.index_map(tdim).size_local
    cells = np.arange(num_cells_local, dtype=np.int32)
    values = np.full(num_cells_local, domain.comm.rank, dtype=np.int32)
    return mesh.meshtags(domain, tdim, cells, values)


outdir = Path("output")
outdir.mkdir(parents=True, exist_ok=True)

# # Output local meshes sent from process s to process with rank r

# r = mesh_big.comm.rank
# for i, s in enumerate(source):
#     with io.XDMFFile(local_meshes[i].comm, outdir/f"mesh_small_{s}_on_{r}.xdmf", "w") as xdmf:
#         xdmf.write_mesh(local_meshes[i])


ct_small = create_partition_tag(mesh_small)
with io.XDMFFile(mesh_small.comm, outdir/"mesh_small.xdmf", "w") as xdmf:
    xdmf.write_mesh(mesh_small)
    xdmf.write_meshtags(ct_small, mesh_small.geometry)
    xdmf.write_meshtags(colliding_small_marker, mesh_small.geometry)

ct_big = create_partition_tag(mesh_big)
with io.XDMFFile(mesh_big.comm, outdir/"mesh_big.xdmf", "w") as xdmf:
    xdmf.write_mesh(mesh_big)
    xdmf.write_meshtags(ct_big, mesh_big.geometry)
    xdmf.write_meshtags(colliding_big_marker, mesh_big.geometry)