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# Copyright (C) 2020 Jørgen S. Dokken and Chris N. Richardson
#
# This file is part of DOLFINx (https://www.fenicsproject.org)
#
# SPDX-License-Identifier: LGPL-3.0-or-later
from mpi4py import MPI
import numpy as np
import pytest
from scipy.spatial.transform import Rotation
import ufl
from basix.ufl import element
from dolfinx import geometry
from dolfinx.geometry import compute_distance_gjk
from dolfinx.mesh import create_mesh
def distance_point_to_line_3D(P1, P2, point):
"""Distance from point to line"""
return np.linalg.norm(np.cross(P2 - P1, P1 - point)) / np.linalg.norm(P2 - P1)
def distance_point_to_plane_3D(P1, P2, P3, point):
"""Distance from point to plane"""
return np.abs(
np.dot(np.cross(P2 - P1, P3 - P1) / np.linalg.norm(np.cross(P2 - P1, P3 - P1)), point - P2)
)
@pytest.mark.parametrize("delta", [0.1, 1e-12, 0, -2])
@pytest.mark.parametrize("dtype", [np.float64, np.float32])
def test_line_point_distance(delta, dtype):
line = np.array([[0.1, 0.2, 0.3], [0.5, 0.8, 0.7]], dtype=dtype)
point_on_line = line[0] + 0.27 * (line[1] - line[0])
normal = np.cross(line[0], line[1])
point = point_on_line + delta * normal
d = compute_distance_gjk(line, point)
distance = np.linalg.norm(d)
actual_distance = distance_point_to_line_3D(line[0], line[1], point)
assert np.isclose(distance, actual_distance, atol=1e-8)
@pytest.mark.parametrize("delta", [0.1, 1e-12, 0])
@pytest.mark.parametrize("dtype", [np.float32, np.float64])
def test_line_line_distance(delta, dtype):
line = np.array([[-0.5, -0.7, -0.3], [1, 2, 3]], dtype=dtype)
point_on_line = line[0] + 0.38 * (line[1] - line[0])
normal = np.cross(line[0], line[1])
point = point_on_line + delta * normal
line_2 = np.array([point, [2, 5, 6]], dtype=dtype)
distance = np.linalg.norm(compute_distance_gjk(line, line_2))
actual_distance = distance_point_to_line_3D(line[0], line[1], line_2[0])
assert np.isclose(distance, actual_distance, atol=1e-7)
@pytest.mark.parametrize("delta", [0.1 ** (3 * i) for i in range(6)])
@pytest.mark.parametrize("dtype", [np.float64])
def test_tri_distance(delta, dtype):
tri_1 = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0]], dtype=dtype)
tri_2 = np.array([[1, delta, 0], [3, 1.2, 0], [1, 1, 0]], dtype=dtype)
P1 = tri_1[2]
P2 = tri_1[1]
point = tri_2[0]
actual_distance = distance_point_to_line_3D(P1, P2, point)
distance = np.linalg.norm(compute_distance_gjk(tri_1, tri_2))
assert np.isclose(distance, actual_distance, atol=1e-6)
@pytest.mark.parametrize("delta", [0.1 * 0.1 ** (3 * i) for i in range(6)])
@pytest.mark.parametrize("dtype", [np.float32, np.float64])
def test_quad_distance2d(delta, dtype):
quad_1 = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0]], dtype=dtype)
quad_2 = np.array([[0, 1 + delta, 0], [2, 2, 0], [2, 4, 0], [4, 4, 0]], dtype=dtype)
P1 = quad_1[2]
P2 = quad_1[3]
point = quad_2[0]
actual_distance = distance_point_to_line_3D(P1, P2, point)
distance = np.linalg.norm(compute_distance_gjk(quad_1, quad_2))
assert np.isclose(distance, actual_distance, atol=1e-8)
@pytest.mark.parametrize("delta", [1 * 0.5 ** (3 * i) for i in range(7)])
def test_tetra_distance_3d(delta):
tetra_1 = np.array([[0, 0, 0.2], [1, 0, 0.1], [0, 1, 0.3], [0, 0, 1]], dtype=np.float64)
tetra_2 = np.array([[0, 0, -3], [1, 0, -3], [0, 1, -3], [0.5, 0.3, -delta]], dtype=np.float64)
actual_distance = distance_point_to_plane_3D(tetra_1[0], tetra_1[1], tetra_1[2], tetra_2[3])
distance = np.linalg.norm(compute_distance_gjk(tetra_1, tetra_2))
assert np.isclose(distance, actual_distance, atol=1e-15)
@pytest.mark.parametrize("delta", [(-1) ** i * np.sqrt(2) * 0.1 ** (3 * i) for i in range(6)])
def test_tetra_collision_3d(delta):
tetra_1 = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1]], dtype=np.float64)
tetra_2 = np.array([[0, 0, -3], [1, 0, -3], [0, 1, -3], [0.5, 0.3, -delta]], dtype=np.float64)
actual_distance = distance_point_to_plane_3D(tetra_1[0], tetra_1[1], tetra_1[2], tetra_2[3])
distance = np.linalg.norm(compute_distance_gjk(tetra_1, tetra_2))
if delta < 0:
assert np.isclose(distance, 0, atol=1e-15)
else:
assert np.isclose(distance, actual_distance, atol=1e-15)
@pytest.mark.parametrize("delta", [0, -0.1, -0.49, -0.51])
def test_hex_collision_3d(delta):
hex_1 = np.array(
[[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], [1, 0, 1], [0, 1, 1], [1, 1, 1]],
dtype=np.float64,
)
P0 = np.array([1.5 + delta, 1.5 + delta, 0.5], dtype=np.float64)
P1 = np.array([2, 2, 1], dtype=np.float64)
P2 = np.array([2, 1.25, 0.25], dtype=np.float64)
P3 = P1 + P2 - P0
quad_1 = np.array([P0, P1, P2, P3], dtype=np.float64)
n = np.cross(quad_1[1] - quad_1[0], quad_1[2] - quad_1[0]) / np.linalg.norm(
np.cross(quad_1[1] - quad_1[0], quad_1[2] - quad_1[0])
)
quad_2 = quad_1 + n
hex_2 = np.zeros((8, 3), dtype=np.float64)
hex_2[:4, :] = quad_1
hex_2[4:, :] = quad_2
actual_distance = np.linalg.norm(np.array([1, 1, P0[2]], dtype=np.float64) - hex_2[0])
distance = np.linalg.norm(compute_distance_gjk(hex_1, hex_2))
if P0[0] < 1:
assert np.isclose(distance, 0, atol=1e-15)
else:
assert np.isclose(distance, actual_distance, atol=1e-15)
@pytest.mark.parametrize("delta", [1e8, 1.0, 1e-6, 1e-12])
@pytest.mark.parametrize("scale", [1000.0, 1.0, 1e-4])
@pytest.mark.parametrize("dtype", [np.float64])
def test_cube_distance(delta, scale, dtype):
cubes = [
scale
* np.array(
[
[-1, -1, -1],
[1, -1, -1],
[-1, 1, -1],
[1, 1, -1],
[-1, -1, 1],
[1, -1, 1],
[-1, 1, 1],
[1, 1, 1],
],
dtype=dtype,
)
]
# Rotate cube 45 degrees around z, so that an edge faces along
# x-axis (vertical)
r = Rotation.from_euler("z", 45, degrees=True)
cubes.append(r.apply(cubes[0]))
# Rotate cube around y, so that a corner faces along the x-axis
r = Rotation.from_euler("y", np.arctan2(1.0, np.sqrt(2)))
cubes.append(r.apply(cubes[1]))
# Rotate cube 45 degrees around y, so that an edge faces along
# x-axis (horizontal)
r = Rotation.from_euler("y", 45, degrees=True)
cubes.append(r.apply(cubes[0]))
# Rotate scene through an arbitrary angle
r = Rotation.from_euler("xyz", [22, 13, -47], degrees=True)
for c0 in range(4):
for c1 in range(4):
dx = cubes[c0][:, 0].max() - cubes[c1][:, 0].min()
cube0 = cubes[c0]
# Separate cubes along x-axis by distance delta
cube1 = cubes[c1] + np.array([dx + delta, 0, 0])
c0rot = r.apply(cube0)
c1rot = r.apply(cube1)
assert c0rot.dtype == dtype
assert c1rot.dtype == dtype
d = compute_distance_gjk(c0rot, c1rot)
assert d.dtype == dtype
distance = np.linalg.norm(d)
assert np.isclose(distance, delta)
@pytest.mark.skip_in_parallel
@pytest.mark.parametrize("dtype", [np.float32, np.float64])
def test_collision_2nd_order_triangle(dtype):
points = np.array(
[[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [0.65, 0.65], [0.0, 0.5], [0.5, 0.0]], dtype=dtype
)
cells = np.array([[0, 1, 2, 3, 4, 5]])
domain = ufl.Mesh(element("Lagrange", "triangle", 2, shape=(2,), dtype=dtype))
mesh = create_mesh(MPI.COMM_WORLD, cells, points, domain)
# Sample points along an interior line of the domain. The last point
# is outside the simplex made by the vertices.
sample_points = np.array([[0.1, 0.3, 0.0], [0.2, 0.5, 0.0], [0.6, 0.6, 0.0]])
# Create boundingboxtree
tree = geometry.bb_tree(mesh, mesh.geometry.dim)
cell_candidates = geometry.compute_collisions_points(tree, sample_points)
colliding_cells = geometry.compute_colliding_cells(mesh, cell_candidates, sample_points)
# Check for collision
for i in range(colliding_cells.num_nodes):
assert len(colliding_cells.links(i)) == 1
# Check if there is a point on the linear approximation of the
# curved facet
def line_through_points(p0, p1):
return lambda x: (p1[1] - p0[1]) / (p1[0] - p0[0]) * (x - p0[0]) + p0[1]
line_func = line_through_points(points[2], points[3])
point = np.array([0.2, line_func(0.2), 0])
# Point inside 2nd order geometry, outside linear approximation
# Useful for debugging on a later stage
# point = np.array([0.25, 0.89320760, 0])
distance = geometry.squared_distance(mesh, mesh.topology.dim - 1, np.array([2]), point)
assert np.isclose(distance, 0)
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