def _generate_all_path_coords(self, waypoints, raster_indices):
# Snap the line string nodes to the raster grid
snapped_points = [
snap_coords_to_grid(raster_indices, *coords)
for coords in waypoints
]
# Generate pairs of consecutive (x,y) coords
path_pairs = list(map(list, zip(snapped_points, snapped_points[1:])))
headings = []
for i in range(1, len(waypoints)):
prev = waypoints[i - 1]
next = waypoints[i]
x = np.sin(next[0] - prev[0]) * np.cos(next[1])
y = np.cos(prev[1]) * np.sin(next[1]) - np.sin(prev[1]) * np.cos(
next[1]) * np.cos(next[0] - prev[0])
angle = (np.arctan2(x, y) + (2 * np.pi)) % (2 * np.pi)
headings.append(angle)
# Feed these pairs into the Bresenham algo to find the intermediate points
path_grid_points = [
bresenham.make_line(*pair[0], *pair[1]) for pair in path_pairs
]
for idx, segment in enumerate(path_grid_points):
n = len(segment)
point_headings = np.full(n, headings[idx])
path_grid_points[idx] = np.column_stack(
(np.array(segment), point_headings))
# Bring all these points together and remove duplicate coords
# Flip left to right as bresenham spits out in (y,x) order
path_grid_points = np.unique(np.concatenate(path_grid_points, axis=0),
axis=0)
return path_grid_points, headings
def get_path_sum(nx, ny, tx, ty, grid):
line = bresenham.make_line(nx, ny, tx, ty)
line_points = grid[line[:, 0], line[:, 1]]
# If the new line crosses any blocked areas the cost is inf
if -1 in line_points:
return np.inf
else:
return line_points.sum()
def test_bounds(self):
start = [2, 0]
end = [4, 4]
path = make_line(*start, *end)
flat_points = np.ravel(path)
result = (flat_points <= 4).all() and (flat_points >= 0).all()
self.assertTrue(result, "Points not bounded within endpoints")
def test_first_quadrant(self):
start = [0, 1] # x, y
end = [6, 4] # x, y
path = make_line(*start, *end)
expected = np.array([[1, 0], [1, 1], [2, 2], [2, 3], [3, 4], [3, 5],
[4, 6]])
result = (path == expected).all() or (path
== np.flipud(expected)).all()
self.assertTrue(result, 'First Quadrant path incorrect')
def test_high_gradient(self):
start = [0, 6] # x, y
end = [6, 0] # x, y
path = make_line(*start, *end)
expected = np.array([[0, 6], [1, 5], [2, 4], [3, 3], [4, 2], [5, 1],
[6, 0]])
result = (path == expected).all() or (path
== np.flipud(expected)).all()
self.assertTrue(result, 'First Quadrant path incorrect')
def test_fourth_quadrant(self):
start = [0, -1] # x, y
end = [6, -4] # x, y
path = make_line(*start, *end)
expected = np.array([[-1, 0], [-1, 1], [-2, 2], [-2, 3], [-3, 4],
[-3, 5], [-4, 6]])
result = (path == expected).all() or (path
== np.flipud(expected)).all()
self.assertTrue(result, 'Fourth Quadrant path incorrect')
def test_third_quadrant(self):
start = [0, -1] # x, y
end = [-6, -4] # x, y
path = make_line(*start, *end)
expected = np.array([[-1, 0], [-2, -1], [-2, -2], [-3, -3], [-3, -4],
[-4, -5], [-4, -6]])
result = (path == expected).all() or (path
== np.flipud(expected)).all()
self.assertTrue(result, 'Third Quadrant path incorrect')
def h(self, node: Tuple[int, int], goal: Tuple[int, int]):
if node == goal:
return 0
dist = abs((node[1] - goal[1])) + abs((node[0] - goal[0]))
line = bresenham.make_line(node[1], node[0], goal[1], goal[0])
integral_val = self.environment.grid[line[:, 0], line[:, 1]].sum()
if integral_val > 1:
return self.k * np.log10(integral_val) + dist
else:
return dist
def annotate(self,
data: List[gpd.GeoDataFrame],
raster_data: Tuple[Dict[str, np.array], np.array],
resolution=20,
**kwargs) -> Overlay:
import geoviews as gv
import scipy.stats as ss
import joblib as jl
bounds = (raster_data[0]['Longitude'].min(),
raster_data[0]['Latitude'].min(),
raster_data[0]['Longitude'].max(),
raster_data[0]['Latitude'].max())
line_coords = list(self.dataframe.iloc[0].geometry.coords)
# Snap the line string nodes to the raster grid
snapped_points = [
snap_coords_to_grid(raster_data[0], *coords)
for coords in line_coords
]
# Generate pairs of consecutive (x,y) coords
path_pairs = list(map(list, zip(snapped_points, snapped_points[1:])))
headings = []
for i in range(1, len(line_coords)):
prev = line_coords[i - 1]
next = line_coords[i]
x = np.sin(next[0] - prev[0]) * np.cos(next[1])
y = np.cos(prev[1]) * np.sin(next[1]) - np.sin(prev[1]) * np.cos(
next[1]) * np.cos(next[0] - prev[0])
angle = (np.arctan2(x, y) + (2 * np.pi)) % (2 * np.pi)
headings.append(angle)
# Feed these pairs into the Bresenham algo to find the intermediate points
path_grid_points = [
bresenham.make_line(*pair[0], *pair[1]) for pair in path_pairs
]
for idx, segment in enumerate(path_grid_points):
n = len(segment)
point_headings = np.full(n, headings[idx])
path_grid_points[idx] = np.column_stack(
(np.array(segment), point_headings))
# Bring all these points together and remove duplicate coords
# Flip left to right as bresenham spits out in (y,x) order
path_grid_points = np.unique(np.concatenate(path_grid_points, axis=0),
axis=0)
bm = BallisticModel(self.aircraft)
samples = 1000
# Conjure up our distributions for various things
alt = ss.norm(self.alt, 5).rvs(samples)
vel = ss.norm(self.vel, 2.5).rvs(samples)
wind_vels = ss.norm(self.wind_vel, 1).rvs(samples)
wind_dirs = bearing_to_angle(
ss.norm(self.wind_dir, np.deg2rad(5)).rvs(samples))
wind_vel_y = wind_vels * np.sin(wind_dirs)
wind_vel_x = wind_vels * np.cos(wind_dirs)
# Create grid on which to evaluate each point of path with its pdf
raster_shape = raster_data[1].shape
x, y = np.mgrid[0:raster_shape[0], 0:raster_shape[1]]
eval_grid = np.vstack((x.ravel(), y.ravel())).T
def wrap_hdg_dists(alt, vel, hdg, wind_vel_y, wind_vel_x):
(mean, cov), v_i, a_i = bm.transform(
alt, vel,
ss.norm(hdg, np.deg2rad(2)).rvs(samples), wind_vel_y,
wind_vel_x, 0, 0)
return hdg, (mean / resolution, cov / resolution, v_i, a_i)
njobs = 1 if len(headings) < 3 else -1
# Hardcode backend to prevent Qt freaking out
res = jl.Parallel(n_jobs=njobs, backend='threading', verbose=1)(
jl.delayed(wrap_hdg_dists)(alt, vel, hdg, wind_vel_y, wind_vel_x)
for hdg in headings)
dists_for_hdg = dict(res)
def point_distr(c):
dist_params = dists_for_hdg[c[2]]
pdf = np.array(ss.multivariate_normal(
dist_params[0] + np.array([c[0], c[1]]),
dist_params[1]).pdf(eval_grid),
dtype=np.longdouble)
return pdf
sm = StrikeModel(raster_data[1].ravel(), resolution * resolution,
self.aircraft.width)
fm = FatalityModel(0.5, 1e6, 34)
ac_mass = self.aircraft.mass
def wrap_pipeline(path_point_state):
impact_pdf = point_distr(path_point_state)
impact_vel = dists_for_hdg[path_point_state[2]][2]
impact_angle = dists_for_hdg[path_point_state[2]][3]
impact_ke = velocity_to_kinetic_energy(ac_mass, impact_vel)
strike_pdf = sm.transform(impact_pdf, impact_angle=impact_angle)
fatality_pdf = fm.transform(strike_pdf, impact_ke=impact_ke)
return fatality_pdf, fatality_pdf.max(), strike_pdf.max()
res = jl.Parallel(n_jobs=-1, backend='threading',
verbose=1)(jl.delayed(wrap_pipeline)(c)
for c in path_grid_points)
fatality_pdfs = [r[0] for r in res]
# PDFs come out in input order so sorting not required
pathwise_fatality_maxs = np.array([r[1] for r in res],
dtype=np.longdouble)
pathwise_strike_maxs = np.array([r[2] for r in res],
dtype=np.longdouble)
import matplotlib.pyplot as mpl
import tempfile
import subprocess
fig, ax = mpl.subplots(1, 1)
path_dist = self.dataframe.to_crs('EPSG:27700').iloc[0].geometry.length
ax.set_yscale('log')
ax.set_ylim(bottom=1e-18)
x = np.linspace(0, path_dist, len(pathwise_fatality_maxs))
ax.axhline(
y=np.median(pathwise_fatality_maxs),
c='y',
label='Fatality Median') # This seems to be as stable as fsum
ax.plot(x, pathwise_fatality_maxs[::-1], c='r', label='Fatality Risk')
ax.axhline(y=np.median(pathwise_strike_maxs),
c='g',
label='Strike Median') # This seems to be as stable as fsum
ax.plot(x, pathwise_strike_maxs[::-1], c='b', label='Strike Risk')
ax.legend()
ax.set_ylabel('Risk [$h^{-1}$]')
ax.set_xlabel('Path Distance [m]')
ax.set_title('Casualty Risk along path')
tmppath = tempfile.mkstemp()[1] + '.png'
fig.savefig(tmppath)
subprocess.run("explorer " + tmppath)
risk_map = np.sum(fatality_pdfs,
axis=0).reshape(raster_shape) * self.event_prob
risk_raster = gv.Image(risk_map,
vdims=['fatality_risk'],
bounds=bounds).options(
alpha=0.7,
cmap='viridis',
tools=['hover'],
clipping_colors={'min': (0, 0, 0, 0)})
risk_raster = risk_raster.redim.range(fatality_risk=(risk_map.min() +
1e-15,
risk_map.max()))
print('Max probability of fatality: ', risk_map.max())
return Overlay([
gv.Contours(self.dataframe).opts(line_width=4,
line_color='magenta'), risk_raster
])
