def apply_slippage(terrain, repose_slope, cell_width):
delta = util.simple_gradient(terrain) / cell_width
smoothed = util.gaussian_blur(terrain, sigma=1.5)
should_smooth = np.abs(delta) > repose_slope
result = np.select([np.abs(delta) > repose_slope], [smoothed], terrain)
return result
def main(argv):
parser = argparse.ArgumentParser(
description="Run a terrain erosion simulation.")
group = parser.add_mutually_exclusive_group()
group.add_argument(
"-f",
"--file",
help="Run simulation using an input image file instead of generating a \
new fBm noise. (Only works with a square image.) If not specified then \
noise will be generated.")
group.add_argument(
"-s",
"--seed",
type=int,
help="Noise generator seed. If not specified then a random seed will be \
used. SEED MUST BE AN INTEGER.")
parser.add_argument(
"-o",
"--output",
help="Output simulation file name (without file extension). If not \
specified then the default file name will be used.")
parser.add_argument("--snapshot",
action="store_true",
help="Save a numbered image of every iteration.")
parser.add_argument("--png",
action="store_true",
help="Automatically save a png of the simulation.")
args = parser.parse_args()
my_dir = os.path.dirname(argv[0])
output_dir = os.path.join(my_dir, 'output')
try:
os.mkdir(output_dir)
except:
pass
if args.output:
output_path = os.path.join(output_dir, args.output)
else:
output_path = os.path.join(output_dir, 'simulation')
if args.seed:
input_seed = args.seed
else:
input_seed = None
# Grid dimension constants if using fBm noise
full_width = 200
dim = 512
shape = [dim] * 2
cell_width = full_width / dim
cell_area = cell_width**2
# `terrain` represents the actual terrain height we're interested in
if not args.file:
terrain = util.fbm(shape, -2.0, seed=input_seed)
else:
terrain = util.image_to_array(args.file)
dim = terrain.shape[0]
shape = terrain.shape
cell_width = full_width / dim
cell_area = cell_width**2
# Snapshotting parameters. Only needed for generating the simulation
# timelapse.
if args.snapshot:
snapshot_dir = os.path.join(output_dir, 'sim_snaps')
snapshot_file_template = 'sim-%05d.png'
try:
os.mkdir(snapshot_dir)
except:
pass
# Water-related constants
rain_rate = 0.0008 * cell_area
evaporation_rate = 0.0005
# Slope constants
min_height_delta = 0.05
repose_slope = 0.03
gravity = 30.0
gradient_sigma = 0.5
# Sediment constants
sediment_capacity_constant = 50.0
dissolving_rate = 0.25
deposition_rate = 0.001
# The numer of iterations is proportional to the grid dimension. This is to
# allow changes on one side of the grid to affect the other side.
iterations = int(1.4 * dim)
# `sediment` is the amount of suspended "dirt" in the water. Terrain will be
# transfered to/from sediment depending on a number of different factors.
sediment = np.zeros_like(terrain)
# The amount of water. Responsible for carrying sediment.
water = np.zeros_like(terrain)
# The water velocity.
velocity = np.zeros_like(terrain)
# Optionally save the unmodified starting noise if we're not using file input.
if args.snapshot and args.png and not args.file:
fbm_path = output_path + '_fbm.png'
util.save_as_png(terrain, fbm_path)
for i in range(0, iterations):
print('Iteration: %d / %d' % (i + 1, iterations))
# Set a deterministic seed for our random number generator
rng = np.random.default_rng(i)
# Add precipitation. This is done via simple uniform random distribution,
# although other models use a raindrop model
water += rng.random(shape) * rain_rate
# Use a different RNG seed for the next step
rng = np.random.default_rng(i + 3)
# Compute the normalized gradient of the terrain height to determine where
# water and sediment will be moving.
gradient = np.zeros_like(terrain, dtype='complex')
gradient = util.simple_gradient(terrain)
gradient = np.select([np.abs(gradient) < 1e-10],
[np.exp(2j * np.pi * rng.random(shape))],
gradient)
gradient /= np.abs(gradient)
# Compute the difference between the current height the height offset by
# `gradient`.
neighbor_height = util.sample(terrain, -gradient)
height_delta = terrain - neighbor_height
# The sediment capacity represents how much sediment can be suspended in
# water. If the sediment exceeds the quantity, then it is deposited,
# otherwise terrain is eroded.
sediment_capacity = (
(np.maximum(height_delta, min_height_delta) / cell_width) *
velocity * water * sediment_capacity_constant)
deposited_sediment = np.select(
[
height_delta < 0,
sediment > sediment_capacity,
],
[
np.minimum(height_delta, sediment),
deposition_rate * (sediment - sediment_capacity),
],
# If sediment <= sediment_capacity
dissolving_rate * (sediment - sediment_capacity))
# Don't erode more sediment than the current terrain height.
deposited_sediment = np.maximum(-height_delta, deposited_sediment)
# Update terrain and sediment quantities.
sediment -= deposited_sediment
terrain += deposited_sediment
sediment = util.displace(sediment, gradient)
water = util.displace(water, gradient)
# Smooth out steep slopes.
terrain = apply_slippage(terrain, repose_slope, cell_width)
# Update velocity
velocity = gravity * height_delta / cell_width
# Apply evaporation
water *= 1 - evaporation_rate
# Snapshot, if applicable.
if args.snapshot:
snapshot_path = os.path.join(snapshot_dir,
snapshot_file_template % i)
util.save_as_png(terrain, snapshot_path)
# Normalize terrain values before saving.
result = util.normalize(terrain)
np.save(output_path, result)
# Optionally save out an image as well.
if args.png:
util.save_as_png(result, output_path + '_gray.png')
util.save_as_png(util.hillshaded(result), output_path + '_hill.png')
def erosion(terrain, enable_snapshotting=False, dirname='snapshots'):
# Grid dimension constants
full_width = 200
shape = terrain.shape
dim = shape[1]
cell_width = full_width / dim
cell_area = cell_width ** 2
# Snapshotting parameters. Only needed for generating the simulation
# timelapse.
enable_snapshotting = False
my_dir = os.path.dirname(dirname)
snapshot_dir = os.path.join(my_dir, 'sim_snaps')
snapshot_file_template = 'sim-%05d.png'
if enable_snapshotting:
try:
os.mkdir(snapshot_dir)
except:
pass
# Water-related constants
rain_rate = 0.0008 * cell_area
evaporation_rate = 0.0005
# Slope constants
min_height_delta = 0.05
repose_slope = 0.03
gravity = 30.0
gradient_sigma = 0.5
# Sediment constants
sediment_capacity_constant = 50.0
dissolving_rate = 0.25
deposition_rate = 0.001
# The numer of iterations is proportional to the grid dimension. This is to
# allow changes on one side of the grid to affect the other side.
iterations = int(1.4 * dim)
# `terrain` represents the actual terrain height we're interested in
# terrain = util.fbm(shape, -2.0)
# `sediment` is the amount of suspended "dirt" in the water. Terrain will be
# transfered to/from sediment depending on a number of different factors.
sediment = np.zeros_like(terrain)
# The amount of water. Responsible for carrying sediment.
water = np.zeros_like(terrain)
# The water velocity.
velocity = np.zeros_like(terrain)
for i in range(0, iterations):
print('%d / %d' % (i + 1, iterations))
# Add precipitation. This is done by via simple uniform random distribution,
# although other models use a raindrop model
water += np.random.rand(*shape) * rain_rate
# Compute the normalized gradient of the terrain height to determine where
# water and sediment will be moving.
gradient = np.zeros_like(terrain, dtype='complex')
gradient = util.simple_gradient(terrain)
gradient = np.select([np.abs(gradient) < 1e-10],
[np.exp(2j * np.pi * np.random.rand(*shape))],
gradient)
gradient /= np.abs(gradient)
# Compute the difference between teh current height the height offset by
# `gradient`.
neighbor_height = util.sample(terrain, -gradient)
height_delta = terrain - neighbor_height
# The sediment capacity represents how much sediment can be suspended in
# water. If the sediment exceeds the quantity, then it is deposited,
# otherwise terrain is eroded.
sediment_capacity = (
(np.maximum(height_delta, min_height_delta) / cell_width) * velocity *
water * sediment_capacity_constant)
deposited_sediment = np.select(
[
height_delta < 0,
sediment > sediment_capacity,
], [
np.minimum(height_delta, sediment),
deposition_rate * (sediment - sediment_capacity),
],
# If sediment <= sediment_capacity
dissolving_rate * (sediment - sediment_capacity))
# Don't erode more sediment than the current terrain height.
deposited_sediment = np.maximum(-height_delta, deposited_sediment)
# Update terrain and sediment quantities.
sediment -= deposited_sediment
terrain += deposited_sediment
sediment = util.displace(sediment, gradient)
water = util.displace(water, gradient)
# Smooth out steep slopes.
terrain = apply_slippage(terrain, repose_slope, cell_width)
# Update velocity
velocity = gravity * height_delta / cell_width
# Apply evaporation
water *= 1 - evaporation_rate
# Snapshot, if applicable.
if enable_snapshotting:
output_path = os.path.join(snapshot_dir, snapshot_file_template % i)
util.save_as_png(terrain, output_path)
return terrain