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Added support for global meshes (stereographic projection) #68

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87 changes: 76 additions & 11 deletions README.md
Original file line number Diff line number Diff line change
Expand Up @@ -275,12 +275,12 @@ extent = om.Region(extent=(-75.00, -70.001, 40.0001, 41.9000), crs=EPSG)
min_edge_length = 0.01 # minimum mesh size in domain in projection
shoreline = om.Shoreline(fname, extent.bbox, min_edge_length)
edge_length = om.distance_sizing_function(shoreline, rate=0.15)
ax = edge_length.plot(
fig, ax, pc = edge_length.plot(
xlabel="longitude (WGS84 degrees)",
ylabel="latitude (WGS84 degrees)",
title="Distance sizing function",
cbarlabel="mesh size (degrees)",
hold=True,
holding=True,
)
shoreline.plot(ax=ax)
```
Expand All @@ -303,12 +303,12 @@ sdf = om.signed_distance_function(shoreline)
edge_length = om.feature_sizing_function(
shoreline, sdf, max_edge_length=0.05, plot=True
)
ax = edge_length.plot(
fig, ax, pc = edge_length.plot(
xlabel="longitude (WGS84 degrees)",
ylabel="latitude (WGS84 degrees)",
title="Feature sizing function",
cbarlabel="mesh size (degrees)",
hold=True,
holding=True,
xlim=[-74.3, -73.8],
ylim=[40.3, 40.8],
)
Expand All @@ -332,12 +332,12 @@ shoreline = om.Shoreline(fname, extent.bbox, min_edge_length)
sdf = om.signed_distance_function(shoreline)
edge_length = om.feature_sizing_function(shoreline, sdf, max_edge_length=0.05)
edge_length = om.enforce_mesh_gradation(edge_length, gradation=0.15)
ax = edge_length.plot(
fig, ax, pc = edge_length.plot(
xlabel="longitude (WGS84 degrees)",
ylabel="latitude (WGS84 degrees)",
title="Feature sizing function with gradation bound",
cbarlabel="mesh size (degrees)",
hold=True,
holding=True,
xlim=[-74.3, -73.8],
ylim=[40.3, 40.8],
)
Expand All @@ -358,7 +358,8 @@ fname = "gshhg-shp-2.3.7/GSHHS_shp/f/GSHHS_f_L1.shp"

min_edge_length = 0.01

dem = om.DEM(fdem, crs=4326)
extent = om.Region(extent=(-74.3, -73.8, 40.3,40.8), crs=4326)
dem = om.DEM(fdem, bbox=extent,crs=4326)
shoreline = om.Shoreline(fname, dem.bbox, min_edge_length)
sdf = om.signed_distance_function(shoreline)
edge_length1 = om.feature_sizing_function(shoreline, sdf, max_edge_length=0.05)
Expand All @@ -368,12 +369,12 @@ edge_length2 = om.wavelength_sizing_function(
# Compute the minimum of the sizing functions
edge_length = om.compute_minimum([edge_length1, edge_length2])
edge_length = om.enforce_mesh_gradation(edge_length, gradation=0.15)
ax = edge_length.plot(
fig, ax, pc = edge_length.plot(
xlabel="longitude (WGS84 degrees)",
ylabel="latitude (WGS84 degrees)",
title="Feature sizing function + wavelength + gradation bound",
cbarlabel="mesh size (degrees)",
hold=True,
holding=True,
xlim=[-74.3, -73.8],
ylim=[40.3, 40.8],
)
Expand All @@ -385,6 +386,7 @@ shoreline.plot(ax=ax)

The distance, feature size, and/or wavelength mesh size functions can lead to coarse mesh resolution in deeper waters that under-resolve and smooth over the sharp topographic gradients that characterize the continental shelf break. These slope features can be important for coastal ocean models in order to capture dissipative effects driven by the internal tides, transmissional reflection at the shelf break that controls the astronomical tides, and trapped shelf waves. The bathymetry field contains often excessive details that are not relevant for most flows, thus the bathymetry can be smoothed by a variety of filters (e.g., lowpass, bandpass, and highpass filters) before calculating the mesh sizes.

<!--pytest-codeblocks:skip-->
```python
import oceanmesh as om

Expand All @@ -394,7 +396,7 @@ fname = "gshhg-shp-2.3.7/GSHHS_shp/f/GSHHS_f_L1.shp"
EPSG = 4326 # EPSG:4326 or WGS84
bbox = (-74.4, -73.4, 40.2, 41.2)
extent = om.Region(extent=bbox, crs=EPSG)
dem = om.DEM(fdem, crs=4326)
dem = om.DEM(fdem, crs=EPSG)

min_edge_length = 0.0025 # minimum mesh size in domain in projection
max_edge_length = 0.10 # maximum mesh size in domain in projection
Expand All @@ -414,7 +416,7 @@ edge_length2 = om.bathymetric_gradient_sizing_function(
min_edge_length=min_edge_length,
max_edge_length=max_edge_length,
crs=EPSG,
)
) # will be reactivated
edge_length3 = om.compute_minimum([edge_length1, edge_length2])
edge_length3 = om.enforce_mesh_gradation(edge_length3, gradation=0.15)
```
Expand Down Expand Up @@ -591,6 +593,69 @@ plt.show()
```
![Multiscale](https://user-images.githubusercontent.com/18619644/136119785-8746552d-4ff6-44c3-9aa1-3e4981ba3518.png)

Global mesh generation
----------------------
Using oceanmesh is now possible for global meshes.
The process is done in two steps:
* first the definition of the sizing functions in WGS84 coordinates,
* then the mesh generation is done in the stereographic projection

```python
import os
import numpy as np
import oceanmesh as om
from oceanmesh.region import to_lat_lon
import matplotlib.pyplot as plt
# utilities functions for plotting
def crosses_dateline(lon1, lon2):
return abs(lon1 - lon2) > 180

def filter_triangles(points, cells):
filtered_cells = []
for cell in cells:
p1, p2, p3 = points[cell[0]], points[cell[1]], points[cell[2]]
if not (crosses_dateline(p1[0], p2[0]) or crosses_dateline(p2[0], p3[0]) or crosses_dateline(p3[0], p1[0])):
filtered_cells.append(cell)
return filtered_cells

# Note: global_stereo.shp has been generated using global_tag() function in pyposeidon
# https://github.com/ec-jrc/pyPoseidon/blob/9cfd3bbf5598c810004def83b1f43dc5149addd0/pyposeidon/boundary.py#L452
fname = "tests/global/global_latlon.shp"
fname2 = "tests/global/global_stereo.shp"

EPSG = 4326 # EPSG:4326 or WGS84
bbox = (-180.00, 180.00, -89.00, 90.00)
extent = om.Region(extent=bbox, crs=4326)

min_edge_length = 0.5 # minimum mesh size in domain in meters
max_edge_length = 2 # maximum mesh size in domain in meters
shoreline = om.Shoreline(fname, extent.bbox, min_edge_length)
sdf = om.signed_distance_function(shoreline)
edge_length = om.distance_sizing_function(shoreline, rate=0.11)

# once the size functions have been defined, wed need to mesh inside domain in
# stereographic projections. This is way we use another coastline which is
# already translated in a sterographic projection
shoreline_stereo = om.Shoreline(fname2, extent.bbox, min_edge_length, stereo=True)
domain = om.signed_distance_function(shoreline_stereo)

points, cells = om.generate_mesh(domain, edge_length, stereo=True, max_iter=100)

# remove degenerate mesh faces and other common problems in the mesh
points, cells = om.make_mesh_boundaries_traversable(points, cells)
points, cells = om.delete_faces_connected_to_one_face(points, cells)

# apply a Laplacian smoother
points, cells = om.laplacian2(points, cells, max_iter=100)
lon, lat = to_lat_lon(points[:, 0], points[:, 1])
trin = filter_triangles(np.array([lon,lat]).T, cells)

fig, ax, pc = edge_length.plot(holding = True, plot_colorbar=True, cbarlabel = "Resolution in °", cmap='magma')
ax.triplot(lon, lat, trin, color="w", linewidth=0.25)
plt.tight_layout()
plt.show()
```
![Global](https://github.com/tomsail/oceanmesh/assets/18373442/a9c45416-78d5-4f3b-a0a3-1afd061d8dbd)

See the tests inside the `testing/` folder for more inspiration. Work is ongoing on this package.

Expand Down
13 changes: 12 additions & 1 deletion oceanmesh/__init__.py
Original file line number Diff line number Diff line change
Expand Up @@ -38,7 +38,14 @@
get_polygon_coordinates,
)
from oceanmesh.grid import Grid, compute_minimum
from oceanmesh.region import Region, warp_coordinates
from oceanmesh.region import (
Region,
stereo_to_3d,
to_3d,
to_lat_lon,
to_stereo,
warp_coordinates,
)
from oceanmesh.signed_distance_function import (
Difference,
Domain,
Expand All @@ -63,6 +70,10 @@
__all__ = [
"create_bbox",
"Region",
"stereo_to_3d",
"to_lat_lon",
"to_3d",
"to_stereo",
"compute_minimum",
"create_circle_coords",
"bathymetric_gradient_sizing_function",
Expand Down
2 changes: 1 addition & 1 deletion oceanmesh/boundary.py
Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
import matplotlib.pyplot as plt
import numpy as np

from .edges import get_winded_boundary_edges
import matplotlib.pyplot as plt

__all__ = ["identify_ocean_boundary_sections"]

Expand Down
2 changes: 1 addition & 1 deletion oceanmesh/clean.py
Original file line number Diff line number Diff line change
Expand Up @@ -256,7 +256,7 @@ def delete_exterior_faces(vertices, faces, min_disconnected_area):
# Delete where nflag == 1 from tmp t1 mesh
t1 = np.delete(t1, nflag == 1, axis=0)
logger.info(
f"ACCEPTED: Deleting {int(np.sum(nflag==0))} faces outside the main mesh"
f"ACCEPTED: Deleting {int(np.sum(nflag == 0))} faces outside the main mesh"
)

# Calculate the remaining area
Expand Down
61 changes: 52 additions & 9 deletions oceanmesh/edgefx.py
Original file line number Diff line number Diff line change
Expand Up @@ -7,15 +7,16 @@
import numpy as np
import scipy.spatial
import skfmm
from _HamiltonJacobi import gradient_limit
from inpoly import inpoly2
from shapely.geometry import LineString
from skimage.morphology import medial_axis

from _HamiltonJacobi import gradient_limit
from oceanmesh.filterfx import filt2

from . import edges
from .grid import Grid
from .region import to_lat_lon, to_stereo

logger = logging.getLogger(__name__)

Expand Down Expand Up @@ -87,7 +88,7 @@ def enforce_mesh_size_bounds_elevation(grid, dem, bounds):
return grid


def enforce_mesh_gradation(grid, gradation=0.15, crs="EPSG:4326"):
def enforce_mesh_gradation(grid, gradation=0.15, crs="EPSG:4326", stereo=False):
"""Enforce a mesh size gradation bound `gradation` on a :class:`grid`

Parameters
Expand Down Expand Up @@ -122,6 +123,46 @@ def enforce_mesh_gradation(grid, gradation=0.15, crs="EPSG:4326"):
cell_size = cell_size.flatten("F")
tmp = gradient_limit([*sz], elen, gradation, 10000, cell_size)
tmp = np.reshape(tmp, (sz[0], sz[1]), "F")
if stereo:
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logger.info("Global mesh: fixing gradient on the north pole...")
# max distortion at the pole: 2 / 180 * PI / (1 - cos(lat))**2
dx_stereo = grid.dx * 1 / 180 * np.pi / 2
# in stereo projection, all north hemisphere is contained in the unit sphere
# we want to fix the gradient close to the north pole,
# so we extract all the coordinates between -1 and 1 in stereographic projection

us, vs = np.meshgrid(
np.arange(-1, 1, dx_stereo), np.arange(-1, 1, dx_stereo), indexing="ij"
)
ulon, vlat = to_lat_lon(us.ravel(), vs.ravel())
utmp = grid.eval((ulon, vlat))
utmp = np.reshape(utmp, us.shape)
szs = utmp.shape
szs = (szs[0], szs[1], 1)
# we choose an excessively large number for the gradiation = 10
# this is merely to fix the north pole gradient
vtmp = gradient_limit([*szs], dx_stereo, 10, 10000, utmp.flatten("F"))
vtmp = np.reshape(vtmp, (szs[0], szs[1]), "F")
# construct stereo interpolating function
grid_stereo = Grid(
bbox=(-1, 1, -1, 1),
dx=dx_stereo,
values=vtmp,
hmin=grid.hmin,
extrapolate=grid.extrapolate,
crs=crs,
)
grid_stereo.build_interpolant()
# reinject back into the original grid and redo the gradient computation
xg, yg = grid.create_grid()
tmp[yg > 0] = grid_stereo.eval(to_stereo(xg[yg > 0], yg[yg > 0]))
logger.info(
"Global mesh: reinject back stereographic gradient and recomputing gradient..."
)
cell_size = tmp.flatten("F")
tmp = gradient_limit([*sz], elen, gradation, 10000, cell_size)
tmp = np.reshape(tmp, (sz[0], sz[1]), "F")

grid_limited = Grid(
bbox=grid.bbox,
dx=grid.dx,
Expand Down Expand Up @@ -453,7 +494,7 @@ def bathymetric_gradient_sizing_function(
nx, ny = dem.nx, dem.ny
coords = (xg, yg)

if crs == "EPSG:4326":
if crs == "EPSG:4326" or crs == 4326:
mean_latitude = np.mean(dem.bbox[2:])
meters_per_degree = (
111132.92
Expand All @@ -463,7 +504,6 @@ def bathymetric_gradient_sizing_function(
)
dy *= meters_per_degree
dx *= meters_per_degree

grid_details = (nx, ny, dx, dy)

if type_of_filter == "barotropic" and filter_quotient > 0:
Expand Down Expand Up @@ -500,7 +540,7 @@ def bathymetric_gradient_sizing_function(
grid.values = (2 * np.pi / slope_parameter) * np.abs(dp) / (bs + eps)

# Convert back to degrees from meters (if geographic)
if crs == "EPSG:4326":
if crs == "EPSG:4326" or crs == 4326:
grid.values /= meters_per_degree

if max_edge_length is not None:
Expand Down Expand Up @@ -818,23 +858,26 @@ def wavelength_sizing_function(
lon, lat = dem.create_grid()
tmpz = dem.eval((lon, lat))

if crs == "EPSG:4326":
dx, dy = dem.dx, dem.dy # for gradient function

if crs == "EPSG:4326" or crs == 4326:
mean_latitude = np.mean(dem.bbox[2:])
meters_per_degree = (
111132.92
- 559.82 * np.cos(2 * mean_latitude)
+ 1.175 * np.cos(4 * mean_latitude)
- 0.0023 * np.cos(6 * mean_latitude)
)

dy *= meters_per_degree
dx *= meters_per_degree
grid = Grid(
bbox=dem.bbox, dx=dem.dx, dy=dem.dy, extrapolate=True, values=0.0, crs=crs
)
tmpz[np.abs(tmpz) < 1] = 1
grid.values = period * np.sqrt(gravity * np.abs(tmpz)) / wl

# Convert back to degrees from meters (if geographic)
if crs == "EPSG:4326":
if crs == "EPSG:4326" or crs == 4326:
grid.values /= meters_per_degree

if min_edgelength is None:
Expand Down Expand Up @@ -892,7 +935,7 @@ def multiscale_sizing_function(
# interpolate all finer nests onto coarse func and enforce gradation rate
for k, finer in enumerate(list_of_grids[idx1 + 1 :]):
logger.info(
f" Interpolating sizing function #{idx1+1 + k} onto sizing function #{idx1}"
f" Interpolating sizing function #{idx1 + 1 + k} onto sizing function #{idx1}"
)
_wkt = finer.crs.to_dict()
if "units" in _wkt:
Expand Down
6 changes: 3 additions & 3 deletions oceanmesh/filterfx.py
Original file line number Diff line number Diff line change
Expand Up @@ -26,7 +26,7 @@ def filt2(Z, res, wl, filtertype, truncate=2.6):
highpass, bandpass or bandstop"
)

if hasattr(wl, "__len__") and type(wl) != np.ndarray:
if hasattr(wl, "__len__") and ~isinstance(type(wl), np.ndarray):
wl = np.array(wl)

if np.any(wl <= 2 * res):
Expand All @@ -37,12 +37,12 @@ def filt2(Z, res, wl, filtertype, truncate=2.6):

if filtertype in ["bandpass", "bandstop"]:
if hasattr(wl, "__len__"):
if len(wl) != 2 or type(wl) == str:
if len(wl) != 2 or isinstance(wl, str):
raise TypeError(
"Wavelength lambda must be a two-element array for a bandpass filter."
)

if type(wl) != np.array:
if ~isinstance(wl, np.ndarray):
wl = np.array(list(wl))

else:
Expand Down
3 changes: 2 additions & 1 deletion oceanmesh/fix_mesh.py
Original file line number Diff line number Diff line change
@@ -1,6 +1,7 @@
import numpy as np
import warnings

import numpy as np


def simp_qual(p, t):
"""Simplex quality radius-to-edge ratio
Expand Down
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