Mesher is a novel multi-objective unstructured mesh generation software that allows mesh generation to be constrained to an arbitrary number of hydrologically important features while maintaining a variable spatial resolution. Triangle quality is guaranteed as well as a smooth graduation from small to large triangles. Including these additional constraints resulted in a better representation of spatial heterogeneity versus classic topography-only constraints.
- A novel multi-objective unstructured mesh generation software, Mesher, is presented
- Heterogeneity in topography is resolved as well as hydrologically important surface and sub-surface attributes
- Spatial heterogeneity is better preserved compared to existing mesh generators
An example of this is shown below, where the triangulation (black lines) are constrained to topography (not shown) and vegetation landclasses (coloured squares).
The software is also designed with large scale in mind and has been run for large extents. Output formats include Paraview compatible vtu files.
Mesher depends heavily upon GDAL to handle the geospatial data and the GDAL python bindings. Mesher's input rasters can be in any 1-band raster that GDAL can open. The triangulation is performed using the Delaunay triangulation code in CGAL.
To compile mesher requires cmake, boost, and cgal. To configure and compile run the following:
cmake .
make -j10
Configuration parameters are set in a second .py file and passed as an argument to mesher.py on the command line. For example:
python mesher.py example_mesher_config.py
The extent of dem_filename is used to define the simulation extent. Input parameters are constrained to this extent. However, parameters need not cover the entire extent.
max_area Is a constraint on the maximum size (m^2) of a triangle.
max_tolerance The maximum difference (vertical distance) between the triangle and the underlying raster
min_area A minimum area (m^2) past which mesher should not refine a triangle further. A good setting is the square area of a DEM cell. This does not mean a triangle won't be smaller than this; rather, if a triangle is below this threshold it will automatically be accepted as valid. This will override the tolerance setting. For example, if the threshold is 3m^, and a 2m^ triangle is checked for validity, it will automatically be accepted, without checking the tolerance. A triangle may end up smaller than this threshold due to other splitting that occurs in order to guarantee triangle quality.
errormetric Assigned an integer value that determines the error metric to use.
'mean_tol' = Mean elevation difference
'max_tol' = Max elevation difference
'rmse' = RMSE tolerance
parameter_files is a dictionary that lists additional parameters. Because a triangle may cover more than one raster cell, the method variable specifies either 'mode' or 'mean'. This controls how the >1 cells are merged and assigned to a triangle. 'Mode' sets the triangle to be the value that is most common out of all cells.
initial_conditions is a dictionary that lists additional parameters. Because a triangle may cover more than one raster cell, the method variable specifies either 'mode' or 'mean'. This controls how the >1 cells are merged and assigned to a triangle. 'Mode' sets the triangle to be the value that is most common out of all cells.
For both initial conditions and parameter files, an optional 'tolerance' can be set. If 'method' is 'mode', then this is a fractional percent of the dominate landcover to cover the triangle area to not split the triangle. Otherwise, it is RMSE in the units of the raster's value.
If the input rasters are of different resolutions, then min_area should be set to approximately 1/4 the size of the coarsest raster. For example, if the dem is LiDAR at 1m x 1m, and landcover is present at 30m x 30m, then min_area = 30^2 / 4 is a good starting point. This is to prevent the creation of small triangles along the coarse mesh edge.
def my_classifier(value):
if value < .98:
value = 0
else:
value = 1
return value
parameter_files = {
'landcover': { 'file' : 'eosd.tif',
'method':'mode',
'tolerance':0.8
}, # mode, mean
'svf':{'file':'wolf_svf1.tif',
'method':'mean',
'classifier':my_classifier
}
}
initial_conditions={
'sm' : {'file': 'granger_sm_2000.tif', 'method': 'mean'},
'swe' : {'file': 'granger_swe_2001.tif', 'method':'mean'}
}The classifier allows for reclassifying data within mesher so that data-loss from classifying on a raster is minimized.
Complex basin shapes might result in the creation of many triangles along the complex edges. Thus simplify=True and simplify_tol can be used to simplify the basin outline. simplify_tol is the simplification tolerance specified in meters. Be careful as too high a tolerance will cause many lines to be outside of the bounds of the raster.
simplify_buffer Sets a negative buffer (i.e., contracts the meshing domain) to give simplify_tol more room to work. That is, usage of the simplify tolerance without this will likely put triangles outside of the valid data domain. Using this allows for the simplification to result in triangles that exist within the data domain. You can disable the use of this buffer by setting no_simplify_buffer=True. simplify_buffer is enabled by default [defaults to 10m] when simplify=True.
# Configuration file for Mesher
dem_filename = 'bow_srtm1.tif'
max_area=1000000
max_tolerance=50
min_area = 30**2
parameter_files={ }
initial_conditions={ }
errormetric = 1
simplify = False
simplify_tol = 5 Mesher creates a directory with the same name as the input dem. This directory has the reprojected files (*_projected), Triangle's intermediary files (.node, .elem, .neigh), and the triangulation shape file (*_USM.shp). A *.vtu file is also created for visualizing in 3D in Paraview.