A Python wrapper of hmm (of which Delatin is a port) for fast terrain mesh generation.

A screenshot of Glacier National Park taken from the demo. The mesh is created using pydelatin, encoded using quantized-mesh-encoder, served on-demand using dem-tiler, and rendered with deck.gl.

With pip:

pip install pydelatin

or with Conda:

conda install -c conda-forge pydelatin

On Windows, installing via Conda is strongly recommended.

If installing with pip on Windows, glm is a prerequisite for building from source. Open an issue if you'd like to help package binary wheels for Windows.

from pydelatin import Delatin

tin = Delatin(terrain, width, height)
# Mesh vertices
tin.vertices
# Mesh triangles
tin.triangles

The API is similar to that of hmm.

Additionally I include a helper function: decode_ele, to decode a Mapbox Terrain RGB or Terrarium PNG array to elevations.

• arr (numpy ndarray): data array. If a 2D array, dimensions are expected to be (height, width). If a 1D array, height and width parameters must be passed, and the array is assumed to be in C order.
• height (int, default: None): height of array; required when arr is not 2D
• width (int, default: None): width of array; required when arr is not 2D
• z_scale (float, default: 1): z scale relative to x & y
• z_exag (float, default: 1): z exaggeration
• max_error (float, default: 0.001): maximum triangulation error
• max_triangles (int, default: None): maximum number of triangles
• max_points (int, default: None): maximum number of vertices
• base_height (float, default: 0): solid base height
• level (bool, default: False): auto level input to full grayscale range
• invert (bool, default: False): invert heightmap
• blur (int, default: 0): gaussian blur sigma
• gamma (float, default: 0): gamma curve exponent
• border_size (int, default: 0): border size in pixels
• border_height (float, default: 1): border z height

• vertices (ndarray of shape (-1, 3)): the interleaved 3D coordinates of each vertex, e.g. [[x0, y0, z0], [x1, y1, z1], ...].
• triangles (ndarray of shape (-1, 3)): represents indices within the vertices array. So [0, 1, 3, ...] would use the first, second, and fourth vertices within the vertices array as a single triangle.
• error (float): the maximum error of the mesh.

A helper function to rescale the vertices output to a new bounding box. Returns an ndarray of shape (-1, 3) with positions rescaled. Each row represents a single 3D point.

• vertices: (np.ndarray) vertices output from Delatin
• bounds: (Tuple[float]) linearly rescale position values to this extent. Expected to be [minx, miny, maxx, maxy].
• flip_y: (bool, default False) Flip y coordinates. Can be useful since images' coordinate origin is in the top left.

A common mesh format for the web is the Quantized Mesh format, which is supported in Cesium and deck.gl (via loaders.gl). You can use quantized-mesh-encoder to save in this format:

import quantized_mesh_encoder
from pydelatin import Delatin
from pydelatin.util import rescale_positions

tin = Delatin(terrain, max_error=30)
vertices, triangles = tin.vertices, tin.triangles

# Rescale vertices linearly from pixel units to world coordinates
rescaled_vertices = rescale_positions(vertices, bounds)

with open('output.terrain', 'wb') as f:
    quantized_mesh_encoder.encode(f, rescaled_vertices, triangles)

Alternatively, you can save to a variety of mesh formats using meshio:

from pydelatin import Delatin
import meshio

tin = Delatin(terrain, max_error=30)
vertices, triangles = tin.vertices, tin.triangles

cells = [("triangle", triangles)]
mesh = meshio.Mesh(vertices, cells)
# Example output format
# Refer to meshio documentation
mesh.write('foo.vtk')

Two popular algorithms for terrain mesh generation are the "Martini" algorithm, found in the JavaScript martini library and the Python pymartini library, and the "Delatin" algorithm, found in the C++ hmm library, this Python pydelatin library, and the JavaScript delatin library.

Which to use?

For most purposes, use pydelatin over pymartini. A good breakdown from a Martini issue:

Martini:

• Only works on square 2^n+1 x 2^n+1 grids.
• Generates a hierarchy of meshes (pick arbitrary detail after a single run)
• Optimized for meshing speed rather than quality.

Delatin:

• Works on arbitrary raster grids.
• Generates a single mesh for a particular detail.
• Optimized for quality (as few triangles as possible for a given error).

The following uses the same dataset as the pymartini benchmarks, a 512x512 pixel heightmap of Mt. Fuji.

For the 30-meter mesh, pydelatin is 25% slower than pymartini, but the mesh is much more efficient: it has 40% fewer vertices and triangles.

pydelatin is 4-5x faster than the JavaScript delatin package.

git clone https://github.com/kylebarron/pydelatin
cd pydelatin
pip install '.[test]'
python bench.py

mesh (max_error=30m): 27.322ms
vertices: 5668, triangles: 11140

mesh (max_error=1m): 282.946ms
mesh (max_error=2m): 215.839ms
mesh (max_error=3m): 163.424ms
mesh (max_error=4m): 127.203ms
mesh (max_error=5m): 106.596ms
mesh (max_error=6m): 91.868ms
mesh (max_error=7m): 82.572ms
mesh (max_error=8m): 74.335ms
mesh (max_error=9m): 65.893ms
mesh (max_error=10m): 60.999ms
mesh (max_error=11m): 55.213ms
mesh (max_error=12m): 54.475ms
mesh (max_error=13m): 48.662ms
mesh (max_error=14m): 47.029ms
mesh (max_error=15m): 44.517ms
mesh (max_error=16m): 42.059ms
mesh (max_error=17m): 39.699ms
mesh (max_error=18m): 37.657ms
mesh (max_error=19m): 36.333ms
mesh (max_error=20m): 34.131ms

This benchmarks against the delatin JavaScript module.

git clone https://github.com/kylebarron/pydelatin
cd test/bench_js/
yarn
wget https://raw.githubusercontent.com/mapbox/delatin/master/index.js
node -r esm bench.js

mesh (max_error=30m): 143.038ms
vertices: 5668
triangles: 11140

mesh (max_error=0m): 1169.226ms
mesh (max_error=1m): 917.290ms
mesh (max_error=2m): 629.776ms
mesh (max_error=3m): 476.958ms
mesh (max_error=4m): 352.907ms
mesh (max_error=5m): 290.946ms
mesh (max_error=6m): 240.556ms
mesh (max_error=7m): 234.181ms
mesh (max_error=8m): 188.273ms
mesh (max_error=9m): 162.743ms
mesh (max_error=10m): 145.734ms
mesh (max_error=11m): 130.119ms
mesh (max_error=12m): 119.865ms
mesh (max_error=13m): 114.645ms
mesh (max_error=14m): 101.390ms
mesh (max_error=15m): 100.065ms
mesh (max_error=16m): 96.247ms
mesh (max_error=17m): 89.508ms
mesh (max_error=18m): 85.754ms
mesh (max_error=19m): 79.838ms
mesh (max_error=20m): 75.607ms

This package wraps @fogleman's hmm, a C++ library that is also MIT-licensed.