Deploying to main from @ meshpro/dmsh-dev@be5a161 🚀

Author: nschloe

.github/workflows/ci.yml

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+name: ci
+
+on:
+  push:
+    branches:
+      - main
+  pull_request:
+    branches:
+      - main
+
+jobs:
+  lint:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Check out repo
+        uses: actions/checkout@v2
+      - name: Set up Python
+        uses: actions/setup-python@v2
+      - name: Run pre-commit
+        uses: pre-commit/[email protected]
+
+  build:
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        python-version: ["3.7", "3.8", "3.9", "3.10"]
+    steps:
+      - uses: actions/setup-python@v2
+        with:
+          python-version: ${{ matrix.python-version }}
+      - uses: actions/checkout@v2
+      - name: Test with tox
+        run: |
+          pip install tox
+          tox -- --cov dmsh --cov-report xml --cov-report term
+      - uses: codecov/codecov-action@v1
+        if: ${{ matrix.python-version == '3.9' }}

README.md

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+<p align="center">
+  <a href="https://github.com/nschloe/dmsh"><img alt="dmsh" src="https://raw.githubusercontent.com/meshpro/dmsh/main/logo/logo-with-text.svg" width="50%"></a>
+  <p align="center">The worst mesh generator you'll ever use.</p>
+</p>
+
+[![PyPi Version](https://img.shields.io/pypi/v/dmsh.svg?style=flat-square)](https://pypi.org/project/dmsh/)
+[![PyPI pyversions](https://img.shields.io/pypi/pyversions/dmsh.svg?style=flat-square)](https://pypi.org/project/dmsh/)
+[![GitHub stars](https://img.shields.io/github/stars/nschloe/dmsh.svg?style=flat-square&logo=github&label=Stars&logoColor=white)](https://github.com/nschloe/dmsh)
+[![PyPi downloads](https://img.shields.io/pypi/dm/dmsh.svg?style=flat-square)](https://pypistats.org/packages/dmsh)
+
+[![Discord](https://img.shields.io/static/v1?logo=discord&label=chat&message=on%20discord&color=7289da&style=flat-square)](https://discord.gg/PBCCvwHqpv)
+
+Inspired by [distmesh](http://persson.berkeley.edu/distmesh/), dmsh can be slow,
+requires a lot of memory, and isn't terribly robust either.
+
+On the plus side,
+
+- it's got a user-friendly interface,
+- is pure Python (and hence easily installable on any system), and
+- it produces pretty high-quality meshes.
+
+Combined with [optimesh](https://github.com/nschloe/optimesh), dmsh produces the
+highest-quality 2D meshes in the west.
+
+### Examples
+
+#### Primitives
+
+| <img alt="circle" src="https://raw.githubusercontent.com/meshpro/dmsh/main/plots/circle.svg" width="100%"> | <img alt="circle" src="https://raw.githubusercontent.com/meshpro/dmsh/main/plots/rectangle.svg" width="100%"> | <img alt="circle" src="https://raw.githubusercontent.com/meshpro/dmsh/main/plots/polygon.svg" width="100%"> |
+| :--------------------------------------------------------------------------------------------------------: | :-----------------------------------------------------------------------------------------------------------: | :---------------------------------------------------------------------------------------------------------: |
+
+```python
+import dmsh
+import meshio
+import optimesh
+
+geo = dmsh.Circle([0.0, 0.0], 1.0)
+X, cells = dmsh.generate(geo, 0.1)
+
+# optionally optimize the mesh
+X, cells = optimesh.optimize_points_cells(X, cells, "CVT (full)", 1.0e-10, 100)
+
+# visualize the mesh
+dmsh.show(X, cells, geo)
+
+# and write it to a file
+meshio.Mesh(X, {"triangle": cells}).write("circle.vtk")
+```
+
+```python
+import dmsh
+
+geo = dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0)
+X, cells = dmsh.generate(geo, 0.1)
+```
+
+```python
+import dmsh
+
+geo = dmsh.Polygon(
+    [
+        [0.0, 0.0],
+        [1.1, 0.0],
+        [1.2, 0.5],
+        [0.7, 0.6],
+        [2.0, 1.0],
+        [1.0, 2.0],
+        [0.5, 1.5],
+    ]
+)
+X, cells = dmsh.generate(geo, 0.1)
+```
+
+#### Combinations
+
+##### Difference
+
+| <img src="https://raw.githubusercontent.com/meshpro/dmsh/main/plots/moon.svg" width="100%"> | <img src="https://raw.githubusercontent.com/meshpro/dmsh/main/plots/pacman.svg" width="100%"> | <img src="https://raw.githubusercontent.com/meshpro/dmsh/main/plots/rectangle-hole-refinement.svg" width="100%"> |
+| :-----------------------------------------------------------------------------------------: | :-------------------------------------------------------------------------------------------: | :--------------------------------------------------------------------------------------------------------------: |
+
+```python
+import dmsh
+
+geo = dmsh.Circle([-0.5, 0.0], 1.0) - dmsh.Circle([+0.5, 0.0], 1.0)
+X, cells = dmsh.generate(geo, 0.1)
+```
+
+```python
+import dmsh
+
+geo = dmsh.Circle([0.0, 0.0], 1.0) - dmsh.Polygon([[0.0, 0.0], [1.5, 0.4], [1.5, -0.4]])
+X, cells = dmsh.generate(geo, 0.1, tol=1.0e-10)
+```
+
+The following example uses a nonconstant edge length; it depends on the distance to the
+circle `c`.
+
+```python
+import dmsh
+import numpy as np
+
+r = dmsh.Rectangle(-1.0, +1.0, -1.0, +1.0)
+c = dmsh.Circle([0.0, 0.0], 0.3)
+geo = r - c
+
+X, cells = dmsh.generate(geo, lambda pts: np.abs(c.dist(pts)) / 5 + 0.05, tol=1.0e-10)
+```
+
+##### Union
+
+| <img src="https://raw.githubusercontent.com/meshpro/dmsh/main/plots/union-circles.svg" width="100%"> | <img src="https://raw.githubusercontent.com/meshpro/dmsh/main/plots/union-rectangles.svg" width="100%"> | <img src="https://raw.githubusercontent.com/meshpro/dmsh/main/plots/union-three-circles.svg" width="100%"> |
+| :--------------------------------------------------------------------------------------------------: | :-----------------------------------------------------------------------------------------------------: | :--------------------------------------------------------------------------------------------------------: |
+
+```python
+import dmsh
+
+geo = dmsh.Circle([-0.5, 0.0], 1.0) + dmsh.Circle([+0.5, 0.0], 1.0)
+X, cells = dmsh.generate(geo, 0.15)
+```
+
+```python
+import dmsh
+
+geo = dmsh.Rectangle(-1.0, +0.5, -1.0, +0.5) + dmsh.Rectangle(-0.5, +1.0, -0.5, +1.0)
+X, cells = dmsh.generate(geo, 0.15)
+```
+
+```python
+import dmsh
+import numpy as np
+
+angles = np.pi * np.array([3.0 / 6.0, 7.0 / 6.0, 11.0 / 6.0])
+geo = dmsh.Union(
+    [
+        dmsh.Circle([np.cos(angles[0]), np.sin(angles[0])], 1.0),
+        dmsh.Circle([np.cos(angles[1]), np.sin(angles[1])], 1.0),
+        dmsh.Circle([np.cos(angles[2]), np.sin(angles[2])], 1.0),
+    ]
+)
+X, cells = dmsh.generate(geo, 0.15)
+```
+
+#### Intersection
+
+| <img src="https://raw.githubusercontent.com/meshpro/dmsh/main/plots/intersection-circles.svg" width="100%"> | <img src="https://raw.githubusercontent.com/meshpro/dmsh/main/plots/intersection-three-circles.svg" width="100%"> | <img src="https://raw.githubusercontent.com/meshpro/dmsh/main/plots/intersection-circle-halfspace.svg" width="100%"> |
+| :---------------------------------------------------------------------------------------------------------: | :---------------------------------------------------------------------------------------------------------------: | :------------------------------------------------------------------------------------------------------------------: |
+
+```python
+import dmsh
+
+geo = dmsh.Circle([0.0, -0.5], 1.0) & dmsh.Circle([0.0, +0.5], 1.0)
+X, cells = dmsh.generate(geo, 0.1, tol=1.0e-10)
+```
+
+```python
+import dmsh
+import numpy as np
+
+angles = np.pi * np.array([3.0 / 6.0, 7.0 / 6.0, 11.0 / 6.0])
+geo = dmsh.Intersection(
+    [
+        dmsh.Circle([np.cos(angles[0]), np.sin(angles[0])], 1.5),
+        dmsh.Circle([np.cos(angles[1]), np.sin(angles[1])], 1.5),
+        dmsh.Circle([np.cos(angles[2]), np.sin(angles[2])], 1.5),
+    ]
+)
+X, cells = dmsh.generate(geo, 0.1, tol=1.0e-10)
+```
+
+The following uses the `HalfSpace` primtive for cutting off a circle.
+
+```python
+import dmsh
+
+geo = dmsh.HalfSpace([1.0, 1.0]) & dmsh.Circle([0.0, 0.0], 1.0)
+X, cells = dmsh.generate(geo, 0.1)
+```
+
+### Rotation, translation, scaling
+
+| <img src="https://raw.githubusercontent.com/meshpro/dmsh/main/plots/rotation.svg" width="100%"> | <img src="https://raw.githubusercontent.com/meshpro/dmsh/main/plots/scaling.svg" width="100%"> |
+| :---------------------------------------------------------------------------------------------: | :--------------------------------------------------------------------------------------------: |
+
+```python
+import dmsh
+import numpy as np
+
+geo = dmsh.Rotation(dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0), 0.1 * np.pi)
+X, cells = dmsh.generate(geo, 0.1, tol=1.0e-10)
+```
+
+```python
+import dmsh
+
+geo = dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0) + [1.0, 1.0]
+X, cells = dmsh.generate(geo, 0.1)
+```
+
+```python
+import dmsh
+
+geo = dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0) * 2.0
+X, cells = dmsh.generate(geo, 0.1, tol=1.0e-5)
+```
+
+### Local refinement
+
+<img alt="local-refinement" src="https://raw.githubusercontent.com/meshpro/dmsh/main/plots/local-refinement.svg" width="30%">
+
+All objects can be used to refine the mesh according to the distance to the object;
+e.g. a `Path`:
+
+```python
+import dmsh
+
+geo = dmsh.Rectangle(0.0, 1.0, 0.0, 1.0)
+
+p1 = dmsh.Path([[0.4, 0.6], [0.6, 0.4]])
+
+
+def target_edge_length(x):
+    return 0.03 + 0.1 * p1.dist(x)
+
+
+X, cells = dmsh.generate(geo, target_edge_length, tol=1.0e-10)
+```
+
+### Custom shapes
+
+It is also possible to define your own geometry. Simply create a class derived from
+`dmsh.Geometry` that contains a `dist` method and a method to project points onto the
+boundary.
+
+```python
+import dmsh
+import numpy as np
+
+
+class MyDisk(dmsh.Geometry):
+    def __init__(self):
+        self.r = 1.0
+        self.x0 = [0.0, 0.0]
+        bounding_box = [-1.0, 1.0, -1.0, 1.0]
+        feature_points = np.array([[], []]).T
+        super().__init__(bounding_box, feature_points)
+
+    def dist(self, x):
+        assert x.shape[0] == 2
+        y = (x.T - self.x0).T
+        return np.sqrt(np.einsum("i...,i...->...", y, y)) - self.r
+
+    def boundary_step(self, x):
+        # project onto the circle
+        y = (x.T - self.x0).T
+        r = np.sqrt(np.einsum("ij,ij->j", y, y))
+        return ((y / r * self.r).T + self.x0).T
+
+
+geo = MyDisk()
+X, cells = dmsh.generate(geo, 0.1)
+```
+
+### Debugging
+
+| ![level-set-poly](https://raw.githubusercontent.com/meshpro/dmsh/main/plots/levelset-polygon.png) | ![level-set-rect-hole](https://raw.githubusercontent.com/meshpro/dmsh/main/plots/levelset-rect-hole.png) |
+| :-----------------------------------------------------------------------------------------------: | :------------------------------------------------------------------------------------------------------: |
+
+dmsh is rather fragile, but sometimes the break-downs are due to an incorrectly defined
+geometry. Use
+
+```
+geo.show()
+```
+
+to inspect the level set function of your domain. (It must be negative inside the
+domain and positive outside. The 0-level set forms the domain boundary.)
+
+### Installation
+
+dmsh is [available from the Python Package
+Index](https://pypi.org/project/dmsh/), so simply type
+
+```
+pip install dmsh
+```
+
+to install.
+
+### Testing
+
+To run the dmsh unit tests, check out this repository and type
+
+```
+tox
+```