<p align="center">
<a href="https://github.com/nschloe/meshzoo"><img alt="meshzoo" src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/meshzoo-logo.svg" width="60%"></a>
</p>
[](https://pypi.org/project/meshzoo/)
[](https://pypi.org/project/meshzoo/)
[](https://github.com/nschloe/meshzoo)
[](https://pepy.tech/project/meshzoo)
<!--[](https://pypistats.org/packages/meshzoo)-->
[](https://discord.gg/PBCCvwHqpv)
When generating meshes for FEM/FVM computations, sometimes your geometry is so simple
that you don't need a complex mesh generator (like
[pygmsh](https://github.com/meshpro/pygmsh/),
[MeshPy](https://github.com/inducer/meshpy),
[mshr](https://bitbucket.org/fenics-project/mshr),
[pygalmesh](https://github.com/meshpro/pygalmesh/),
[dmsh](https://github.com/meshpro/dmsh/)),
but something simple and fast that makes use of the structure of the domain. Enter
meshzoo.
### Installation
Install meshzoo [from PyPI](https://pypi.org/project/meshzoo/) with
```
pip install meshzoo
```
### How to get a license
Licenses for personal and academic use can be purchased
[here](https://buy.stripe.com/5kA3eV8t8af83iE9AE).
You'll receive a confirmation email with a license key.
Install the key with
```
plm add <your-license-key>
```
on your machine and you're good to go.
For commercial use, please contact support@mondaytech.com.
### Examples
#### Triangle
<img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/triangle.svg" width="20%">
```python
import meshzoo
bary, cells = meshzoo.triangle(8)
# corners = np.array(
# [
# [0.0, -0.5 * numpy.sqrt(3.0), +0.5 * numpy.sqrt(3.0)],
# [1.0, -0.5, -0.5],
# ]
# )
# points = np.dot(corners, bary).T
# Process the mesh, e.g., write it to a file using meshio
# meshio.write_points_cells("triangle.vtk", points, {"triangle": cells})
```
#### Rectangle
<table width="100%">
<tr width="100%">
<td width="50%"><img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/rectangle.svg"/></td>
<td width="50%"><img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/rectangle-quad.svg"/></td>
</tr>
</table>
```python
import meshzoo
import numpy as np
points, cells = meshzoo.rectangle_tri(
np.linspace(0.0, 1.0, 11),
np.linspace(0.0, 1.0, 11),
variant="zigzag", # or "up", "down", "center"
)
points, cells = meshzoo.rectangle_quad(
np.linspace(0.0, 1.0, 11),
np.linspace(0.0, 1.0, 11),
cell_type="quad4", # or "quad8", "quad9"
)
```
#### Regular polygon
| <img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/4gon.svg" width="70%"> | <img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/6gon.svg" width="70%"> | <img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/9gon.svg" width="70%"> |
| :---------------------------------------------------------------------------------------: | :---------------------------------------------------------------------------------------: | :---------------------------------------------------------------------------------------: |
| `meshzoo.ngon(4, 8)` | `meshzoo.ngon(6, 8)` | `meshzoo.ngon(9, 8)` |
```python
import meshzoo
points, cells = meshzoo.ngon(5, 11)
```
#### Disk
| <img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets//4gon_disk.svg" width="70%"> | <img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/6gon_disk.svg" width="70%"> | <img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/9gon_disk.svg" width="70%"> |
| :---------------------------------------------------------------------------------------------: | :--------------------------------------------------------------------------------------------: | :--------------------------------------------------------------------------------------------: |
| `meshzoo.disk(4, 8)` | `meshzoo.disk(6, 8)` | `meshzoo.disk(9, 8)` |
The disk meshes are inflations of regular polygons.
```python
import meshzoo
points, cells = meshzoo.disk(6, 11)
points, cells = meshzoo.disk_quad(10, cell_type="quad4") # or "quad8", "quad9"
```
#### Möbius strip
<img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/moebius.png" width="20%">
```python
import meshzoo
points, cells = meshzoo.moebius(num_twists=1, nl=60, nw=11)
```
#### Sphere (surface)
| <img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/uv_sphere.png" width="80%"> | <img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/geo-sphere.png" width="60%"> |
| :--------------------------------------------------------------------------------------------: | :---------------------------------------------------------------------------------------------: |
```python
import meshzoo
points, cells = meshzoo.uv_sphere(num_points_per_circle=20, num_circles=10, radius=1.0)
points, tri, quad = meshzoo.geo_sphere(
num_points_per_circle=20, num_circles=10, radius=1.0
)
```
Spheres can also be generated by refining the faces of [platonic
solids](https://en.wikipedia.org/wiki/Platonic_solid) and then "inflating" them. meshzoo
implements a few of them. The sphere generated from the icosahedron has the
highest-quality (most equilateral) triangles.
All cells are oriented such that its normals point outwards.
| <img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/tetra-sphere.png" width="70%"> | <img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/octa-sphere.png" width="70%"> | <img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/icosa-sphere.png" width="70%"> |
| :-----------------------------------------------------------------------------------------------: | :----------------------------------------------------------------------------------------------: | :-----------------------------------------------------------------------------------------------: |
| `meshzoo.tetra_sphere(10)` | `meshzoo.octa_sphere(10)` | `meshzoo.icosa_sphere(10)` |
#### Ball (solid)
| <img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/ball-tetra.png" width="70%"> | <img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/ball-hexa.png" width="70%"> |
| :---------------------------------------------------------------------------------------------: | :--------------------------------------------------------------------------------------------: |
```python
import meshzoo
points, cells = meshzoo.ball_tetra(10)
points, cells = meshzoo.ball_hexa(10)
```
#### Tube
<img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/tube.png" width="20%">
```python
import meshzoo
points, cells = meshzoo.tube(length=1.0, radius=1.0, n=30)
```
#### Cube
| <img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/cube.png" width="70%"> | <img src="https://raw.githubusercontent.com/meshpro/meshzoo/assets/cube-hexa.png" width="50%"> |
| :---------------------------------------------------------------------------------------: | :--------------------------------------------------------------------------------------------: |
```python
import meshzoo
import numpy as np
points, cells = meshzoo.cube_tetra(
np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11)
)
points, cells = meshzoo.cube_hexa(
np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11)
)
```
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"description": "<p align=\"center\">\n <a href=\"https://github.com/nschloe/meshzoo\"><img alt=\"meshzoo\" src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/meshzoo-logo.svg\" width=\"60%\"></a>\n</p>\n\n[](https://pypi.org/project/meshzoo/)\n[](https://pypi.org/project/meshzoo/)\n[](https://github.com/nschloe/meshzoo)\n[](https://pepy.tech/project/meshzoo)\n\n<!--[](https://pypistats.org/packages/meshzoo)-->\n\n[](https://discord.gg/PBCCvwHqpv)\n\nWhen generating meshes for FEM/FVM computations, sometimes your geometry is so simple\nthat you don't need a complex mesh generator (like\n[pygmsh](https://github.com/meshpro/pygmsh/),\n[MeshPy](https://github.com/inducer/meshpy),\n[mshr](https://bitbucket.org/fenics-project/mshr),\n[pygalmesh](https://github.com/meshpro/pygalmesh/),\n[dmsh](https://github.com/meshpro/dmsh/)),\nbut something simple and fast that makes use of the structure of the domain. Enter\nmeshzoo.\n\n### Installation\n\nInstall meshzoo [from PyPI](https://pypi.org/project/meshzoo/) with\n\n```\npip install meshzoo\n```\n\n### How to get a license\n\nLicenses for personal and academic use can be purchased\n[here](https://buy.stripe.com/5kA3eV8t8af83iE9AE).\nYou'll receive a confirmation email with a license key.\nInstall the key with\n\n```\nplm add <your-license-key>\n```\n\non your machine and you're good to go.\n\nFor commercial use, please contact support@mondaytech.com.\n\n### Examples\n\n#### Triangle\n\n<img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/triangle.svg\" width=\"20%\">\n\n```python\nimport meshzoo\n\nbary, cells = meshzoo.triangle(8)\n\n# corners = np.array(\n# [\n# [0.0, -0.5 * numpy.sqrt(3.0), +0.5 * numpy.sqrt(3.0)],\n# [1.0, -0.5, -0.5],\n# ]\n# )\n# points = np.dot(corners, bary).T\n\n# Process the mesh, e.g., write it to a file using meshio\n# meshio.write_points_cells(\"triangle.vtk\", points, {\"triangle\": cells})\n```\n\n#### Rectangle\n\n<table width=\"100%\">\n <tr width=\"100%\">\n <td width=\"50%\"><img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/rectangle.svg\"/></td>\n <td width=\"50%\"><img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/rectangle-quad.svg\"/></td>\n </tr>\n</table>\n\n```python\nimport meshzoo\nimport numpy as np\n\npoints, cells = meshzoo.rectangle_tri(\n np.linspace(0.0, 1.0, 11),\n np.linspace(0.0, 1.0, 11),\n variant=\"zigzag\", # or \"up\", \"down\", \"center\"\n)\n\npoints, cells = meshzoo.rectangle_quad(\n np.linspace(0.0, 1.0, 11),\n np.linspace(0.0, 1.0, 11),\n cell_type=\"quad4\", # or \"quad8\", \"quad9\"\n)\n```\n\n#### Regular polygon\n\n| <img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/4gon.svg\" width=\"70%\"> | <img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/6gon.svg\" width=\"70%\"> | <img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/9gon.svg\" width=\"70%\"> |\n| :---------------------------------------------------------------------------------------: | :---------------------------------------------------------------------------------------: | :---------------------------------------------------------------------------------------: |\n| `meshzoo.ngon(4, 8)` | `meshzoo.ngon(6, 8)` | `meshzoo.ngon(9, 8)` |\n\n```python\nimport meshzoo\n\npoints, cells = meshzoo.ngon(5, 11)\n```\n\n#### Disk\n\n| <img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets//4gon_disk.svg\" width=\"70%\"> | <img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/6gon_disk.svg\" width=\"70%\"> | <img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/9gon_disk.svg\" width=\"70%\"> |\n| :---------------------------------------------------------------------------------------------: | :--------------------------------------------------------------------------------------------: | :--------------------------------------------------------------------------------------------: |\n| `meshzoo.disk(4, 8)` | `meshzoo.disk(6, 8)` | `meshzoo.disk(9, 8)` |\n\nThe disk meshes are inflations of regular polygons.\n\n```python\nimport meshzoo\n\npoints, cells = meshzoo.disk(6, 11)\n\npoints, cells = meshzoo.disk_quad(10, cell_type=\"quad4\") # or \"quad8\", \"quad9\"\n```\n\n#### M\u00f6bius strip\n\n<img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/moebius.png\" width=\"20%\">\n\n```python\nimport meshzoo\n\npoints, cells = meshzoo.moebius(num_twists=1, nl=60, nw=11)\n```\n\n#### Sphere (surface)\n\n| <img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/uv_sphere.png\" width=\"80%\"> | <img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/geo-sphere.png\" width=\"60%\"> |\n| :--------------------------------------------------------------------------------------------: | :---------------------------------------------------------------------------------------------: |\n\n```python\nimport meshzoo\n\npoints, cells = meshzoo.uv_sphere(num_points_per_circle=20, num_circles=10, radius=1.0)\npoints, tri, quad = meshzoo.geo_sphere(\n num_points_per_circle=20, num_circles=10, radius=1.0\n)\n```\n\nSpheres can also be generated by refining the faces of [platonic\nsolids](https://en.wikipedia.org/wiki/Platonic_solid) and then \"inflating\" them. meshzoo\nimplements a few of them. The sphere generated from the icosahedron has the\nhighest-quality (most equilateral) triangles.\n\nAll cells are oriented such that its normals point outwards.\n\n| <img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/tetra-sphere.png\" width=\"70%\"> | <img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/octa-sphere.png\" width=\"70%\"> | <img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/icosa-sphere.png\" width=\"70%\"> |\n| :-----------------------------------------------------------------------------------------------: | :----------------------------------------------------------------------------------------------: | :-----------------------------------------------------------------------------------------------: |\n| `meshzoo.tetra_sphere(10)` | `meshzoo.octa_sphere(10)` | `meshzoo.icosa_sphere(10)` |\n\n#### Ball (solid)\n\n| <img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/ball-tetra.png\" width=\"70%\"> | <img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/ball-hexa.png\" width=\"70%\"> |\n| :---------------------------------------------------------------------------------------------: | :--------------------------------------------------------------------------------------------: |\n\n```python\nimport meshzoo\n\npoints, cells = meshzoo.ball_tetra(10)\npoints, cells = meshzoo.ball_hexa(10)\n```\n\n#### Tube\n\n<img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/tube.png\" width=\"20%\">\n\n```python\nimport meshzoo\n\npoints, cells = meshzoo.tube(length=1.0, radius=1.0, n=30)\n```\n\n#### Cube\n\n| <img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/cube.png\" width=\"70%\"> | <img src=\"https://raw.githubusercontent.com/meshpro/meshzoo/assets/cube-hexa.png\" width=\"50%\"> |\n| :---------------------------------------------------------------------------------------: | :--------------------------------------------------------------------------------------------: |\n\n```python\nimport meshzoo\nimport numpy as np\n\npoints, cells = meshzoo.cube_tetra(\n np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11)\n)\npoints, cells = meshzoo.cube_hexa(\n np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11)\n)\n```\n",
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