pyTDGL

https://py-tdgl.readthedocs.io/en/latest/
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Python package for solving time-dependent Ginzburg-Landau equations in 2D to simulate vortex and...
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### Install pyTDGL

Source: https://py-tdgl.readthedocs.io/en/latest/notebooks/quickstart.html

Automatically install tdgl from GitHub only if running in Google Colab.

```python
# Automatically install tdgl from GitHub only if running in Google Colab
if "google.colab" in str(get_ipython()):
    %pip install --quiet git+https://github.com/loganbvh/py-tdgl.git
    !apt install ffmpeg
```

--------------------------------

### Temporary directory setup

Source: https://py-tdgl.readthedocs.io/en/latest/notebooks/quickstart.html

Sets up a temporary directory for saving data, which will be removed at the end of the notebook.

```python
tempdir = tempfile.TemporaryDirectory()
```

--------------------------------

### Solver Options and Applied Field Setup

Source: https://py-tdgl.readthedocs.io/en/latest/notebooks/quickstart.html

Configures the TDGL solver options and sets up the applied vector potential, which can be a linear ramp or a constant field.

```python
options = tdgl.SolverOptions(
    solve_time=200,
    output_file=os.path.join(tempdir.name, "weak-link-zero-current.h5"),
    field_units = "mT",
    current_units="uA",
)

RAMP_FIELD = True

if RAMP_FIELD:
    from tdgl.sources import LinearRamp, ConstantField

    # Ramp the applied field from 0 to 0.4 mT between t=0 and t=100, then hold it at 0.4 mT.
    applied_vector_potential = (
        LinearRamp(tmin=0, tmax=100)
        * ConstantField(0.4, field_units=options.field_units, length_units=device.length_units)
    )
else:
    # If applied_vector_potential is given as a single number,
    # it is interpreted to mean the vector potential associated with a
    # uniform out-of-plane magnetic field with the specified strength.
    # This is simply shorthand for
    # ConstantField(0.4, field_units=options.field_units, length_units=device.length_units).
    applied_vector_potential = 0.4

zero_current_solution = tdgl.solve(
    device,
    options,
    applied_vector_potential=applied_vector_potential,
)

```

--------------------------------

### Plotting Order Parameter and Fluxoid Calculation Setup

Source: https://py-tdgl.readthedocs.io/en/latest/notebooks/quickstart.html

Plots the order parameter and defines fluxoid polygons for later calculation. This helps visualize vortex positions.

```python
fig, axes = zero_current_solution.plot_order_parameter(figsize=(5.5, 4))

fluxoid_polygons = {
    # name: (circle radius, circle center)
    "Top vortex": (1, (0, 6)),
    "Round hole": (1.5, (0, 3.5)),
    "Square hole": (1.5, (0, -3.5)),
    "Bottom vortex": (1, (0, -6)),
}
for name, (radius, center) in fluxoid_polygons.items():
    polygon = circle(radius, center=center, points=201)
    for ax in axes:
        ax.plot(*polygon.T)

```

--------------------------------

### Draw the device

Source: https://py-tdgl.readthedocs.io/en/latest/notebooks/quickstart.html

Draws the device geometry.

```python
fig, ax = device.draw()
```

--------------------------------

### Install UMFPACK

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/installation.rst.txt

Installs the UMFPACK sparse solver using conda and pip.

```bash
# After activating your conda environment for tdgl
conda install -c conda-forge suitesparse

pip install swig scikit-umfpack
# or pip install tdgl[umfpack]
```

--------------------------------

### Plot the mesh

Source: https://py-tdgl.readthedocs.io/en/latest/notebooks/quickstart.html

Plots the generated mesh for the device.

```python
fig, ax = device.plot(mesh=True, legend=False)
_ = ax.set_ylim(-5, 5)
```

--------------------------------

### Install PARDISO

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/installation.rst.txt

Installs the MKL PARDISO sparse solver using pip or conda.

```bash
# After activating your conda environment for tdgl
pip install pypardiso
# or conda install -c conda-forge pypardiso
# or pip install tdgl[pardiso]
```

--------------------------------

### Install PARDISO

Source: https://py-tdgl.readthedocs.io/en/latest/installation.html

Installs PyPardiso using pip or conda, or alternatively installs pyTDGL with PARDISO support.

```bash
# After activating your conda environment for tdgl
pip install pypardiso
# or conda install -c conda-forge pypardiso
# or pip install tdgl[pardiso]

```

--------------------------------

### Polygon Bounding Box

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/notebooks/polygons.ipynb.txt

Example of getting the bounding box of a polygon.

```python
from py_tdgl import Polygon

coords = [(0, 0), (2, 0), (2, 1), (0, 1)]
polygon = Polygon(coords)
bounding_box = polygon.bounds
print(f"The bounding box of the polygon is: {bounding_box}")
```

--------------------------------

### Import necessary libraries

Source: https://py-tdgl.readthedocs.io/en/latest/notebooks/quickstart.html

Imports for plotting, numerical operations, and the tdgl library.

```python
%config InlineBackend.figure_formats = {"retina", "png"}

import os
import tempfile

os.environ["OPENBLAS_NUM_THREADS"] = "1"

from IPython.display import HTML, display
import h5py
import matplotlib.pyplot as plt
import numpy as np

plt.rcParams["figure.figsize"] = (5, 4)

import tdgl
from tdgl.geometry import box, circle
from tdgl.visualization.animate import create_animation
```

--------------------------------

### Install pyTDGL from GitHub

Source: https://py-tdgl.readthedocs.io/en/latest/installation.html

Installs the pyTDGL package directly from its GitHub repository using pip.

```bash
pip install git+https://github.com/loganbvh/py-tdgl.git

```

--------------------------------

### Install pyTDGL from GitHub

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/installation.rst.txt

Installs the pyTDGL package directly from its GitHub repository using pip.

```bash
pip install git+https://github.com/loganbvh/py-tdgl.git
```

--------------------------------

### Install pyTDGL from PyPI

Source: https://py-tdgl.readthedocs.io/en/latest/installation.html

Installs the pyTDGL package from the Python Package Index using pip.

```bash
pip install tdgl

```

--------------------------------

### Mesh statistics

Source: https://py-tdgl.readthedocs.io/en/latest/notebooks/quickstart.html

Prints statistics about the generated mesh.

```python
device.mesh_stats()
```

--------------------------------

### Plotting dynamics

Source: https://py-tdgl.readthedocs.io/en/latest/notebooks/quickstart.html

This code snippet plots the dynamics of the voltage across the device.

```python
fig, axes = field_current_solution.dynamics.plot(tmin=10, mean_voltage=False)
```

--------------------------------

### Editable installation for development

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/installation.rst.txt

Installs an editable version of pyTDGL for development purposes, including development and documentation dependencies.

```bash
git clone https://github.com/loganbvh/py-tdgl.git
cd py-tdgl
pip install -e ".[dev,docs]"
```

--------------------------------

### Install pyTDGL from PyPI

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/installation.rst.txt

Installs the pyTDGL package from the Python Package Index (PyPI) using pip.

```bash
pip install tdgl
```

--------------------------------

### Voltage measurement points

Source: https://py-tdgl.readthedocs.io/en/latest/notebooks/quickstart.html

Defines the points for voltage measurements.

```python
probe_points = [(0, total_length / 2.5), (0, -total_length / 2.5)]
```

--------------------------------

### Editable installation for development

Source: https://py-tdgl.readthedocs.io/en/latest/installation.html

Installs an editable version of pyTDGL for development purposes, including development and documentation dependencies.

```bash
git clone https://github.com/loganbvh/py-tdgl.git
cd py-tdgl
pip install -e ".[dev,docs]"

```

--------------------------------

### Helper function for creating animations

Source: https://py-tdgl.readthedocs.io/en/latest/notebooks/quickstart.html

A helper function that animates a tdgl.Solution object for embedding in a notebook.

```python
def make_video_from_solution(
    solution,
    quantities=("order_parameter", "phase"),
    fps=20,
    figsize=(5, 4),
):
    """Generates an HTML5 video from a tdgl.Solution."""
    with tdgl.non_gui_backend():
        with h5py.File(solution.path, "r") as h5file:
            anim = create_animation(
                h5file,
                quantities=quantities,
                fps=fps,
                figure_kwargs=dict(figsize=figsize),
            )
            video = anim.to_html5_video()
        return HTML(video)
```

--------------------------------

### Run tdgl test suite from terminal

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/installation.rst.txt

Verifies the installation by running the tdgl test suite using a command-line interface.

```bash
python -m tdgl.testing
```

--------------------------------

### Cleaning up temporary directory

Source: https://py-tdgl.readthedocs.io/en/latest/notebooks/quickstart.html

This code snippet cleans up the temporary directory used for storing simulation output.

```python
tempdir.cleanup()
```

--------------------------------

### Device definition

Source: https://py-tdgl.readthedocs.io/en/latest/notebooks/quickstart.html

Creates the tdgl.Device object with the defined geometry, terminals, and probe points.

```python
device = tdgl.Device(
    "weak_link",
    layer=layer,
    film=film,
    holes=[round_hole, square_hole],
    terminals=[source, drain],
    probe_points=probe_points,
    length_units=length_units,
)
```

--------------------------------

### Current terminals

Source: https://py-tdgl.readthedocs.io/en/latest/notebooks/quickstart.html

Defines the source and drain terminals for current flow.

```python
source = (
    tdgl.Polygon("source", points=box(1.1 * total_width, total_length / 100))
    .translate(dy=total_length / 2)
)
drain = source.scale(yfact=-1).set_name("drain")
```

--------------------------------

### Animation flag

Source: https://py-tdgl.readthedocs.io/en/latest/notebooks/quickstart.html

Flag to control whether animations are generated.

```python
MAKE_ANIMATIONS = True
```

--------------------------------

### Polygon Example

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/notebooks/polygons.ipynb.txt

Demonstrates the creation and basic usage of a Polygon object.

```python
from py_tdgl import Polygon

# Example usage
polygon = Polygon()
polygon.add_point(0, 0)
polygon.add_point(1, 0)
polygon.add_point(1, 1)
polygon.add_point(0, 1)

print(polygon.get_area())
print(polygon.get_perimeter())
```

--------------------------------

### Polygon Example

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/notebooks/polygons.ipynb.txt

An example of an SVG polygon element.

```svg
<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="100.0" height="100.0" viewBox="-3.8183766184073566 -3.8183766184073558 7.636753236814711 7.636753236814697" preserveAspectRatio="xMinYMin meet"><g transform="matrix(1,0,0,-1,0,-1.4210854715202004e-14)"><path fill-rule="evenodd" fill="#66cc99" stroke="#555555" stroke-width="0.15273506473629422" opacity="0.6" d="M -3.5355339059327378,-2.82842712474619 L -3.3803153442088614,-2.9836456864700662 L -3.2250967824849854,-3.138864248193942 L -3.069878220761109,-3.2940828099178185 L -2.9146596590372327,-3.449301371641695 L -2.7594410973133563,-3.466547878499903 L -2.6042225355894804,-3.311329316776027 L -2.449003973865604,-3.1561107550521506 L -2.2937854121417276,-3.0008921933282746 L -2.1385668504178517,-2.8456736316043982 L -1.9833482886939755,-2.690455069880522 L -1.8281297269700991,-2.535236508156646 L -1.6729111652462227,-2.3800179464327695 L -1.5176926035223464,-2.2247993847088936 L -1.36247404179847,-2.069580822985017 L -1.2072554800745938,-1.914362261261141 L -1.0520369183507172,-1.7591436995372647 L -0.896818356626841,-1.6039251378133883 L -0.7415997949029647,-1.4487065760895124 L -0.5863812331790887,-1.2934880143656362 L -0.4311626714552126,-1.1382694526417598 L -0.27594410973133665,-0.9830508909178839 L -0.12072554800746003,-0.8278323291940073 L 0.034493013716416554,-0.7415997949029633 L 0.18971157544029288,-0.89681835662684 L 0.34493013716416854,-1.0520369183507159 L 0.5001486988880448,-1.2072554800745925 L 0.6553672606119207,-1.3624740417984684 L 0.8105858223357971,-1.5176926035223448 L 0.9658043840596734,-1.672911165246221 L 1.1210229457835492,-1.8281297269700967 L 1.2762415075074254,-1.983348288693973 L 1.4314600692313015,-2.1385668504178494 L 1.5866786309551775,-2.2937854121417254 L 1.741897192679054,-2.4490039738656018 L 1.89711575440293,-2.604222535589478 L 2.0523343161268066,-2.7594410973133545 L 2.2075528778506825,-2.9146596590372305 L 2.362771439574558,-3.069878220761106 L 2.5179900012984358,-3.2250967824849837 L 2.673208563022313,-3.3803153442088605 L 2.828427124746189,-3.535533905932737 L 2.983645686470064,-3.380315344208863 L 3.138864248193941,-3.2250967824849863 L 3.2940828099178177,-3.06987822076111 L 3.4493013716416945,-2.914659659037233 L 3.466547878499903,-2.7594410973133563 L 3.3113293167760256,-2.604222535589479 L 3.15611075505215,-2.449003973865603 L 3.000892193328275,-2.2937854121417285 L 2.8456736316043982,-2.138566850417851 L 2.6904550698805223,-1.9833482886939753 L 2.535236508156646,-1.8281297269700985 L 2.38001794643277,-1.672911165246223 L 2.224799384708894,-1.517692603522347 L 2.069580822985017,-1.36247404179847 L 1.9143622612611413,-1.207255480074594 L 1.7591436995372653,-1.052036918350718 L 1.6039251378133885,-0.8968183566268411 L 1.4487065760895133,-0.7415997949029659 L 1.293488014365635,-0.5863812331790875 L 1.1382694526417585,-0.43116267145521125 L 0.983050890917882,-0.2759441097313348 L 0.8278323291940062,-0.120725548007459 L 0.7415997949029656,0.03449301371641811 L 0.8968183566268414,0.1897115754402939 L 1.0520369183507172,0.34493013716416976 L 1.2072554800745943,0.5001486988880468 L 1.3624740417984702,0.6553672606119227 L 1.517692603522348,0.8105858223358002 L 1.672911165246223,0.9658043840596755 L 1.8281297269700982,1.1210229457835508 L 1.9833482886939748,1.2762415075074272 L 2.138566850417852,1.4314600692313044 L 2.2937854121417276,1.5866786309551801 L 2.4490039738656044,1.741897192679057 L 2.604222535589481,1.8971157544029331 L 2.759441097313357,2.0523343161268097 L 2.9146596590372362,2.2075528778506888 L 3.0698782207611126,2.3627714395745647 L 3.225096782484989,2.517990001298442 L 3.3803153442088654,2.673208563022318 L 3.535533905932735,2.8284271247461925 L 3.380315344208859,2.9836456864700684 L 3.2250967824849828,3.138864248193945 L 3.069878220761104,3.2940828099178234 L 2.914659659037228,3.4493013716417 L 2.7594410973133514,3.466547878499898 L 2.6042225355894772,3.311329316776024 L 2.4490039738656013,3.156110755052148 L 2.293785412141722,3.000892193328269 L 2.1385668504178454,2.8456736316043925 L 1.9833482886939693,2.6904550698805156 L 1.828129726970093,2.5352365081566397 L 1.6729111652462139,2.3800179464327607 L 1.5176926035223366,2.224799384708884 L 1.36247404179846,2.069580822985007 L 1.2072554800745865,1.9143622612611337 L 1.052036918350709,1.7591436995372565 L 0.8968183566268312,1.6039251378133785 L 0.7415997949029559,1.4487065760895035 L 0.5863812331790812,1.2934880143656287 L 0.43116267145520504,1.1382694526417523 L 0.2759441097313285,0.9830508909178757 L 0.12072554800744997,0.8278323291939972 L -0.03449301371642597,0.7415997949029728 L -0.18971157544030165,0.8968183566268487 L -0.3449301371641773,1.0520369183507248 L -0.500148698888053,1.2072554800746007 L -0.6553672606119326,1.3624740417984804 L -0.810585822335809,1.5176926035223568 L -0.9658043840596859,1.6729111652462336 L -1.121022945783563,1.8281297269701104 L -1.2762415075074391,1
```

--------------------------------

### Run tdgl test suite from Python session

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/installation.rst.txt

Verifies the installation by running the tdgl test suite within a Python interactive session.

```python
>>> import tdgl.testing
>>> tdgl.testing.run()
```

--------------------------------

### Animation Generation

Source: https://py-tdgl.readthedocs.io/en/latest/notebooks/quickstart.html

This code snippet generates a video animation from a simulation solution if the MAKE_ANIMATIONS flag is true.

```python
if MAKE_ANIMATIONS:
    zero_current_video = make_video_from_solution(zero_current_solution)
    display(zero_current_video)
```

--------------------------------

### Plotting Supercurrent Density

Source: https://py-tdgl.readthedocs.io/en/latest/notebooks/quickstart.html

This code snippet plots the supercurrent density flowing in the device.

```python
fig, ax = zero_current_solution.plot_currents(min_stream_amp=0.075, vmin=0, vmax=10)
```

--------------------------------

### Outer geometry of the film

Source: https://py-tdgl.readthedocs.io/en/latest/notebooks/quickstart.html

Defines the outer geometry of the film, including notches and holes.

```python
right_notch = (
    tdgl.Polygon(points=box(total_width))
    .rotate(45)
    .translate(dx=(np.sqrt(2) * total_width + link_width) / 2)
)
left_notch = right_notch.scale(xfact=-1)
film = (
    tdgl.Polygon("film", points=box(total_width, total_length))
    .difference(right_notch, left_notch)
    .resample(401)
    .buffer(0)
)
```

--------------------------------

### Creating a Polygon

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/notebooks/polygons.ipynb.txt

Example of creating a simple polygon from a list of coordinates.

```python
from py_tdgl import Polygon

coords = [(0, 0), (1, 0), (1, 1), (0, 1)]
polygon = Polygon(coords)
print(polygon)
```

--------------------------------

### SolverOptions for Adaptive Time Step

Source: https://py-tdgl.readthedocs.io/en/latest/background.html

Example of how to configure adaptive time step parameters in pyTDGL.

```python
tdgl.SolverOptions(..., adaptive=False, ...)
```

--------------------------------

### Polygon Visualization

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/notebooks/polygons.ipynb.txt

Basic example of how to visualize a polygon using matplotlib.

```python
import matplotlib.pyplot as plt
from matplotlib.patches import Polygon as MplPolygon

fig, ax = plt.subplots()

# Convert polygon coordinates to a format matplotlib understands
mpl_poly = MplPolygon(polygon.coordinates, closed=True, fill=None, edgecolor='blue')
ax.add_patch(mpl_poly)

# Set plot limits and aspect ratio
ax.set_xlim(-1, 2)
ax.set_ylim(-1, 2)
ax.set_aspect('equal', adjustable='box')

plt.title("Polygon Visualization")
plt.xlabel("X-axis")
plt.ylabel("Y-axis")
plt.grid(True)
plt.show()

```

--------------------------------

### Polygon Perimeter Calculation

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/notebooks/polygons.ipynb.txt

Example of calculating the perimeter of a polygon.

```python
from TDGL import Polygon

vertices = [(0, 0), (1, 0), (1, 1), (0, 1)]
polygon = Polygon(vertices)
perimeter = polygon.perimeter()
print(f"The perimeter of the polygon is: {perimeter}")
```

--------------------------------

### Polygon Bounding Box

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/notebooks/polygons.ipynb.txt

Explains how to get the bounding box of a polygon.

```python
from py_tdgl.geometry import Polygon

coordinates = [(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)]
polygon = Polygon(coordinates)
bounding_box = polygon.bounds
print(f"The bounding box of the polygon is: {bounding_box}")
```

--------------------------------

### Transform a Polygon

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/notebooks/polygons.ipynb.txt

Example of applying a transformation (e.g., translation) to a polygon.

```python
from tdgl import Polygon

points = [(0, 0), (1, 0), (1, 1), (0, 1)]
polygon = Polygon(points)

translated_polygon = polygon.translate(dx=5, dy=5)
print(f"Original polygon: {polygon}")
print(f"Translated polygon: {translated_polygon}")
```

--------------------------------

### Polygon Intersection

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/notebooks/polygons.ipynb.txt

Example of finding the intersection of two polygons.

```python
from TDGL import Polygon

polygon1_vertices = [(0, 0), (2, 0), (2, 2), (0, 2)]
polygon2_vertices = [(1, 1), (3, 1), (3, 3), (1, 3)]

polygon1 = Polygon(polygon1_vertices)
polygon2 = Polygon(polygon2_vertices)

intersection = polygon1.intersection(polygon2)

if intersection:
    print("Intersection found:")
    print(intersection)
else:
    print("Polygons do not intersect.")
```

--------------------------------

### Polygon Bounding Box

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/notebooks/polygons.ipynb.txt

Explains how to get the bounding box of a polygon.

```python
from py_tdgl.geometry import Polygon

vertices = [(0, 0), (1, 0), (1, 1), (0, 1)]
polygon = Polygon(vertices)

# Get the bounding box
bounding_box = polygon.bounds

print(f"The bounding box of the polygon is: {bounding_box}")
```

--------------------------------

### Polygon Operations

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/notebooks/polygons.ipynb.txt

Examples of common operations like translation and rotation.

```python
from tdgl import Polygon
import math

vertices = [
    (0, 0),
    (1, 0),
    (1, 1),
    (0, 1),
    (0, 0)
]
polygon = Polygon(vertices)

# Translate the polygon
translated_polygon = polygon.translate(dx=2, dy=3)
print(f"Translated Polygon: {translated_polygon}")

# Rotate the polygon (e.g., by 45 degrees)
angle_rad = math.radians(45)
rotated_polygon = polygon.rotate(angle=angle_rad, origin=(0.5, 0.5))
print(f"Rotated Polygon: {rotated_polygon}")
```

--------------------------------

### Polygon Example

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/notebooks/polygons.ipynb.txt

This snippet demonstrates how to create and manipulate polygons using the py-tdgl library.

```python
from py_tdgl.geometry import Polygon

# Create a polygon from a list of vertices
polygon = Polygon([(0, 0), (1, 0), (1, 1), (0, 1)])

# Get the area of the polygon
area = polygon.area
print(f"The area of the polygon is: {area}")

# Get the centroid of the polygon
centroid = polygon.centroid
print(f"The centroid of the polygon is: {centroid}")

# Check if a point is inside the polygon
point = (0.5, 0.5)
print(f"Is the point {point} inside the polygon? {polygon.contains(point)}")
```

--------------------------------

### Polygon Difference

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/notebooks/polygons.ipynb.txt

Example of calculating the difference between two polygons.

```python
from py_tdgl import Polygon

polygon1_coords = [(0, 0), (2, 0), (2, 2), (0, 2)]
polygon2_coords = [(1, 1), (3, 1), (3, 3), (1, 3)]
polygon1 = Polygon(polygon1_coords)
polygon2 = Polygon(polygon2_coords)
difference_polygon = polygon1.difference(polygon2)
print(f"The difference (polygon1 - polygon2) is: {difference_polygon}")
```

--------------------------------

### Polygon Bounding Box

Source: https://py-tdgl.readthedocs.io/en/latest/_sources/notebooks/polygons.ipynb.txt

Demonstrates how to get the minimum bounding rectangle (axis-aligned) for a polygon.

```python
from typing import List, Tuple

from shapely.geometry import Polygon


def create_polygon(points: List[Tuple[float, float]]) -> Polygon:
    """Create a shapely Polygon from a list of points.

    Args:
        points: A list of (x, y) tuples representing the polygon vertices.

    Returns:
        A shapely Polygon object.
    """
    return Polygon(points)


def get_polygon_bounding_box(polygon: Polygon) -> Tuple[float, float, float, float]:
    """Get the bounding box of a shapely Polygon.

    Args:
        polygon: A shapely Polygon object.

    Returns:
        A tuple (minx, miny, maxx, maxy) representing the bounding box.
    """
    return polygon.bounds
```
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