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alpha-shapes-0.0.1
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مشاهده بیشتر
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مشاهده بیشتر
تبلیغات ما
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مشاهده بیشتر
تبلیغات ما
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مشاهده بیشترتوضیحات
reconstruct the shape of a 2D point cloud.
| ویژگی | مقدار |
|---|---|
| سیستم عامل | OS Independent |
| نام فایل | alpha-shapes-0.0.1 |
| نام | alpha-shapes |
| نسخه کتابخانه | 0.0.1 |
| نگهدارنده | [] |
| ایمیل نگهدارنده | [] |
| نویسنده | Panagiotis Zestanakis |
| ایمیل نویسنده | panosz@gmail.com |
| آدرس صفحه اصلی | https://github.com/panosz/alpha_shapes |
| آدرس اینترنتی | https://pypi.org/project/alpha-shapes/ |
| مجوز | - |
# alpha_shapes
A Python package for reconstructing the shape of a 2D point cloud on the plane.
## Table of Contents
* **[Introduction](#introduction)**
* **[Usage](#usage)**
* **[Features](#features)**
* **[Optimization](#optimization)**
* **[Normalization](#normalization)**
* **[Inspiration](#inspiration)**
## Introduction
Given a finite set of points (or point cloud) in the Euclidean plane, [alpha shapes](https://en.wikipedia.org/wiki/Alpha_shape) are members of a family of closed polygons on the 2D plane associated with the shape of this point cloud. Each alpha shape is associated with a single non negative parameter **α**.
Intuitively an alpha shape can be conceptualized as follows. Imagine carving out the plane using a cookie scoop of radius 1/**α**, without removing any of the points in the point cloud. The shape that remains **is** the shape of the point cloud. If we replace the arc-like edges, due to the circular rim of the scoop, with straight segments, we are left with the alpha shape of parameter **α**.
## Usage
Imports:
```python
import matplotlib.pyplot as plt
from descartes import PolygonPatch
from alpha_shapes.alpha_shapes import Alpha_Shaper
```
Define a set of points:
```python
points = [(0., 0.), (0., 1.), (1., 1.1),
(1., 0.), (0.25, 0.15), (0.65, 0.45),
(0.75, 0.75), (0.5, 0.5), (0.5, 0.25),
(0.5, 0.75), (0.25, 0.5), (0.75, 0.25),
(0., 2.), (0., 2.1), (1., 2.1),
(0.5, 2.5), (-0.5, 1.5), (-0.25, 1.5),
(-0.25, 1.25), (0, 1.25), (1.5, 1.5),
(1.25, 1.5), (1.25, 1.25), (1, 1.25),
(0.5, 2.25), (1., 2.), (0.25, 2.15),
(0.65, 2.45), (0.75, 2.75), (0.5, 2.25),
(0.5, 2.75), (0.25, 2.5), (0.75, 2.25)]
```
Create the alpha shaper:
```python
shaper = Alpha_Shaper(points)
```
For the alpha shape to be calculated, the user must choose a value for the `alpha` parameter.
Here, let us set `alpha` to 3.0:
```python
alpha = 3.0
alpha_shape = shaper.get_shape(alpha=alpha)
```
Visualize the result:
```python
fig, (ax0, ax1) = plt.subplots(1, 2)
ax0.scatter(*zip(*points))
ax0.set_title('data')
ax1.scatter(*zip(*points))
ax1.add_patch(PolygonPatch(alpha_shape, alpha=0.2, color='r'))
ax1.set_title(f"$\\alpha={alpha:.2}$")
for ax in (ax0, ax1):
ax.set_aspect('equal')
plt.show()
```
The resulting shape is only a rough outline of the figure formed by the point set.
However, increasing the value of `alpha` to 4.5 yields much better results.
```python
alpha = 4.5
alpha_shape = shaper.get_shape(alpha=alpha)
```
## Features
### Optimization
A satisfactory calculation of the alpha shape requires a successful guess of the alpha parameter. While trial and error might work well in some cases, users can let the `Alpha_Shaper` choose a value for them. That is what the `optimize` method is about.
```python
>>> alpha_opt, alpha_shape = shaper.optimize()
>>> alpha_opt
5.331459512629295
```
The optimize method runs efficiently for relatively large point clouds. Here we calculate the optimal alpha shape of an ensemble of 1000 random points uniformly distributed on the unit square.
```python
>>> from time import time
>>> points = np.random.random((1000, 2))
>>> alpha_shaper = Alpha_Shaper(points)
>>> ts = time()
>>> alpha_opt, alpha_shape = alpha_shaper.optimize()
>>> te = time()
>>> print(f'optimization took: {te-ts:.2} sec')
optimization took: 0.41 sec
```
### Normalization
Before calculating the alpha shape, Alpha_Shaper normalizes by default the input points so that they are distributed on the unit square. When there is a scale separation along the x and y direction, deactivating this feature may yield surprising results.
```python
import numpy as np
# Scale the points along the x-dimension
x_scale = 1e-3
points = np.array(points)
points[:, 0] *= x_scale
# Create the alpha shape without accounting for the x and y scale separation
unnormalized_shaper = Alpha_Shaper(points, normalize=False)
_, alpha_shape_unscaled = unnormalized_shaper.optimize()
# If the characteristic scale along each axis varies significantly,
# it may make sense to turn on the `normalize` option.
shaper = Alpha_Shaper(points, normalize=True)
_, alpha_shape_scaled = shaper.optimize()
# Scale the points along the x-dimension
x_scale = 1e-3
points = np.array(points)
points[:, 0] *= x_scale
# Create the alpha shape without accounting for the x and y scale separation
unnormalized_shaper = Alpha_Shaper(points, normalize=False)
_, alpha_shape_unscaled = unnormalized_shaper.optimize()
# If the characteristic scale along each axis varies significantly,
# it may make sense to turn on the `normalize` option.
shaper = Alpha_Shaper(points, normalize=True)
_, alpha_shape_scaled = shaper.optimize()
```
## Inspiration
This library is inspired by the [alphashape](https://github.com/bellockk/alphashape) library.
نیازمندی
| مقدار | نام |
|---|---|
| - | numpy |
| - | shapely |
| - | matplotlib |
زبان مورد نیاز
| مقدار | نام |
|---|---|
| >=3.7 | Python |
نحوه نصب
نصب پکیج whl alpha-shapes-0.0.1:
pip install alpha-shapes-0.0.1.whl
نصب پکیج tar.gz alpha-shapes-0.0.1:
pip install alpha-shapes-0.0.1.tar.gz