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bezier-2021.2.12
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مشاهده بیشترتوضیحات
Helper for Bézier Curves, Triangles, and Higher Order Objects
| ویژگی | مقدار |
|---|---|
| سیستم عامل | - |
| نام فایل | bezier-2021.2.12 |
| نام | bezier |
| نسخه کتابخانه | 2021.2.12 |
| نگهدارنده | [] |
| ایمیل نگهدارنده | [] |
| نویسنده | Danny Hermes |
| ایمیل نویسنده | daniel.j.hermes@gmail.com |
| آدرس صفحه اصلی | https://github.com/dhermes/bezier |
| آدرس اینترنتی | https://pypi.org/project/bezier/ |
| مجوز | Apache 2.0 |
``bezier``
==========
Helper for B |eacute| zier Curves, Triangles, and Higher Order Objects
|circle-build| |github-actions-build| |appveyor-build| |coverage|
|docs| |zenodo| |JOSS|
.. |eacute| unicode:: U+000E9 .. LATIN SMALL LETTER E WITH ACUTE
:trim:
This library provides:
* Support for B |eacute| zier `Curves`_
* Support for B |eacute| zier `Triangles`_
Dive in and take a look!
.. image:: https://raw.githubusercontent.com/dhermes/bezier/2021.2.12/docs/images/triangles6Q_and_7Q.png
:align: center
Why B |eacute| zier?
--------------------
A B |eacute| zier curve (and triangle, etc.) is a parametric curve
that uses the `Bernstein basis`_:
.. image:: https://raw.githubusercontent.com/dhermes/bezier/2021.2.12/docs/images/bernstein_basis.png
:align: center
to define a curve as a linear combination:
.. image:: https://raw.githubusercontent.com/dhermes/bezier/2021.2.12/docs/images/bezier_defn.png
:align: center
This comes from the fact that the weights sum to one:
.. image:: https://raw.githubusercontent.com/dhermes/bezier/2021.2.12/docs/images/sum_to_unity.png
:align: center
This can be generalized to higher order by considering three, four, etc.
non-negative weights that sum to one (in the above we have the two
non-negative weights ``s`` and ``1 - s``).
Due to their simple form, B |eacute| zier curves:
* can easily model geometric objects as parametric curves, triangles, etc.
* can be computed in an efficient and numerically stable way via
`de Casteljau's algorithm`_
* can utilize convex optimization techniques for many algorithms (such as
curve-curve intersection), since curves (and triangles, etc.)
are convex combinations of the basis
Many applications -- as well as the history of their development --
are described in
"The Bernstein polynomial basis: A centennial `retrospective`_",
for example;
* aids physical analysis using finite element methods (`FEM`_) on
isogeometric models by using geometric shape functions called
`NURBS`_ to represent data
* used in robust control of dynamic systems; utilizes convexity to
create a hull of curves
.. _retrospective: https://dx.doi.org/10.1016/j.cagd.2012.03.001
.. _Bernstein basis: https://en.wikipedia.org/wiki/Bernstein_polynomial
.. _de Casteljau's algorithm: https://en.wikipedia.org/wiki/De_Casteljau%27s_algorithm
.. _FEM: https://en.wikipedia.org/wiki/Finite_element_method
.. _NURBS: https://en.wikipedia.org/wiki/Non-uniform_rational_B-spline
Installing
----------
The ``bezier`` Python package can be installed with `pip`_:
.. code-block:: console
$ python -m pip install --upgrade bezier
$ python3.9 -m pip install --upgrade bezier
$ # To install optional dependencies, e.g. SymPy
$ python -m pip install --upgrade bezier[full]
To install a pure Python version (i.e. with no binary extension):
.. code-block:: console
$ BEZIER_NO_EXTENSION=true \
> python -m pip install --upgrade bezier --no-binary=bezier
``bezier`` is open-source, so you can alternatively grab the source
code from `GitHub`_ and install from source.
.. _pip: https://pip.pypa.io
.. _GitHub: https://github.com/dhermes/bezier/
Getting Started
---------------
For example, to create a curve:
.. code-block:: python
>>> nodes1 = np.asfortranarray([
... [0.0, 0.5, 1.0],
... [0.0, 1.0, 0.0],
... ])
>>> curve1 = bezier.Curve(nodes1, degree=2)
The intersection (points) between two curves can
also be determined:
.. code-block:: python
>>> nodes2 = np.asfortranarray([
... [0.0, 0.25, 0.5, 0.75, 1.0],
... [0.0, 2.0 , -2.0, 2.0 , 0.0],
... ])
>>> curve2 = bezier.Curve.from_nodes(nodes2)
>>> intersections = curve1.intersect(curve2)
>>> intersections
array([[0.31101776, 0.68898224, 0. , 1. ],
[0.31101776, 0.68898224, 0. , 1. ]])
>>> s_vals = np.asfortranarray(intersections[0, :])
>>> points = curve1.evaluate_multi(s_vals)
>>> points
array([[0.31101776, 0.68898224, 0. , 1. ],
[0.42857143, 0.42857143, 0. , 0. ]])
and then we can plot these curves (along with their
intersections):
.. code-block:: python
>>> import seaborn
>>> seaborn.set()
>>>
>>> ax = curve1.plot(num_pts=256)
>>> _ = curve2.plot(num_pts=256, ax=ax)
>>> lines = ax.plot(
... points[0, :], points[1, :],
... marker="o", linestyle="None", color="black")
>>> _ = ax.axis("scaled")
>>> _ = ax.set_xlim(-0.125, 1.125)
>>> _ = ax.set_ylim(-0.0625, 0.625)
.. image:: https://raw.githubusercontent.com/dhermes/bezier/2021.2.12/docs/images/curves1_and_13.png
:align: center
For API-level documentation, check out the B |eacute| zier Python
`package`_ documentation.
Development
-----------
To work on adding a feature or to run the functional tests, see the
`DEVELOPMENT doc`_ for more information on how to get
started.
Citation
--------
For publications that use ``bezier``, there is a `JOSS paper`_ that can be
cited. The following BibTeX entry can be used:
.. code-block:: rest
@article{Hermes2017,
doi = {10.21105/joss.00267},
url = {https://doi.org/10.21105%2Fjoss.00267},
year = {2017},
month = {Aug},
publisher = {The Open Journal},
volume = {2},
number = {16},
pages = {267},
author = {Danny Hermes},
title = {Helper for B{\'{e}}zier Curves, Triangles, and Higher Order Objects},
journal = {The Journal of Open Source Software}
}
A **particular** version of this library can be cited via a Zenodo DOI; see
a full `list by version`_.
.. _JOSS paper: https://joss.theoj.org/papers/10.21105/joss.00267
.. _list by version: https://zenodo.org/search?page=1&size=20&q=conceptrecid:%22838307%22&sort=-version&all_versions=True
License
-------
``bezier`` is made available under the Apache 2.0 License. For more
details, see `the LICENSE`_.
.. _Curves: https://bezier.readthedocs.io/en/2021.2.12/python/reference/bezier.curve.html
.. _Triangles: https://bezier.readthedocs.io/en/2021.2.12/python/reference/bezier.triangle.html
.. _package: https://bezier.readthedocs.io/en/2021.2.12/python/reference/bezier.html
.. _DEVELOPMENT doc: https://github.com/dhermes/bezier/blob/2021.2.12/DEVELOPMENT.rst
.. _the LICENSE: https://github.com/dhermes/bezier/blob/2021.2.12/LICENSE
.. |docs| image:: https://readthedocs.org/projects/bezier/badge/?version=2021.2.12
:target: https://bezier.readthedocs.io/en/2021.2.12/
:alt: Documentation Status
.. |circle-build| image:: https://raw.githubusercontent.com/dhermes/bezier/2021.2.12/docs/circleci-passing.svg?sanitize=true
:target: https://circleci.com/gh/dhermes/bezier/1900
:alt: CircleCI Build
.. |github-actions-build| image:: https://raw.githubusercontent.com/dhermes/bezier/2021.2.12/docs/macos-passing.svg?sanitize=true
:target: https://github.com/dhermes/bezier/actions/runs/564975428
:alt: GitHub Actions Build
.. |appveyor-build| image:: https://raw.githubusercontent.com/dhermes/bezier/2021.2.12/docs/appveyor-passing.svg?sanitize=true
:target: https://ci.appveyor.com/project/dhermes/bezier/build/1.0.1539.main
:alt: AppVeyor CI Build
.. |coverage| image:: https://s3.amazonaws.com/assets.coveralls.io/badges/coveralls_100.svg
:target: https://coveralls.io/builds/37113814
:alt: Code Coverage
.. |zenodo| image:: https://zenodo.org/badge/73047402.svg
:target: https://zenodo.org/badge/latestdoi/73047402
:alt: Zenodo DOI for ``bezier``
.. |JOSS| image:: https://joss.theoj.org/papers/10.21105/joss.00267/status.svg
:target: https://dx.doi.org/10.21105/joss.00267
:alt: "Journal of Open Source Science" DOI for ``bezier``
نحوه نصب
نصب پکیج whl bezier-2021.2.12:
pip install bezier-2021.2.12.whl
نصب پکیج tar.gz bezier-2021.2.12:
pip install bezier-2021.2.12.tar.gz