https://github.com/ashkarin/pyellipsoid

PyEllipsoid is the package for drawing and analysis of ellipsoids in 3D volumetric images (3D arrays).
https://github.com/ashkarin/pyellipsoid

Last synced: about 2 months ago
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PyEllipsoid is the package for drawing and analysis of ellipsoids in 3D volumetric images (3D arrays).

• Host: GitHub
• URL: https://github.com/ashkarin/pyellipsoid
• Owner: ashkarin
• License: mit
• Created: 2019-05-08T09:40:24.000Z (over 5 years ago)
• Default Branch: master
• Last Pushed: 2020-06-02T12:56:32.000Z (over 4 years ago)
• Last Synced: 2024-10-07T21:19:32.785Z (3 months ago)
• Language: Python
• Size: 18.6 KB
• Stars: 5
• Watchers: 2
• Forks: 2
• Open Issues: 0
• Metadata Files:
  • Readme: README.rst
  • License: LICENSE.txt

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README

        
================

PyEllipsoid

================

.. image:: https://travis-ci.org/ashkarin/pyellipsoid.svg?branch=master

    :target: https://travis-ci.org/ashkarin/pyellipsoid

**PyEllipsoid** is the package for drawing and analysis of ellipsoids in 3D volumetric images (3D arrays).

Installation

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

The easiest way to install the latest version is by using pip::

    $ pip install pyellipsoid

You may also use Git to clone the repository and install it manually::

    $ git clone https://github.com/ashkarin/pyellipsoid.git

    $ cd pyellipsoid

    $ python setup.py install

How to use

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

To draw an ellipsoid:

.. code-block:: python

  import numpy as np

  from pyellipsoid import drawing

  # Define an image shape, axis order is: Z, Y, X

  image_shape = (128, 128, 128)

  # Define an ellipsoid, axis order is: X, Y, Z

  ell_center = (64, 64, 64)

  ell_radii = (5, 50, 30)

  ell_angles = np.deg2rad([80, 30, 20]) # Order of rotations is X, Y, Z

  # Draw a 3D binary image containing the ellipsoid

  image = drawing.make_ellipsoid_image(image_shape, ell_center, ell_radii, ell_angles)

To compute inertia ellipsoid for given ellipsoid image:

.. code-block:: python

  import numpy as np

  from pyellipsoid import drawing, analysis

  # Draw a 3D binary image containing an ellipsoid

  image_shape = (128, 128, 128)

  ell_center = (64, 64, 64)

  ell_radii = (5, 50, 30)

  ell_angles = np.deg2rad([80, 30, 20])

  image = drawing.make_ellipsoid_image(image_shape, ell_center, ell_radii, ell_angles)

  # Compute inertia ellipsoid

  points = analysis.sample_random_points(image)

  inertia_ellipsoid = analysis.compute_inertia_ellipsoid(points)

To rotate axes and find relative rotation between the original and rotated axes:

.. code-block:: python

  import numpy as np

  from pyellipsoid import geometry

  original_axes = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])

  rot_angles = np.deg2rad([0, 0, 45]) # Rotate around Z-axis by 45 deg

  # Build rotation matrix and rotate the axes

  rotm = geometry.build_rotation_matrix(*rot_angles)

  rotated_axes = np.dot(rotm, np.transpose(original_axes)).T

  # Find relative rotation

  rel_rotm = geometry.find_relative_axes_rotation(original_axes, rotated_axes)

  # Validate relative rotation matrix

  rel_rotated_axes = np.dot(rel_rotm, np.transpose(original_axes)).T

  assert(np.all(rotated_axes == rel_rotated_axes))

  # Compute rotation angles

  # Please note, that these angles might differ from rot_angles!

  rel_rot_angles = geometry.rotation_matrix_to_angles(rel_rotm)

  print(np.rad2deg(rel_rot_angles))