# 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:

```
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:

```
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:

```
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))
```