# Source code for dclab.features.volume

```#!/usr/bin/python
# -*- coding: utf-8 -*-
"""Computation of volume for RT-DC measurements based on a rotation
of the contours"""
from __future__ import division, print_function, unicode_literals
import numpy as np

[docs]def get_volume(cont, pos_x, pos_y, pix):
"""Calculate the volume of a polygon revolved around an axis

The volume estimation assumes rotational symmetry.
Green`s theorem and the Gaussian divergence theorem allow to
formulate the volume as a line integral.

Parameters
----------
cont: ndarray or list of ndarrays of shape (N,2)
A 2D array that holds the contour of an event [px]
e.g. obtained using `mm.contour` where  `mm` is an instance
of `RTDCBase`. The first and second columns of `cont`
correspond to the x- and y-coordinates of the contour.
pos_x: float or ndarray of length N
The x coordinate(s) of the centroid of the event(s) [µm]
e.g. obtained using `mm.pos_x`
pos_y: float or ndarray of length N
The y coordinate(s) of the centroid of the event(s) [µm]
e.g. obtained using `mm.pos_y`
px_um: float
The detector pixel size in µm.
e.g. obtained using: `mm.config["image"]["pix size"]`

Returns
-------
volume: float or ndarray
volume in um^3

Notes
-----
The computation of the volume is based on a full rotation of the
upper and the lower halves of the contour from which the
average is then used.

The volume is computed radially from the the center position
given by (`pos_x`, `pos_y`). For sufficiently smooth contours,
such as densely sampled ellipses, the center position does not
play an important role. For contours that are given on a coarse
grid, as is the case for RT-DC, the center position must be
given.

References
----------
- Halpern et al. :cite:`Halpern2002`, chapter 5, Section 5.4
- This is a translation from a `Matlab script
<http://de.mathworks.com/matlabcentral/fileexchange/36525-volrevolve>`_
by Geoff Olynyk.
"""
if np.isscalar(pos_x):
cont = [cont]
ret_list = False
else:
ret_list = True

# Convert input to 1D arrays
pos_x = np.atleast_1d(pos_x)
pos_y = np.atleast_1d(pos_y)

if pos_x.size != pos_y.size:
raise ValueError("Size of `pos_x` and `pos_y` must match!")

if pos_x.size > 1 and len(cont) <= 1:
raise ValueError("Number of given contours too small!")

# results are stored in a separate array initialized with nans
v_avg = np.zeros_like(pos_x, dtype=float)*np.nan

# v_avg has the shape of `pos_x`. We are iterating over the smallest
# length for `cont` and `pos_x`.
for ii in range(min(len(cont), pos_x.shape)):
# If the contour has less than 4 pixels, the computation will fail.
# In that case, the value np.nan is already assigned.
cc = cont[ii]
if cc.shape >= 4:
# Center contour coordinates with given centroid
contour_x = cc[:, 0] - pos_x[ii] / pix
contour_y = cc[:, 1] - pos_y[ii] / pix
# Make sure contour is counter-clockwise
contour_x, contour_y = counter_clockwise(contour_x, contour_y)
# Which points are below the x-axis? (y<0)?
ind_low = np.where(contour_y < 0)
# These points will be shifted up to y=0 to build an x-axis
# (wont contribute to lower volume).
contour_y_low = np.copy(contour_y)
contour_y_low[ind_low] = 0
# Which points are above the x-axis? (y>0)?
ind_upp = np.where(contour_y > 0)
# These points will be shifted down to y=0 to build an x-axis
# (wont contribute to upper volume).
contour_y_upp = np.copy(contour_y)
contour_y_upp[ind_upp] = 0
# Move the contour to the left
Z = contour_x
# Last point of the contour has to overlap with the first point
Z = np.hstack([Z, Z])
Zp = Z[0:-1]
dZ = Z[1:]-Zp

# Last point of the contour has to overlap with the first point
contour_y_low = np.hstack([contour_y_low, contour_y_low])
contour_y_upp = np.hstack([contour_y_upp, contour_y_upp])

vol_low = _vol_helper(contour_y_low, Z, Zp, dZ, pix)
vol_upp = _vol_helper(contour_y_upp, Z, Zp, dZ, pix)

v_avg[ii] = (vol_low + vol_upp) / 2

if not ret_list:
# Do not return a list if the input contour was not in a list
v_avg = v_avg

return v_avg

def counter_clockwise(cx, cy):
"""Put contour coordinates into counter-clockwise order

Parameters
----------
cx, cy: 1d ndarrays
The x- and y-coordinates of the contour

Returns
-------
cx_cc, cy_cc:
The x- and y-coordinates of the contour in
counter-clockwise orientation.
"""
# test orientation
angles = np.unwrap(np.arctan2(cy, cx))
return cx[::-1], cy[::-1]
else:
return cx, cy

def _vol_helper(contour_y, Z, Zp, dZ, pix):
# Instead of x and y, describe the contour by a Radius vector R and y
# The Contour will be rotated around the x-axis. Therefore it is
# Important that the Contour has been shifted onto the x-Axis
R = np.sqrt(Z**2 + contour_y**2)
Rp = R[0:-1]
dR = R[1:] - Rp
# 4 volume parts
v1 = dR * dZ * Rp
v2 = 2 * dZ * Rp**2
v3 = -1 * dR**2 * dZ
v4 = -2 * dR * Rp * Zp

V = (np.pi/3) * (v1 + v2 + v3 + v4)
vol = np.sum(V) * pix**3
return abs(vol)
```