#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Part of the PsychoPy library
# Copyright (C) 2002-2018 Jonathan Peirce (C) 2019-2025 Open Science Tools Ltd.
# Distributed under the terms of the GNU General Public License (GPL).
"""Functions and classes related to coordinate system conversion
"""
import numpy
from numpy import radians
[docs]
def cart2pol(x, y, units='deg'):
"""Convert from cartesian to polar coordinates.
:usage:
theta, radius = cart2pol(x, y, units='deg')
units refers to the units (rad or deg) for theta that should be returned
"""
radius = numpy.hypot(x, y)
theta = numpy.arctan2(y, x)
if units in ('deg', 'degs'):
theta = theta * 180 / numpy.pi
return theta, radius
[docs]
def pol2cart(theta, radius, units='deg'):
"""Convert from polar to cartesian coordinates.
usage::
x,y = pol2cart(theta, radius, units='deg')
"""
if units in ('deg', 'degs'):
theta = theta * numpy.pi / 180.0
xx = radius * numpy.cos(theta)
yy = radius * numpy.sin(theta)
return xx, yy
[docs]
def cart2sph(z, y, x):
"""Convert from cartesian coordinates (x,y,z) to spherical (elevation,
azimuth, radius). Output is in degrees.
usage:
array3xN[el,az,rad] = cart2sph(array3xN[x,y,z])
OR
elevation, azimuth, radius = cart2sph(x,y,z)
If working in DKL space, z = Luminance, y = S and x = LM
"""
width = len(z)
elevation = numpy.empty([width, width])
radius = numpy.empty([width, width])
azimuth = numpy.empty([width, width])
radius = numpy.sqrt(x**2 + y**2 + z**2)
azimuth = numpy.arctan2(y, x)
# Calculating the elevation from x,y up
elevation = numpy.arctan2(z, numpy.sqrt(x**2 + y**2))
# convert azimuth and elevation angles into degrees
azimuth *= 180.0 / numpy.pi
elevation *= 180.0 / numpy.pi
sphere = numpy.array([elevation, azimuth, radius])
sphere = numpy.rollaxis(sphere, 0, 3)
return sphere
[docs]
def sph2cart(*args):
"""Convert from spherical coordinates (elevation, azimuth, radius)
to cartesian (x,y,z).
usage:
array3xN[x,y,z] = sph2cart(array3xN[el,az,rad])
OR
x,y,z = sph2cart(elev, azim, radius)
"""
if len(args) == 1: # received an Nx3 array
elev = args[0][0, :]
azim = args[0][1, :]
radius = args[0][2, :]
returnAsArray = True
elif len(args) == 3:
elev = args[0]
azim = args[1]
radius = args[2]
returnAsArray = False
z = radius * numpy.sin(radians(elev))
x = radius * numpy.cos(radians(elev)) * numpy.cos(radians(azim))
y = radius * numpy.cos(radians(elev)) * numpy.sin(radians(azim))
if returnAsArray:
return numpy.asarray([x, y, z])
else:
return x, y, z
