I3Position

The I3Position class stores a position in cartesian coordinates. It can be initialized in either cartesian, cylindrical, or spherical coordinates.

• Cartesian: x, y, z

• Spherical: r, θ, φ

• Cylindrical: ρ, φ, z

The class allows for rotation of coordinates around x, y, and z axis and also transforms between the different coordinate parametrizations. Additionally, it computes the magnitude of the position vector and the cross product of two position vectors.

Examples

For initialization and transformation between coordinate systems:

>>> # initialization in cartesian coordinates.
>>> # dataclasses.I3Position(x, y, z, RefFrame)
>>> # Default RefFrame (reference frame) is the cartesian: dataclasses.I3Position.car = dataclasses.RefFrame.car
>>> position = dataclasses.I3Position(1, 2, 3)
>>> # cartesian coordinates
>>> position.x
1.0
>>> position.y
2.0
>>> position.z
3.0

>>> # spherical coordinates
>>> position.theta
0.6405223126794245
>>> position.phi
1.1071487177940904
>>> position.r
3.7416573867739413

>>> # cylindrical coordinates
>>> position.rho
2.2360679774997894
>>> position.phi
1.1071487177940904
>>> position.z
3.0

>>> # initialize a position in a cylindrical coordinates (cylindrical reference frame):
>>> position2 = dataclasses.I3Position(4, 5, 6, dataclasses.I3Position.cyl)
>>> position2 # the position itself is still by standard given in cartesian coordinates
I3Position(1.13465,-3.8357,6)
>>> position2.x
1.134648741852905
>>> position2.rho
4.0
>>> position2.phi
5.0
>>> position2.z
6.0

>>> # initialize in spherical coordinates:
>>> position2 = dataclasses.I3Position(4, 5, 6, dataclasses.I3Position.sph)
>>> position2
I3Position(-3.68292,1.07175,1.13465)
>>> position2.r
4.0
>>> position2.theta
5.0
>>> position2.phi
6.0

Operations on I3Position:

>>> # calculate magnitude = sqrt(x^2 + y^2 + z^2)
>>> position
I3Position(1,2,3)
>>> position.magnitude
3.7416573867739413
>>> # calculate x^2 + y^2 + z^2
>>> position.mag2
14.0

>>> # cross product between two positions vectors: position and position2
>>> position2 = dataclasses.I3Position(4, 5, 6)
>>> position.cross(position2)
I3Position(-3,6,-3)

Rotation of position vector with x, y, or z as rotation axis around an angle a given in radians:

>>> # rotation of position vector around an angle a in radians
>>> position
I3Position(1,2,3)
>>> a = 3.1415 # rotate 180°
>>> position.rotate_x(a) # rotate 180° around x axis
>>> position
I3Position(1,-2.00028,-2.99981)
>>> position.rotate_x(a)
>>> position
I3Position(1,2.00056,2.99963)
>>> position.rotate_x(-2 * a) # rotate -360° around x axis
>>> position
I3Position(1,2,3)
>>> position.rotate_y(a) # rotate 180° around y axis
>>> position
I3Position(-0.999722,2,-3.00009)
>>> position.rotate_z(a) # rotate 180° around z axis
>>> position
I3Position(0.999537,-2.00009,-3.00009)