r3f 1.1.4

A library for three-dimensional, reference-frame conversions

Rotation of 3-dimensional Frames

Functions

This library includes four sets of functions: general array checks, attitude-representation conversions, reference-frame conversions, and rotation matrix (direction cosine matrix) utilities. The following table shows all the attitude-representation conversions provided, where 'Vector' is short for 'rotation vector,' 'RPY is short for 'roll, pitch, and yaw,' and 'DCM' is short for 'direction cosine matrix':

To \ From	Vector	Axis-angle	RPY	DCM	Quaternion
Vector	-	x
Axis-angle	x	-	x	x	x
RPY		x	-	x	x
DCM		x	x	-	x
Quaternion		x	x	x	-

Because the conversion from rotation vector to axis-angle is so trivial, none of the other attitude representations have conversions to rotation vectors. Here is a list of the functions::

axis_angle_to_vector -> vec     
    (ax, ang, degs=False)
vector_to_axis_angle -> ax, ang 
    (vec, degs=False)
rpy_to_axis_angle -> ax, ang 
    (r, p, y, degs=False)
axis_angle_to_rpy -> r, p, y 
    (ax, ang, degs=False)
dcm_to_axis_angle -> ax, ang 
    (C, degs=False)
axis_angle_to_dcm -> C       
    (ax, ang, degs=False)
quat_to_axis_angle -> ax, ang 
    (q, degs=False)
axis_angle_to_quat -> q       
    (ax, ang, degs=False)
dcm_to_rpy -> r, p, y 
    (C, degs=False)
rpy_to_dcm -> C       
    (r, p, y, degs=False)
rot -> C       
    (ang, ax=2, degs=False)
quat_to_rpy -> r, p, y 
    (q, degs=False)
rpy_to_quat -> q       
    (r, p, y, degs=False)
quat_to_dcm -> C       
    (q)
dcm_to_quat -> q       
    (C)

In addition to the conversion from the z, y, x sequence of Euler angles to a DCM, the function rot is also provided for creating a DCM from a generic set of Euler angles in any desired sequence of axes. Although this rot function could be used, two additional functions are provided for generating rotation matrices: dcm_inertial_to_ecef and dcm_ecef_to_navigation.

This library includes all twelve possible conversions among the following four frames: ECEF (Earth-centered, Earth-fixed), geodetic (latitude, longitude, and height above ellipsoid), local-level tangent, and local-level curvilinear::

geodetic_to_ecef -> xe, ye, ze
    (lat, lon, hae, degs=None)
ecef_to_geodetic -> lat, lon, hae
    (xe, ye, ze, degs=None)
tangent_to_ecef -> xe, ye, ze
    (xt, yt, zt, xe0=None, ye0=None, ze0=None, ned=None)
ecef_to_tangent -> xt, yt, zt
    (xe, ye, ze, xe0=None, ye0=None, ze0=None, ned=None)
curvilinear_to_ecef -> xe, ye, ze
    (xc, yc, zc, xe0=None, ye0=None, ze0=None, ned=None)
ecef_to_curvilinear -> xc, yc, zc
    (xe, ye, ze, xe0=None, ye0=None, ze0=None, ned=None)
tangent_to_geodetic -> lat, lon, hae
    (xt, yt, zt, lat0=None, lon0=None, hae0=None, ned=None, degs=None)
geodetic_to_tangent -> xt, yt, zt
    (lat, lon, hae, lat0=None, lon0=None, hae0=None, ned=None, degs=None)
curvilinear_to_geodetic -> lat, lon, hae
    (xc, yc, zc, lat0=None, lon0=None, hae0=None, ned=None, degs=None)
geodetic_to_curvilinear -> xc, yc, zc
    (lat, lon, hae, lat0=None, lon0=None, hae0=None, ned=None, degs=None)
curvilinear_to_tangent -> xt, yt, zt
    (xc, yc, zc, lat0=None, lon0=None, hae0=None, ned=None, degs=None)
tangent_to_curvilinear -> xc, yc, zc
    (xt, yt, zt, xe0=None, ye0=None, ze0=None, ned=None)

Passive Rotations

Unless specifically otherwise stated, all rotations are interpreted as passive. This means they represent rotations of reference frames, not of vectors.

Vectorization

When possible, the functions are vectorized in order to handle processing batches of values. A set of scalars is a 1D array. A set of vectors is a 2D array, with each vector in a column. So, a (3, 7) array is a set of seven vectors, each with 3 elements. A set of matrices is a 3D array with each matrix in a stack. The first index is the stack number. So, a (5, 3, 3) array is a stack of five 3x3 matrices. Roll, pitch, and yaw are not treated as a vector but as three separate quantities. The same is true for latitude, longitude, and height above ellipsoid. A quaternion is passed around as an array.

Robustness

In general, the functions in this library check that the inputs are of the correct type and shape. They do not generally handle converting inputs which do not conform to the ideal type and shape. Generally, the allowed types are float, int, list, and np.ndarray.