r3f 1.0.1

A library for three-dimensional, reference-frame conversions

Rotation of 3-dimensional Frames

Conversions

This library includes three sets of functions: general array checks, attitude-representation conversions, and reference-frame conversions. 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.

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.

This library also includes various conversions among Earth-specific and navigation frames:

To \ From	e	d	t	c
e (ECEF)	-	x	x
d (geodetic)	x	-		x
t (tangent)	x		-
c (curvilinear)		x		-

Passive Rotations

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 (2, 5, 5) array is a stack of two 5x5 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.

Provided Functions

The following functions are provided:

Attitude-representation Conversions

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

Reference-frame Conversions

Returns	Name	Parameters
xe, ye, ze	geodetic_to_ecef	lat, lon, hae, degs=False
lat, lon, hae	ecef_to_geodetic	xe, ye, ze, degs=False
xt, yt, zt	ecef_to_tangent	xe, ye, ze, xe0, ye0, ze0, ned=True
xe, ye, ze	tangent_to_ecef	xt, yt, zt, xe0, ye0, ze0, ned=True
xc, yc, zc	geodetic_to_curlin	lat, lon, hae, lat0, lon0, hae0,
		ned=True, degs=False
lat, lon, hae	curlin_to_geodetic	xc, yc, zc, lat0, lon0, hae0,
		ned=True, degs=False