Angular distance in radians
Calculate Quaternion Distance
Calculate the quaternion distance between a single quaternion and each element of a vector of quaternions. Define the quaternions using Euler angles.
q = quaternion([0,0,0],"eulerd","ZYX","frame")
q = quaternion 1 + 0i + 0j + 0k
qArray = quaternion([0,45,0;0,90,0;0,180,0;0,-90,0;0,-45,0],"eulerd","ZYX","frame")
qArray = 5x1 quaternion array 0.92388 + 0i + 0.38268j + 0k 0.70711 + 0i + 0.70711j + 0k 6.1232e-17 + 0i + 1j + 0k 0.70711 + 0i - 0.70711j + 0k 0.92388 + 0i - 0.38268j + 0k
quaternionDistance = rad2deg(dist(q,qArray))
quaternionDistance = 5×1 45.0000 90.0000 180.0000 90.0000 45.0000
If both arguments to
dist are vectors, the quaternion distance is calculated between corresponding elements. Calculate the quaternion distance between two quaternion vectors.
angles1 = [30,0,15; ... 30,5,15; ... 30,10,15; ... 30,15,15]; angles2 = [30,6,15; ... 31,11,15; ... 30,16,14; ... 30.5,21,15.5]; qVector1 = quaternion(angles1,"eulerd","ZYX","frame"); qVector2 = quaternion(angles2,"eulerd","ZYX","frame"); rad2deg(dist(qVector1,qVector2))
ans = 4×1 6.0000 6.0827 6.0827 6.0287
Note that a quaternion represents the same rotation as its negative. Calculate a quaternion and its negative.
qPositive = quaternion([30,45,-60],"eulerd","ZYX","frame")
qPositive = quaternion 0.72332 - 0.53198i + 0.20056j + 0.3919k
qNegative = -qPositive
qNegative = quaternion -0.72332 + 0.53198i - 0.20056j - 0.3919k
Find the distance between the quaternion and its negative.
ans = 0
The components of a quaternion may look different from the components of its negative, but both expressions represent the same rotation.
quatA,quatB — Quaternions to calculate distance between
quaternion objects | arrays of
Quaternions to calculate distance between, specified as comma-separated
quaternion objects or arrays of
objects of any dimensionality.
quatB must have compatible sizes:
size(quatA) == size(quatB), or
numel(quatA) == 1, or
numel(quatB) == 1, or
[Adim1,…,AdimN] = size(quatA)and
[Bdim1,…,BdimN] = size(quatB), then for
i = 1:N, either
If one of the quaternion arguments contains only one quaternion, then this function returns the distances between that quaternion and every quaternion in the other argument.
distance — Angular distance (radians)
numeric scalar | numeric array
Angular distance in radians, returned as a numeric scalar or numeric
array. The dimensions are the maximum of the union of
dist function returns the angular distance between two
A quaternion may be defined by an axis (ub,uc,ud) and angle of rotation θq: .
Given a quaternion in the form, , where a is the real part, you can solve for the angle of q as .
Consider two quaternions, p and q, and the product . As p approaches q, the angle of z goes to 0, and z approaches the unit quaternion.
The angular distance between two quaternions can be expressed as .
quaternion data type syntax, the angular distance is
angularDistance = 2*acos(abs(parts(p*conj(q))));
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