quatrotate

Rotate vector by quaternion

Syntax

n = quatrotate(q,r)

Description

n = quatrotate(q,r) calculates the rotated vector, n, for a quaternion, q, and a vector, r. If quaternions are not yet normalized, the function normalizes them.

Aerospace Toolbox uses quaternions that are defined using the scalar-first convention.

Examples

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Rotate a 1-by-3 Vector

Open Live Script

This example shows how to rotate a 1-by-3 vector by a 1-by-4 quaternion.

q = [1 0 1 0];
r = [1 1 1];
n = quatrotate(q, r)

n = 1×3

   -1.0000    1.0000    1.0000

Rotate Two 1-by-3 Vectors by a 1-by-4 Quaternion

Open Live Script

This example shows how to rotate two 1-by-3 vectors by a 1-by-4 quaternion.

q = [1 0 1 0];
r = [1 1 1; 2 3 4];
n = quatrotate(q, r)

n = 2×3

   -1.0000    1.0000    1.0000
   -4.0000    3.0000    2.0000

Rotate a 1-by-3 Vector by Two 1-by-4 Quaternions

Open Live Script

This example shows how to rotate a 1-by-3 vector by two 1-by-4 quaternions.

q = [1 0 1 0; 1 0.5 0.3 0.1];
r = [1 1 1];
n = quatrotate(q, r)

n = 2×3

   -1.0000    1.0000    1.0000
    0.8519    1.4741    0.3185

Rotate Multiple Vectors by Multiple Quaternions

Open Live Script

This example shows how to rotate multiple vectors by multiple quaternions.

q = [1 0 1 0; 1 0.5 0.3 0.1];
r = [1 1 1; 2 3 4];
n = quatrotate(q, r)

n = 2×3

   -1.0000    1.0000    1.0000
    1.3333    5.1333    0.9333

Input Arguments

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`q` — Quaternion
m-by-4 matrix | 1-by-4 array

Quaternion or set of quaternions, specified as an m-by-4 matrix containing m quaternions, or a single 1-by-4 quaternion. Each element must be real.

q must have its scalar number as the first column.

Data Types: double | single

`r` — Vector
m-by-3 matrix | 1-by-3 array

Vector or set of vectors to be rotated, specified as an m-by-3 matrix, containing m vectors, or a single 1-by-3 array. Each element must be real.

Data Types: double | single

Output Arguments

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`n` — Rotated vector
m-by-3 matrix

Rotated vector, returned as an m-by-3 matrix.

More About

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q

Quaternion q has the form:

$q = q_{0} + i q_{1} + j q_{2} + k q_{3}$

r

Vector r has the form:

$v = i v_{1} + j v_{2} + k v_{3}$

n

Rotated vector n has the form:

$v^{'} = [\begin{matrix} v_{1}^{'} \\ v_{2}^{'} \\ v_{3}^{'} \end{matrix}] = [\begin{matrix} (1 - 2 q_{2}^{2} - 2 q_{3}^{2}) & 2 (q_{1} q_{2} + q_{0} q_{3}) & 2 (q_{1} q_{3} - q_{0} q_{2}) \\ 2 (q_{1} q_{2} - q_{0} q_{3}) & (1 - 2 q_{1}^{2} - 2 q_{3}^{2}) & 2 (q_{2} q_{3} + q_{0} q_{1}) \\ 2 (q_{1} q_{3} + q_{0} q_{2}) & 2 (q_{2} q_{3} - q_{0} q_{1}) & (1 - 2 q_{1}^{2} - 2 q_{2}^{2}) \end{matrix}] [\begin{matrix} v_{1} \\ v_{2} \\ v_{3} \end{matrix}]$