normalize

Quaternion normalization

Syntax

quatNormalized = normalize(quat)

Description

quatNormalized = normalize(quat) normalizes the quaternion.

Given a quaternion of the form $$Q=a+b\text{i}+c\text{j}+d\text{k}$$, the normalized quaternion is defined as $$Q/\sqrt{a^2+b^2+c^2+d^2}$$.

Examples

Normalize Elements of Quaternion Vector

Quaternions can represent rotations when normalized. You can use normalize to normalize a scalar, elements of a matrix, or elements of a multi-dimensional array of quaternions. Create a column vector of quaternions, then normalize them.

quatArray = quaternion([1,2,3,4; ...
                        2,3,4,1; ...
                        3,4,1,2]);
quatArrayNormalized = normalize(quatArray)

quatArrayNormalized = 3×1 quaternion array
     0.18257 + 0.36515i + 0.54772j +  0.7303k
     0.36515 + 0.54772i +  0.7303j + 0.18257k
     0.54772 +  0.7303i + 0.18257j + 0.36515k

Input Arguments

quat — Quaternion to normalize

quaternion object | array of quaternion objects

Quaternion to normalize, specified as a quaternion object or an array of quaternion objects of any dimensionality.

Output Arguments

quatNormalized — Normalized quaternion

quaternion object | array of quaternion objects

Normalized quaternion, returned as a quaternion object or an array of quaternion objects of the same size as the quat argument.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2020b