quatinterp

Quaternion interpolation between two quaternions

Syntax

qi=quatinterp(p,q,f,method)

Description

qi=quatinterp(p,q,f,method) calculates the quaternion interpolation between two normalized quaternions p and q by interval fraction f.

p and q are the two extremes between which the function calculates the quaternion.

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

Examples

Quaternion Interpolation Between Two Quaternions

This example shows how to use interpolation to calculate quaternion between two quaternions p=[1.0 0 1.0 0] and q=[-1.0 0 1.0 0] using the SLERP method. This example uses the quatnormalize function to first-normalize the two quaternions to pn and qn.

pn = quatnormalize([1.0 0 1.0 0])

pn = 1×4

    0.7071         0    0.7071         0

qn = quatnormalize([-1.0 0 1.0 0])

qn = 1×4

   -0.7071         0    0.7071         0

qi = quatinterp(pn,qn,0.5,'slerp')

qi = 1×4

     0     0     1     0

Input Arguments

p — First-normalized quaternion

M-by-4 matrix

First normalized quaternion for which to calculate the interpolation, specified as an M-by-4 matrix containing M quaternions. This quaternion must be a normalized quaternion.

Data Types: double

q — Quaternions

M-by-4 matrix

Second normalized quaternion for which to calculate the interpolation, specified as an M-by-4 matrix containing M quaternions. This quaternion must be a normalized quaternion.

Data Types: double

f — Interval fraction

M-by-1 matrix

Interval fraction by which to calculate the quaternion interpolation, specified as an M-by-1 matrix containing M fractions (scalar). f varies between 0 and 1. It represents the intermediate rotation of the quaternion to be calculated.

q_i=(q_p,q_n,q_f), where:

• If f equals 0, q_i equals q_p.

• If f is between 0 and 1, q_i equals method.

• If f equals 1, q_i equals q_n.

Data Types: double

method — Quaternion interpolation method

'slerp' (default) | 'lerp' | 'nlerp'

Quaternion interpolation method to calculate the quaternion interpolation. These methods have different rotational velocities, depending on the interval fraction. For more information on interval fractions, see [1].

• slerp

  Quaternion slerp. Spherical linear quaternion interpolation method. This method is most accurate, but also most computation intense.

  $$Slerp(p,q,h)=p{(p^{*}q)}^h$$ with $$h\in [0,1].$$

• lerp

  Quaternion lerp. Linear quaternion interpolation method. This method is the quickest, but is also least accurate. The method does not always generate normalized output.

  $$LERP(p,q,h)=p(1-h)+qh$$ with $$h\in [0,1].$$

• nlerp

  Normalized quaternion linear interpolation method.

  With $$r=LERP(p,q,h),$$ $$NLERP(p,q,h)=\frac{r}{\left|r\right|}.$$

Data Types: char

Output Arguments

qi — Interpolation of quaternion

M-by-4 matrix

Interpolation of quaternion.

References

[1] ==Dam, Erik B., Martin Koch, Martin Lillholm. "Quaternions, Interpolation, and Animation." University of Copenhagen, København, Denmark, 1998.

Version History

Introduced in R2016a