Quaternion Interpolation

Quaternion interpolation between two quaternions

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Libraries:
Aerospace Blockset / Utilities / Math Operations

Description

The Quaternion Interpolation block calculates the quaternion interpolation between two normalized quaternions by an interval fraction. Aerospace Blockset™ uses quaternions that are defined using the scalar-first convention. Select the interpolation method from SLERP, LERP, or NLERP. For equations used for the interpolation methods, see Algorithms.

The two normalized quaternions are the two extremes between which the block calculates the quaternion.

Ports

Input

q₀ — First normalized quaternion

4-by-1 vector | 1-by-4 vector

First normalized quaternion for which to calculate the interpolation. This quaternion must be a normalized quaternion

Data Types: double

q₁ — Second normalized quaternion

4-by-1 vector | 1-by-4 vector

Second normalized quaternion for which to calculate the interpolation, specified as a 4-by-1 vector or 1-by-4 vector. This quaternion must be a normalized quaternion.

Data Types: double

f — Interval fraction

scalar

Interval fraction by which to calculate the quaternion interpolation. This value varies between 0 and 1. It represents the intermediate rotation of the quaternion to be calculated. This fraction affects the interpolation method rotational velocities.

Dependencies

The interval fraction affects the rotational velocities of the interpolation methods for the Methods parameter. For more information on interval fractions, see [1].

Data Types: double

Output

q_f — Natural logarithm

vector

Natural logarithm of quaternion, returned as a vector.

Data Types: double

Parameters

Methods — Quaternion interpolation method

SLERP (default) | LERP | NLERP

Quaternion interpolation method to calculate the quaternion interpolation, specified as:

• SLERP

  Quaternion slerp. Spherical linear quaternion interpolation method.

• LERP

  Quaternion lerp. Linear quaternion interpolation method.

• NLERP

  Normalized quaternion linear interpolation method.

Dependencies

These methods have different rotational velocities, depending on the interval fraction from input port f. For more information on interval fractions, see [1].

Programmatic Use

Block Parameter: method

Type: character vector

Values: 'SLERP' | 'LERP' | 'NLERP'

Default: 'SLERP'

Action for out-of-range input — Out-of-range block behavior

None (default) | Warning | Error

Out-of-range block behavior, specified as:

Action	Description
None	No action.
Warning	Warning in the Diagnostic Viewer, model simulation continues.
Error (default)	Error in the Diagnostic Viewer, model simulation stops.

Programmatic Use

Block Parameter: action

Type: character vector

Values: 'None' | 'Warning' | 'Error'

Default: 'Warning'

Algorithms

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

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

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

References

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

Extended Capabilities

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

Version History

Introduced in R2016a