Operators

# axis_angle_to_quat (Operator)

## Name

axis_angle_to_quat — Create a rotation quaternion.

## Signature

axis_angle_to_quat( : : AxisX, AxisY, AxisZ, Angle : Quaternion)

## Description

Quaternions are an extension of the complex numbers. The set of quaternions is given by . In HALCON, quaternions are represented by a tuple containing four elements: [x_{0},x_{1},x_{2},x_{3}].

Unit quaternions can be used to describe rotations. A quaternion is a unit quaternion if its norm is 1. A counterclockwise rotation around an unit vector v (AxisX, AxisY, AxisZ) by an angle a (Angle) can be described by the unit quaternion q =(cos(a/2), sin(a/2) v).

The operator axis_angle_to_quat can be used to create such a quaternion. To rotate a point using Quaternion use the operator quat_rotate_point_3d.

Note that two rotations can be concatenated using the operator quat_compose. Further, you can use a rotation quaternion to set the orientation of the 3D plot in set_paint.

## Attention

The operator axis_angle_to_quat does not check whether the vector (AxisX, AxisY, AxisZ) is of unit length (i.e. of length 1). If this is not the case, Quaternion will be no valid rotation quaternion.

## Parallelization

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Processed without parallelization.

## Parameters

AxisX (input_control)  real (real / integer)

X component of the rotation axis.

AxisY (input_control)  real (real / integer)

Y component of the rotation axis.

AxisZ (input_control)  real (real / integer)

Z component of the rotation axis.

Angle (input_control)  real (real / integer)

Quaternion (output_control)  quaternion (real / integer)

Rotation quaternion.

## Example (HDevelop)

```** Normalize a vector and create a rotation quaternion
Length := sqrt(AxisX*AxisX+AxisY*AxisY+AxisZ*AxisZ)
AxisX := AxisX/Length
AxisY := AxisY/Length
AxisZ := AxisZ/Length
axis_angle_to_quat (AxisX, AxisY, AxisZ, rad(90), Quaternion)
```