QuatEnum_EulerAnglesType

Core and matricesclassOpenCV 5.0.0

import { QuatEnum_EulerAnglesType } from '@banou/opencv-wasm'

Use after await initOpenCV(). See the initialization and named imports guide.

ARGUMENTSConstructor or factory

CLASSQuatEnum_EulerAnglesType

RETURN TYPEOwned native handle

Call structure. A void return can still write to destination arguments. The parameter descriptions define inputs, outputs and ownership.

Native object: release it with using or delete(). Factories can return null; check before calling methods.

Enum of Euler angles type.

Without considering the possibility of using two different conversions for the definition of the rotation axes , there exists twelve possible sequences of rotation axes, divided into two groups:

Proper Euler angles (Z-X-Z, X-Y-X, Y-Z-Y, Z-Y-Z, X-Z-X, Y-X-Y)
Tait-Bryan angles (X-Y-Z, Y-Z-X, Z-X-Y, X-Z-Y, Z-Y-X, Y-X-Z).

The three elemental rotations may be extrinsic (rotations about the axes xyz of the original coordinate system, which is assumed to remain motionless), or intrinsic(rotations about the axes of the rotating coordinate system XYZ, solidary with the moving body, which changes its orientation after each elemental rotation).

Extrinsic and intrinsic rotations are relevant.

The definition of the Euler angles is as following,

\theta_1 represents the first rotation angle,
\theta_2 represents the second rotation angle,
\theta_3 represents the third rotation angle.

For intrinsic rotations in the order of X-Y-Z, the rotation matrix R can be calculated by:

R =X(\theta_1) Y(\theta_2) Z(\theta_3)

For extrinsic rotations in the order of X-Y-Z, the rotation matrix R can be calculated by:

R =Z({\theta_3}) Y({\theta_2}) X({\theta_1})

where

X({\theta_1})={\begin{bmatrix}1&0&0\\0&\cos {\theta_1} &-\sin {\theta_1} \\0&\sin {\theta_1} &\cos {\theta_1} \\\end{bmatrix}},
Y({\theta_2})={\begin{bmatrix}\cos \theta_{2}&0&\sin \theta_{2}\\0&1 &0 \\\ -sin \theta_2& 0&\cos \theta_{2} \\\end{bmatrix}},
Z({\theta_3})={\begin{bmatrix}\cos\theta_{3} &-\sin \theta_3&0\\\sin \theta_3 &\cos \theta_3 &0\\0&0&1\\\end{bmatrix}}.

The function is designed according to this set of conventions:

Right handed reference frames are adopted, and the right hand rule is used to determine the sign of angles.
Each matrix is meant to represent an active rotation (the composing and composed matrices are supposed to act on the coordinates of vectors defined in the initial fixed reference frame and give as a result the coordinates of a rotated vector defined in the same reference frame).
For \theta_1 and \theta_3, the valid range is (−π, π].

For \theta_2, the valid range is [−π/2, π/2] or [0, π].

For Tait-Bryan angles, the valid range of \theta_2 is [−π/2, π/2]. When transforming a quaternion to Euler angles, the solution of Euler angles is unique in condition of \theta_2 \in (−π/2, π/2) . If \theta_2 = −π/2 or \theta_2 = π/2, there are infinite solutions. The common name for this situation is gimbal lock. For Proper Euler angles,the valid range of \theta_2 is in [0, π]. The solutions of Euler angles are unique in condition of \theta_2 \in (0, π) . If \theta_2 =0 or \theta_2 =π , there are infinite solutions and gimbal lock will occur.

QuatEnum_EulerAnglesType

Constructors and members