tfg.geometry.transformation.quaternion.from_euler_with_small_angles_approximation

Converts small Euler angles to quaternions.

tfg.geometry.transformation.quaternion.from_euler_with_small_angles_approximation(
    angles, name=None
)

Under the small angle assumption,

$$\sin(x)$$

and

$$\cos(x)$$

can be approximated by their second order Taylor expansions, where

$$\sin(x) \approx x$$

and

$$\cos(x) \approx 1 - \frac{x^2}{2}$$

. In the current implementation, the smallness of the angles is not verified.

Uses the z-y-x rotation convention (Tait-Bryan angles).

In the following, A1 to An are optional batch dimensions.

Args
`angles`	A tensor of shape `[A1, ..., An, 3]`, where the last dimension represents the three Euler angles. `[..., 0]` is the angle about `x` in radians, `[..., 1]` is the angle about `y` in radians and `[..., 2]` is the angle about `z` in radians. name: A name for this op that defaults to "quaternion_from_euler".

Returns
A tensor of shape `[A1, ..., An, 4]`, where the last dimension represents a normalized quaternion.

Raises
`ValueError`	If the shape of `angles` is not supported.

Args