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# 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.

#### Note:

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

#### Note:

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.