tfg.geometry.transformation.axis_angle.rotate

Rotates a 3d point using an axis-angle by applying the Rodrigues' formula.

tfg.geometry.transformation.axis_angle.rotate(
    point: type_alias.TensorLike,
    axis: type_alias.TensorLike,
    angle: type_alias.TensorLike,
    name: str = 'axis_angle_rotate'
) -> tf.Tensor

Rotates a vector \(\mathbf{v} \in {\mathbb{R}^3}\) into a vector \(\mathbf{v}' \in {\mathbb{R}^3}\) using the Rodrigues' rotation formula:

\[\mathbf{v}'=\mathbf{v}\cos(\theta)+(\mathbf{a}\times\mathbf{v})\sin(\theta) +\mathbf{a}(\mathbf{a}\cdot\mathbf{v})(1-\cos(\theta)).\]

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

Args
point	A tensor of shape [A1, ..., An, 3], where the last dimension represents a 3d point to rotate.
axis	A tensor of shape [A1, ..., An, 3], where the last dimension represents a normalized axis.
angle	A tensor of shape [A1, ..., An, 1], where the last dimension represents an angle.
name	A name for this op that defaults to "axis_angle_rotate".

Returns
A tensor of shape [A1, ..., An, 3], where the last dimension represents a 3d point.

Raises
ValueError	If point, axis, or angle are of different shape or if their respective shape is not supported.