pycvcam.FisheyeDistortion._polar_to_cartesian#

FisheyeDistortion._polar_to_cartesian(polar, dx=True)[source]#

Convert polar coordinates to cartesian coordinates.

The input polar points are given in the form \((r, \theta)\) with shape (n_points, 2), where \(r = \sqrt{x^2 + y^2}\) and \(\theta = \arctan2(y, x)\). The output cartesian points are given in the form \((x, y)\) with shape (n_points, 2).

\[\begin{split}\begin{bmatrix} x \\ y \\ \end{bmatrix} = \begin{bmatrix} r \cos(\theta) \\ r \sin(\theta) \\ \end{bmatrix}\end{split}\]

The jacobian with respect to the polar points is an array with shape (n_points, 2, 2).

\[\begin{split}J = \begin{bmatrix} \frac{\partial x}{\partial r} & \frac{\partial x}{\partial \theta} \\ \frac{\partial y}{\partial r} & \frac{\partial y}{\partial \theta} \\ \end{bmatrix} = \begin{bmatrix} \cos(\theta) & -r\sin(\theta) \\ \sin(\theta) & r\cos(\theta) \\ \end{bmatrix}\end{split}\]

Warning

This method is not intended to be used directly, but rather through the pycvcam.core.Transform.transform() method. Please ensure, the shape of the input polar is (n_points, 2) before calling this method.

Parameters:

  • polar (numpy.ndarray) – The polar points to be converted. Shape (n_points, 2).

  • dx (bool, optional) – If True, the jacobian with respect to the polar points is computed. Default is True.

Returns:

  • cartesian (numpy.ndarray) – The cartesian points. Shape (n_points, 2).

  • jacobian_dx (Optional[numpy.ndarray]) – The jacobian of the cartesian points with respect to the polar points. Shape (n_points, 2, 2) if dx is True, otherwise None.

Return type:

Tuple[ndarray, ndarray | None]