pycvcam.FisheyeDistortion._cartesian_to_polar#

FisheyeDistortion._cartesian_to_polar(cartesian, dx=True)[source]#

Convert cartesian coordinates to polar coordinates.

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

\[\begin{split}\begin{bmatrix} r \\ \theta \\ \end{bmatrix} = \begin{bmatrix} \sqrt{x^2 + y^2} \\ \arctan2(y, x) \\ \end{bmatrix}\end{split}\]

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

\[\begin{split}J = \begin{bmatrix} \frac{\partial r}{\partial x} & \frac{\partial r}{\partial y} \\ \frac{\partial \theta}{\partial x} & \frac{\partial \theta}{\partial y} \\ \end{bmatrix} = \begin{bmatrix} \frac{x}{\sqrt{x^2 + y^2}} & \frac{y}{\sqrt{x^2 + y^2}} \\ -\frac{y}{x^2 + y^2} & \frac{x}{x^2 + y^2} \\ \end{bmatrix}\end{split}\]

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 cartesian is (n_points, 2) before calling this method.

Parameters:

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

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

Returns:

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

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

Return type:

Tuple[ndarray, ndarray | None]