MagnetReferencingCalcs

Description

The fit_circle_3D function performs a fitting process to find a 3D circle that best represents a set of 3D points. The process involves the following steps:

1. Fitting a Plane:
   Initially, a plane is fitted to the given 3D points using the fit_plane function. This plane represents the best linear fit to the data.

2. Point Projection:
   The points are then projected onto the fitted plane. The projection of a point ((X, Y, Z)) onto a plane with coefficients ((a, b, c, d)) can be calculated as follows:

   [ x_{\text{proj}} = X - \frac{a(X + bY + cZ + d)}{a^2 + b^2 + c^2} ]

   [ y_{\text{proj}} = Y - \frac{b(X + bY + cZ + d)}{a^2 + b^2 + c^2} ]

   [ z_{\text{proj}} = Z - \frac{c(X + bY + cZ + d)}{a^2 + b^2 + c^2} ]

3. Rotation Transformation:
   A rotation transformation is applied to align the plane with the XY plane. This transformation ensures that the normal vector of the plane becomes parallel to the Z-axis. The rotation matrix ( R ) for aligning the plane's normal vector ((a, b, c)) with the Z-axis ((0, 0, 1)) can be computed using the function rotation_matrix_from_vectors and applied to each point.

4. Point-to-Point Distance Check:
   The distances between the original and transformed points are compared using the compare_distances function. This check helps identify any discrepancies introduced during the transformation.

5. Fitting a 2D Circle:
   After transformation, the 3D problem is transformed into a 2D circle fitting problem on the XY plane. The function fit_circle_2d is then used to fit a circle to the transformed points.

Parameters

• data_tuple: A tuple containing a dictionary of 3D points and the associated file path.
• output_unit: A dictionary specifying the desired output units for distances.
• point_transform_check_tolerance: Tolerance for checking differences in point-to-point distances after transformation.
• log_statistics (optional): If True, log statistics will be generated and stored.

Returns

A dictionary containing various information about the fitted circle, including:

• Center
• Radius
• Circle's normal vector
• Circle's name
• Offsets
• Plane statistics
• Plane angles parameters
• Circle statistics