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Editing: _geometric_slerp.cpython-311.pyc
� d�c � �b � d dl mZ dgZd dlZd dlmZ d dlZd dlm Z erd dl mZ d� Z ddd�Z dS )� )� annotations�geometric_slerpN)� TYPE_CHECKING)� euclideanc � � t j | |g� � }t j � |j � � \ }}dt j |� � dk z dz }|j |j d d �t j f z }|j |j d d �t j f z }t j | |� � }t j � |� � }t j ||� � } |\ } }t j || z � � }t j || z � � }| |d d �t j f z ||d d �t j f z z S )N� r � ) �np�vstack�linalg�qr�T�diag�newaxis�dot�det�arctan2�sin�cos) �start�end�t�basis�Q�R�signs�c�s�omegas �@/usr/lib/python3/dist-packages/scipy/spatial/_geometric_slerp.py�_geometric_slerpr! s � � �I�u�c�l� #� #�E� �9�<�<��� � �D�A�q� ������q� � !�A� %�E� ��e�g�a�a�a���m�$�$�A� ��e�g�a�a�a���m�$�$�A� ��u�c���A� � � � �a���A� �J�q�!� � �E� �J�E�3� ��q�5�y���A� ��q�5�y���A� �1�Q�Q�Q�� �]�#� #�c�A�a�a�a���m�,<�&<� <�<� �H�����z>r � npt.ArrayLiker r �tol�float�return� np.ndarrayc �: � t j | t j �� � } t j |t j �� � }t j |� � }|j dk rt d� � �| j dk s |j dk rt d� � �| j |j k rt d� � �| j dk s |j dk rt d� � �t j | |� � rt j | | |j � � S | |fD ]F}t j t j � |� � dd d � � � st d � � ��Gt |t � � st d � � �t j |� � }t | |� � }t j |dd |� � � rt j d� � t j |t j �� � }|j d k rt j d | j f� � S |� � � d k s|� � � dk rt d� � �|j d k r5t) | |t j |� � � � � � � S t) | ||� � S )a� Geometric spherical linear interpolation. The interpolation occurs along a unit-radius great circle arc in arbitrary dimensional space. Parameters ---------- start : (n_dimensions, ) array-like Single n-dimensional input coordinate in a 1-D array-like object. `n` must be greater than 1. end : (n_dimensions, ) array-like Single n-dimensional input coordinate in a 1-D array-like object. `n` must be greater than 1. t : float or (n_points,) 1D array-like A float or 1D array-like of doubles representing interpolation parameters, with values required in the inclusive interval between 0 and 1. A common approach is to generate the array with ``np.linspace(0, 1, n_pts)`` for linearly spaced points. Ascending, descending, and scrambled orders are permitted. tol : float The absolute tolerance for determining if the start and end coordinates are antipodes. Returns ------- result : (t.size, D) An array of doubles containing the interpolated spherical path and including start and end when 0 and 1 t are used. The interpolated values should correspond to the same sort order provided in the t array. The result may be 1-dimensional if ``t`` is a float. Raises ------ ValueError If ``start`` and ``end`` are antipodes, not on the unit n-sphere, or for a variety of degenerate conditions. See Also -------- scipy.spatial.transform.Slerp : 3-D Slerp that works with quaternions Notes ----- The implementation is based on the mathematical formula provided in [1]_, and the first known presentation of this algorithm, derived from study of 4-D geometry, is credited to Glenn Davis in a footnote of the original quaternion Slerp publication by Ken Shoemake [2]_. .. versionadded:: 1.5.0 References ---------- .. [1] https://en.wikipedia.org/wiki/Slerp#Geometric_Slerp .. [2] Ken Shoemake (1985) Animating rotation with quaternion curves. ACM SIGGRAPH Computer Graphics, 19(3): 245-254. Examples -------- Interpolate four linearly-spaced values on the circumference of a circle spanning 90 degrees: >>> import numpy as np >>> from scipy.spatial import geometric_slerp >>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> ax = fig.add_subplot(111) >>> start = np.array([1, 0]) >>> end = np.array([0, 1]) >>> t_vals = np.linspace(0, 1, 4) >>> result = geometric_slerp(start, ... end, ... t_vals) The interpolated results should be at 30 degree intervals recognizable on the unit circle: >>> ax.scatter(result[...,0], result[...,1], c='k') >>> circle = plt.Circle((0, 0), 1, color='grey') >>> ax.add_artist(circle) >>> ax.set_aspect('equal') >>> plt.show() Attempting to interpolate between antipodes on a circle is ambiguous because there are two possible paths, and on a sphere there are infinite possible paths on the geodesic surface. Nonetheless, one of the ambiguous paths is returned along with a warning: >>> opposite_pole = np.array([-1, 0]) >>> with np.testing.suppress_warnings() as sup: ... sup.filter(UserWarning) ... geometric_slerp(start, ... opposite_pole, ... t_vals) array([[ 1.00000000e+00, 0.00000000e+00], [ 5.00000000e-01, 8.66025404e-01], [-5.00000000e-01, 8.66025404e-01], [-1.00000000e+00, 1.22464680e-16]]) Extend the original example to a sphere and plot interpolation points in 3D: >>> from mpl_toolkits.mplot3d import proj3d >>> fig = plt.figure() >>> ax = fig.add_subplot(111, projection='3d') Plot the unit sphere for reference (optional): >>> u = np.linspace(0, 2 * np.pi, 100) >>> v = np.linspace(0, np.pi, 100) >>> x = np.outer(np.cos(u), np.sin(v)) >>> y = np.outer(np.sin(u), np.sin(v)) >>> z = np.outer(np.ones(np.size(u)), np.cos(v)) >>> ax.plot_surface(x, y, z, color='y', alpha=0.1) Interpolating over a larger number of points may provide the appearance of a smooth curve on the surface of the sphere, which is also useful for discretized integration calculations on a sphere surface: >>> start = np.array([1, 0, 0]) >>> end = np.array([0, 0, 1]) >>> t_vals = np.linspace(0, 1, 200) >>> result = geometric_slerp(start, ... end, ... t_vals) >>> ax.plot(result[...,0], ... result[...,1], ... result[...,2], ... c='k') >>> plt.show() )�dtyper z:The interpolation parameter value must be one dimensional.z1Start and end coordinates must be one-dimensionalz;The dimensions of start and end must match (have same size)r zLThe start and end coordinates must both be in at least two-dimensional spaceg �?g��&� .>r )�rtol�atolz(start and end are not on a unit n-sphereztol must be a floatg @z_start and end are antipodes using the specified tolerance; this may cause ambiguous slerp pathsz)interpolation parameter must be in [0, 1])r �asarray�float64�ndim� ValueError�size� array_equal�linspace�allcloser �norm� isinstancer& �fabsr �warnings�warn�empty�min�maxr! � atleast_1d�ravel)r r r r% �coord� coord_dists r r r # s� � �^ �J�u�B�J� /� /� /�E� �*�S�� � +� +� +�C� � �1� � �A��v��z�z�� :� ;� ;� ;� �z�Q���#�(�a�-�-�� 3� 4� 4� 4� �z�S�X� � �� ;� <� <� <� �z�A�~�~���A� � �� !� "� "� "� �~�e�S�!�!� 1��{�5�%���0�0�0� �� � 4� 4���{�2�9�>�>�%�0�0�#� $� !�#� #� #� 4� � 3� 4� 4� 4� 4� �c�5� !� !� ��.�/�/�/��g�c�l�l���5�#�&�&�J� �{�:�s���5�5�5� ?�� � >� ?� ?� ?� � �1�B�J�'�'�'�A��v��{�{��x��E�J��(�(�(��u�u�w�w��{�{�a�e�e�g�g��k�k��D�E�E�E��v��{�{� �� #� "� �a� 0� 0�2� 2�27�%�'�'� :� �� #� !�#� #� #r" )r# ) r r$ r r$ r r$ r% r& r' r( )� __future__r �__all__r8 �typingr �numpyr �scipy.spatial.distancer � numpy.typing�nptr! r � r" r �<module>rI s� �� "� "� "� "� "� "� � �� ���� � � � � � � � � � � ,� ,� ,� ,� ,� ,�� � � � � � � �=� =� =�0 � L#� L#� L#� L#� L#� L#� L#r"
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