a BCCf-ã@snddlmZdgZddlZddlmZddlZddlm Z erJddl mZ dd„Z dd d d d d d œd d„Z dS)é)Ú annotationsÚgeometric_slerpN)Ú TYPE_CHECKING)Ú euclideanc CsÞt ||g¡}tj |j¡\}}dt |¡dkd}|j|jdd…tjf}|j|jdd…tjf}t ||¡}tj |¡}t  ||¡} |\}}t  || ¡}t  || ¡}||dd…tjf||dd…tjfS)Néré) ÚnpZvstackÚlinalgZqrÚTZdiagZnewaxisÚdotZdetZarctan2ÚsinÚcos) ÚstartÚendÚtZbasisÚQÚRZsignsÚcÚsÚomega©rúZ/var/www/html/django/DPS/env/lib/python3.9/site-packages/scipy/spatial/_geometric_slerp.pyÚ_geometric_slerps   rçH¯¼šò×z>z npt.ArrayLikeÚfloatz np.ndarray)rrrÚtolÚreturncCs tj|tjd}tj|tjd}t |¡}|jdkr>> 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() )Zdtyperz: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)rzLThe start and end coordinates must both be in at least two-dimensional spacegð?g•Ö&è .>r)ZrtolZatolz(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 paths)Ú stacklevelz)interpolation parameter must be in [0, 1]N)rZasarrayZfloat64ÚndimÚ ValueErrorÚsizeZ array_equalZlinspaceZallcloser ZnormÚ isinstancerÚfabsrÚwarningsÚwarnÚemptyÚminÚmaxrZ atleast_1dZravel)rrrrZcoordZ coord_distrrrr#sT     þ     ý  þþ)r)Ú __future__rÚ__all__r#ÚtypingrÚnumpyrZscipy.spatial.distancerZ numpy.typingZnptrrrrrrÚs    ü