a ߙfb^"@sdZgdZddlZddlmZddlmZm Z ddZ ddZ d d Z d d Z dddZdddZddlmZddlmZgdZeD]*Zedededdeeeee<qdS)z This module contains utility functions for working with angles. These are both used internally in astropy.coordinates.angles, and of possible )angular_separationposition_angle offset_bygolden_spiral_grid uniform_spherical_random_surfaceuniform_spherical_random_volumeN)UnitSphericalRepresentationSphericalRepresentationc Cst||}t||}t|}t|}t|}t|} | |} |||| |} |||| |} tt| | | S)a- Angular separation between two points on a sphere. Parameters ---------- lon1, lat1, lon2, lat2 : `~astropy.coordinates.Angle`, `~astropy.units.Quantity` or float Longitude and latitude of the two points. Quantities should be in angular units; floats in radians. Returns ------- angular separation : `~astropy.units.Quantity` ['angle'] or float Type depends on input; ``Quantity`` in angular units, or float in radians. Notes ----- The angular separation is calculated using the Vincenty formula [1]_, which is slightly more complex and computationally expensive than some alternatives, but is stable at at all distances, including the poles and antipodes. .. [1] https://en.wikipedia.org/wiki/Great-circle_distance )npsincosarctan2Zhypot) lon1lat1lon2lat2ZsdlonZcdlonZslat1Zslat2Zclat1Zclat2Znum1Znum2 denominatorrBlib/python3.9/site-packages/astropy/coordinates/angle_utilities.pyrs    rc Csxddlm}||}t|}t|t||t|t|}t||}|t||tjdtj S)aX Position Angle (East of North) between two points on a sphere. Parameters ---------- lon1, lat1, lon2, lat2 : `~astropy.coordinates.Angle`, `~astropy.units.Quantity` or float Longitude and latitude of the two points. Quantities should be in angular units; floats in radians. Returns ------- pa : `~astropy.coordinates.Angle` The (positive) position angle of the vector pointing from position 1 to position 2. If any of the angles are arrays, this will contain an array following the appropriate `numpy` broadcasting rules. Angleih) anglesrr r r r uradianwrap_atdeg) rrrrrZdeltalonZcolatxyrrrr>s   ,rcCs0ddlm}t|}t|}t|}t|}t|} t|} ||||| } || |} || |} |t| | tj}|dk}|rdtj |dtj ||tj tj }|j rt ||j }||||<n|}||tj|dtj  tj }|t| tj tj }||fS)a Point with the given offset from the given point. Parameters ---------- lon, lat, posang, distance : `~astropy.coordinates.Angle`, `~astropy.units.Quantity` or float Longitude and latitude of the starting point, position angle and distance to the final point. Quantities should be in angular units; floats in radians. Polar points at lat= +/-90 are treated as limit of +/-(90-epsilon) and same lon. Returns ------- lon, lat : `~astropy.coordinates.Angle` The position of the final point. If any of the angles are arrays, these will contain arrays following the appropriate `numpy` broadcasting rules. 0 <= lon < 2pi. rrg-q=Zgv@)rrr r r r rranyrtoradshapeZ broadcast_torarcsin)lonlatZposangZdistancerZcos_aZsin_aZcos_cZsin_cZcos_BZsin_BZcos_bZxsin_AZxcos_AAZ small_sin_cZA_poleZoutlonZoutlatrrrr[s*        ,$rcCsVd}tjd|tdd}dtj||tj}tdd||tj}t||S)aGenerate a grid of points on the surface of the unit sphere using the Fibonacci or Golden Spiral method. .. seealso:: `Evenly distributing points on a sphere `_ Parameters ---------- size : int The number of points to generate. Returns ------- rep : `~astropy.coordinates.UnitSphericalRepresentation` The grid of points. gw?r)Zdtypeg?r)r Zarangefloatpirr"r$r)sizeZgolden_rZgridr%r&rrrrs rrcCsFtj}|ddtj|tj}t|jdd|dtj}t||S)aGenerate a random sampling of points on the surface of the unit sphere. Parameters ---------- size : int The number of points to generate. Returns ------- rep : `~astropy.coordinates.UnitSphericalRepresentation` The random points. rr(rr+)r randomuniformr*rr"r$r)r+rngr%r&rrrrsrcCs@tj}t|d}t|j|dtj|dd}t|j|j |S)aGenerate a random sampling of points that follow a uniform volume density distribution within a sphere. Parameters ---------- size : int The number of points to generate. max_radius : number, quantity-like, optional A dimensionless or unit-ful factor to scale the random distances. Returns ------- rep : `~astropy.coordinates.SphericalRepresentation` The random points. r-F)copy) r r.rZcbrtr/rZQuantityr r%r&)r+Z max_radiusr0Zusphrrrrrs  r) deprecated) angle_formats)Zcheck_hms_rangesZdegrees_to_dmsZdegrees_to_stringZdms_to_degreesformat_exceptionZhms_to_degreesZ hms_to_dmsZ hms_to_hoursZhms_to_radiansZhours_to_decimalZ hours_to_hmsZhours_to_radiansZhours_to_stringZ parse_angleZradians_to_degreesZradians_to_dmsZradians_to_hmsZradians_to_hoursZsexagesimal_to_stringz$astropy.coordinates.angle_utilities.z"astropy.coordinates.angle_formats.zv4.3)nameZ alternativeZsince)r)rr)__doc____all__Znumpyr Z astropy.unitsZunitsrZ"astropy.coordinates.representationrr rrrrrrZastropy.utils.decoratorsr3Zastropy.coordinatesr4Z__old_angle_utilities_funcsfuncnamegetattrvarsrrrrs( (B