
    \h                         S SK Jr  S SKJrJr  S SKJr  S SKJrJ	r	  S SK
JrJrJrJrJrJrJr  S SKJr  S SKJrJrJrJrJrJrJrJrJr  \" S5      rS	 rS
 r g)    )pi)cossin)
CoordSys3D)ParametricRegionparametric_region_list)PointSegmentCurveEllipseLineParabolaPolygon)raises)	abrtxyzthetaphiCc                     [        S5      n U R                  S:X  d   eU R                  S:X  d   eU R                  0 :X  d   eU R                  S:X  d   e[        [
        [
        4[
        SS45      nUR                  [
        [
        4:X  d   eUR                  [
        4:X  d   eUR                  S:X  d   e[        [        [        [        4[        [        SS45      nUR                  [        [        [        4:X  d   eUR                  [        [        4:X  d   eUR                  [        S0:X  d   eUR                  S:X  d   e[        S[        -  S	[        -  4[        SS4[        S
S45      nUR                  S[        -  S	[        -  4:X  d   eUR                  [        [        4:X  d   eUR                  [        S[        S0:X  d   eUR                  S:X  d   e[        [        [        S-  4[        5      nUR                  [        4:X  d   eUR                  0 :X  d   eUR                  S:X  d   e[        [        [        [        5      -  [        [        [        5      -  4[        [        SS[        -  45      nUR                  [        [        [        5      -  [        [        [        5      -  4:X  d   eUR                  S:X  d   e[        [        [        [        5      -  [        [        [        5      -  4[        SS4[        S[        45      nUR                  [        [        [        5      -  [        [        [        5      -  4:X  d   eUR                  [        [        4:X  d   eUR                  [        S[        S[        40:X  d   eUR                  S:X  d   e[        [        [        [        5      -  [        [        [        5      -  4[        SS45      nUR                  [        4:X  d   eUR                  [        S0:X  d   eUR                  S:X  d   e[        [        [        [        5      -  [        [        [        5      -  [        4[        SS4[        SS[        -  4[        SS45      nUR                  [        [        [        4:X  d   eUR                  S:X  d   e[        [        [        [         5      -  [        [        5      -  [        [        [         5      -  [        [        5      -  [        [        [         5      -  4[        [        SS[        -  4[         S[        45      n	U	R                  [        [        [         5      -  [        [        5      -  [        [        [         5      -  [        [        5      -  [        [        [         5      -  4:X  d   eU	R                  [        [        [         4:X  d   eU	R                  S:X  d   e[#        [$        S 5        [#        [$        S 5        g )N)       r            )r   r!   	   i)r   r!   )r#   r    r   )r$   r!      )r   r%   r   c                  b    [        [        [        S-  -  S[        -  [        -  4[        S45      $ )Nr!   r$   )r   r   r   r       `/var/www/auris/envauris/lib/python3.13/site-packages/sympy/vector/tests/test_parametricregion.py<lambda>'test_ParametricRegion.<locals>.<lambda>E   s$    /1a41Q!RIr'   c                  l    [        [        [        4[        S-  [        [        5      4[        SSS45      $ )Nr!   r      )r   r   r   r   r   r'   r(   r)   r*   F   s'    /AAs1vAqRSUr'   )r   
definition
parameterslimits
dimensionsr   r   r   r   r   r   r   r   r   r   r   r   r   
ValueError)
pointline_xyline_yzp1p2circlehalfdiscellipsecylinderspheres
             r(   test_ParametricRegionr<      s   V$Ev%%%r!!!<<2q    1v1ay1G1a&(((!%%%""" !AwAq!95G!Aa(((!Q'''>>a[((("""	1Q3A,Aq	Ar1:	>B==QqS#a%L(((==QF"""99FAw////==A	1ad)Q	'B==QD   99??==AqU|Qs5z\:Aq!B$?OPF3u:qU| <<<<!!!3u:qU| <q"aj5RSUW.YH1SZ<3u:">>>>1e*,,,??q'51b'::::!####a&!CF(3aAY?G!%%%>>a[((("""3u:qU|Q ?!QUTUWXY[W[L\_`bcef^ghH1eQ-///!###qSz#e*4Qs3xZE
5JAcRUhJW !E1ad#3c1b\CF3s8CJ!6qSz#e*7LaPSTWPXj YYYYE3///!!!
:IJ
:UVr'   c            
        ^ [        SS5      n [        U 5      [        S5      /:X  d   e[        [        SS5      SS5      n[        U[        5      [        S[        [        5      -  S-   S[        [        5      -  S-   4[        SS[        -  45      /:X  d   e[        [        [        S-  4[        S	S45      n[        U5      [        [        [        S-  4[        S	S45      /:X  d   e[        [        SS
S5      [        SSS	5      5      n[        U[        5      [        SS[        -  -
  S
S[        -  -
  S
[        -  S-
  4[        SS45      /:X  d   e[        [        SS5      S5      n[        U[        5      [        [        S4[        SS45      /:X  d   e[        [        SSS5      [        SSS	5      5      n[        U[        5      [        SSS[        -  S-   4[        SS45      /:X  d   e[        [        SS5      [        SS5      5      n[        U5      [        S5      /:X  d   e[        SSS5      n[        U[        5      [        SS[        -  -
  S	[        -  S-   4[        SS45      [        S	[        -  S-
  SS[        -  -
  4[        SS45      [        S[        -
  S[        -
  4[        SS45      /:X  d   e[        [        SS5      [        [        S	S5      [        SS5      5      5      m[        [        U4S j5        g )N   )r>   r?   r!   r%   r,   r   r   r       ir"   r   )r   r   8   )r?   rA   )r   r   )r%   )r!   r   r      c                     > [        T 5      $ )N)r   )r5   s   r(   r)   -test_parametric_region_list.<locals>.<lambda>a   s    5b9r'   )r	   r   r   r   r   r   r   r   r   r
   r   r   r   r   r1   )	r2   ecss1s2s3polyr5   s	           @r(   test_parametric_region_listrM   I   sA   "bME!%(-=h-G,HHHHaQ"A!!Q',<aAhlAcRSfHWXL=Y\]_`bcdfbf[g,h+iiiiq!Q$i!Q#A!!$)91ad)aAY)O(PPPPaR %1a.1A!!Q',<a!A#grAaCxQSTUQUXYQY=Z]^`acd\e,f+gggg	q!f	%B!"a(-=q!fq!Qi-P,QQQQ	q!Qq!Q	0B!"a(-=q!QqS1WoPQSTVWy-Y,ZZZZ	r2b"	.B!"%*:8*D)EEEE5'6*D!$*/?QqS!A#PQ'@RUVXY[\T]/^`prsturuxyry{|  @A  BC  @C  |C  rD  GH  JK  MN  FO  aP  Rb  de  hi  di  kl  op  kp  cq  tu  wx  z{  s|  R}  /~  ~  ~  ~	%1+tE!QKq<	=B
:9:r'   N)!sympy.core.numbersr   (sympy.functions.elementary.trigonometricr   r   sympy.vector.coordsysrectr   sympy.vector.parametricregionr   r   sympy.geometryr	   r
   r   r   r   r   r   sympy.testing.pytestr   	sympy.abcr   r   r   r   r   r   r   r   r   r   r<   rM   r   r'   r(   <module>rU      s=    ! ? 0 R R R R ' 5 5 5 sO:Wz;r'   