
    Mi                     .    S SK rSSKJr  SSKJr  SS jrg)    N   )util)tol_pathc           	         [         R                  " U SS9u  p[         R                  " USS9u  pU[         R                  " U5      R                  S5      -  n[        R
                  " [        R                  " [        R                  " USS95      5      [        R                  :  a  gU u  pEUu  pgXT-
  nUc8  [        R                  " Xv5      nU[        R                  R                  U5      -  n[        R                  " Xb5      n	U	[        R                  R                  U	5      -  n	[        R                  R                  U5      n
U
[        R                  :  a5  [        [        R                  " X(U
-  5      5      [        R                  :  a  g[        R                  " U	* U5      [        R                  " X5      -  nX[U-  -   nSUSSU-
   4$ )	a5  
Find the intersection between two lines.
Uses terminology from:
http://geomalgorithms.com/a05-_intersect-1.html

line 1:    P(s) = p_0 + sU
line 2:    Q(t) = q_0 + tV

Parameters
---------
origins : (2, d) float
  Points on lines (d in [2,3])
directions : (2, d) float
  Direction vectors
plane_normal : (3, ) float
  If not passed computed from cross

Returns
---------
intersects : bool
  Whether the lines intersect.
    In 2D, false if the lines are parallel
    In 3D, false if lines are not coplanar
intersection : (d,) float or None
  Point of intersection
T)	return_2D)   r   )axis)FNN   )r   stack_3Drow_normreshapenpsumabsdifftolzerocrosslinalgnormdot)origins
directionsplane_normalis_2Dq_0p_0vuwv_perpw_norms_Iintersections                t/var/www/eduai.edurigo.com/storigo/production/storigo_env/lib/python3.13/site-packages/trimesh/path/intersections.py	line_liner'      sd   8 ]]7d;NGjDAJ $--
+33G<<J 
vvbffRWWZa012SXX= HCDA	A xx~		|44 XXa&F
biinnV$$F
 YY^^AFS&j!ABSXXM &&&!
rvvf0
0Cq=LmU,,,    )N)numpyr    r   	constantsr   r   r'    r(   r&   <module>r-      s      'B-r(   