
    =h=R                        d Z ddlZddlmZmZ ddlmZ ddlZ	ddl
mZmZ ddlZddlmZ ddlmZ ddlmZ ddlmZ ddlZd	 Zd
 Zd Zdej"                  dej"                  fdZdej"                  dej"                  fdZd ZddlmZ ddlmZ  ej<                  g dg dg dg      d   j?                         jA                         Z!d Z"d Z#d Z$d Z%d5dZ&d Z'd Z(d Z)d6dZ*d6d Z+d!ej"                  fd"Z,d#ej"                  fd$Z-d%ej"                  d&ej"                  d'ej"                  dej"                  fd(Z.d)ej"                  d*ej"                  dej"                  fd+Z/d,ej"                  d*ej"                  dej"                  fd-Z0d.ej"                  d/ej"                  dej"                  fd0Z1d%ej"                  d'ej"                  dej"                  fd1Z2d%ej"                  d'ej"                  d*ej"                  dej"                  fd2Z3d%ej"                  d'ej"                  d*ej"                  dej"                  fd3Z4d7d4Z5y)8z<Multi-view geometry & proejction code.. (most from vincent)     N)	rearrangerepeat)
functional)ceillog2)einsum)Float)Tensorc                 d    t        j                  | t        j                  | ddgf         fd      S )N.r   )torchcat	ones_likexs    5/home/cameronsmith/repos/rotation_testing/geometry.py<lambda>r      s)    eii5??1S!W:#> ?C     c                 .    | dd df   d| ddd f   z   z  S )N.r   h㈵> r   s    r   r   r      s%    aCRCj$qRSz/2 r   c                 B    t        t        j                  d||             S )Nzb...cij,b...ckj->b...cki)unhomr   r   )crdsKs     r   r   r      s    5.HD!QR r   d6returnc                    | dd df   | ddd f   }}t        j                  |d      }|||z  j                  dd      |z  z
  }t        j                  |d      }t        j                  ||d      }t        j
                  |||fd      S )N.   r   dimTkeepdim)F	normalizesumr   crossstack)r   a1a2b1b2b3s         r   rotation_6d_to_matrixr/      s    RaR["S!"W+B	
RR	 B	rBwmmBm-2	2B	
RR	 B	R	$B;;B|,,r   matrixc                     | j                         d d }| dd dd d f   j                         j                  |dz         S )Nr$   .   )   )sizeclonereshape)r0   	batch_dims     r   matrix_to_rotation_6dr8      sB    cr"I#rr1*##%--i$.>??r   c           
      ~   t        j                  d| d d |f   j                         t        |            dd df   }t        j                  d| d d t	        d|dz
        f   j                         t        |            dd df   }t        |d   |d dd f         d   }t        |d   |d dd f         d   }||z
  }|S )Nz
pij,pj->pi.r   r      NN)r   r   )r   r   inversehommaxproject)	pose_perpixview_imeansr   pos_ipos_adjpos_i_2d
pos_adj_2dflow_2ds	            r   compute_flowrH       s    ll<AfH(=(E(E(GE
STWXZYZXZTZ[Ell<Ac!F1Ho4E(F(N(N(PQTUZQ[\]`acbcac]cdG+AbqbgJ7<H+AbqbgJ7<J!GNr   )KMeans)Rotation)r   r   r   r:   )r:   r   r   r:   )r   r:   r   r:   c                 D    t        t        dd df   | dd df         d   S )N.r   r   )
procrustesunit_tri)triss    r   tris_to_transfrO   /   s-    hs2A2v&tCF|4R88r   c                 ~    t        j                  d| j                         t        j	                               dd df   S )Nbij,bkj->bki.r   )r   r   cudarM   float)transfs    r   transf_to_trirU   1   s3    %,,~fkkmHNNL\"]^abdcdbd^d"eer   c                    t        j                  d      d    j                  t        |       dd      j	                         }||d d d ddf<   | j                  d      dk(  rt        |       |d d d dd df<   n5t        j                  j                  j                  |       |d d d dd df<   t        j                  d|j	                         t        j                               dd df   }||fS )N   r   r   r3   rQ   .)r   eyeexpandlenrR   r4   r/   korniageometryconversionsquaternion_to_rotation_matrixr   rM   rS   )rottransrT   
transf_tris       r   rot_trans_to_trisrb   2   s    99Q<$$SXb499;FF1RaR7O
xx|Q(=c(Bq!BQBw //55SSTWX&2A2bqb/nV[[]8>>;KLSQSRSQSVTJfr   c                    t        j                  d      d    j                  t        |       dd      }||d d d ddf<   t        j
                  j                  j                  t        j                  t	        j
                  j                  j                  | j                  d       d            |d d d dd df<   |d d d ddf   }t        j                  t	        j
                  j                  j                  t        j
                  j                  j                  |d d d dd df         j                  d       d      }y )NrW   r   r   r:   )r   rX   rY   rZ   r[   r\   r]   r^   r)   quaternion_from_eulerunbindeuler_from_quaternionrotation_matrix_to_quaternion)r_   r`   rT   trans2rot2s        r   rot_trans_to_tris_rj   :   s   99Q<$$SXb4FF1RaR7OOO//MMekkZ`ZiZiZuZu  [L  [L  NQ  NX  NX  YZ  N[  [\  ]_  O`  aF1RaR7O!BQBr'?F	V__00FFHcHc  IB  IB  CI  JK  LN  MN  LN  OQ  PQ  OQ  JQ  CR  IS  IZ  IZ  []  I^  _  `b  
cDr   c                    | d d d d d ddf   j                  | j                  d      d      }| d d d d d dd df   j                  ddd      j                         j                         }t	        j
                  t        j                  |      j                         | j                        }|j                  | j                  d      d      }t	        j                  ||gd      j                         j                         }t        |d      j                  |      }|j                  }t	        j
                  |j                  | j                        }	g }
t        |      D ]  }t	        j                   t	        j
                  |      |k(        d   }|j#                         dk(  rE	 ||   }t	        j$                  t	        j
                  || j                        |	|   z
  d      }|
j'                  | ||j)                                       |st	        j*                  |
      S t	        j*                  |
      |fS #  Y xY w)	Nr   r   r   devicer:   r    *   )
n_clustersrandom_state)r6   r4   cpunumpyr   tensorRfrom_matrixas_quatrm   r   rI   fitlabels_cluster_centers_rangewherenumelnormappendargminr)   )posesro   return_labelstranslations	rotationsquaternionsfeatureskmeanslabelscentersrepresentativesicluster_indicescluster_features	distancess                  r   cluster_and_representr   C   s   Arr1%--ejjmR@LaBQBl#++B1599;AACI,,q}}Y7??A%,,WK%%ejjmR8Kyy,4!<@@BHHJH z;??IF^^Fll6225<<HG O: ++ell6&:a&?@C  "a'	'8

5<<0@#VY`abYc#cijkI""59I9I9K)L#MN 0=5;;'g5;;C_`fBgg 	xs   +A&IIc                     t        j                  d      d   j                  g |d   j                  d d dd j	                         }t
        j                  j                  j                  |d   dd df         |dd dd df<   |d   ddd f   |dd ddf<   t        | j                        dk(  r| d    n| |d d |f   j                         z  } t        |      t        k(  r	 t        |||d   |      }t        j                  |d	   |fd      }t        j                  d
| t!        |d               dd df   }t
        j                  j                  j#                  | d d d dd df   d      |d   z  }	t%        ||	|d   j'                  d      |d   |t        j                  d      j	                         d    ||d   |d   dt        j(                  |      d d dz         S )NrW   r;   
lie_perpixr2   r   .r   rB   colorsz
kij,kj->kir   epsquatsscalesg?)r>   	opacitiesr:   r   zRGB+D)render_modebackgrounds)r   rX   rY   shaperR   r[   r\   r]   r^   rZ   r<   typerS   rH   r   r   r=   rg   rasterizationclip
zeros_like)
posetimestepimsizer   
splat_varsr@   flowcolors_imeans_iquats_is
             r   	do_renderr   ]   sG   0%))A,y)00[*\2J2P2PQSRS2T[UW[XZ[``bK#__88VVWabnWopstvuvtvpvWwxKBQBrr	'5c!"f=KBQBr	djj/1,DJ$+aj:Q:Y:Y:[[DH~u HZ-@CDyy*X.t4R8HLLd3z'/B+CDS!VLGOO''EEd1RaRPRQRPR7mX\E]^hip^qqG'7Jx,@,E,E",E,MzZeOfhprwr{r{|}r~  sD  sD  sF  GK  sL  NO  QW  XY  QZ  \b  cd  \e  ry((22A6q8: :r   c                 
   t        dt        | d   d         dz        }t        j                  t        j
                  j                  j                  | d   dd dd df   d	      | d   dd dd
f   fd
      }|j                  t        | d   d   j                  dd            d
d
      | d<   t        j                  j                  | d   d   j                  dd      d d |         t        j                  j                  | d   d   j                  dd      d d |   dz  dz         t        j                  j                  t        j                  t        | d   d   j                  dd      d d |         d      j                               t        j                  j                  t        j                  t        | d   d   j                  dd      d d |               j                         dz        t        j                  j                  t        j                  t        | d   d   j                  dd      d d |         d      j                         dz        t        j                  j                  | d   d d |         dS )Nr:   
world_crdsr      r   .r   g-C6?r   r   lie_crdsrgb_crdsg      ?rW   g?g{Gz?)rB   r   r   r   r   r   )r>   rZ   r   r   r[   r\   r]   rg   rY   flattennn	ParameteronesrR   )scenestride	poses_lies      r   format_splat_varsr   q   s   qU<(+,b01F 		6??66TTUZ[bUcdghjijhjkmlmkmdmUnswTxy~  @G  zH  IL  MO  NO  MO  PR  IR  zS  T  UW  XI!((U<-@-C-K-KAa-P)QRTUWXE*  ((,,U<-@-C-K-KAa-PQYSYQY-Z[((,,U:->q-A-I-I!A-NxQWx-XY[-[\^-^`((,,UZZE,<OPQ<R<Z<Z[\]^<_`hbh`h<i8jkl-m-r-r-tv((,,UZZE,<OPQ<R<Z<Z[\]^<_`hbh`h<i8j-k-p-p-rsv-vx((,,UZZE,<OPQ<R<Z<Z[\]^<_`hbh`h<i8jkl-m-r-r-tux-xz 88--eJ.?&.IJ r   c                 0	   t        | j                        dkD  rut        | j                  dd      |j                  dd      |j                  dd      |j                  dd            }|d   |d   j	                  d| j                  d d       fS 	 t        j                  dt
        j                        5  | j                  ddd      } |j                  ddd      }|j                  ddd      }d}d}|j                  |	      }||j                  d
d      |z   z  }| |z  j                  dd      }||z  j                  dd      }	|j                  |	      }| |z
  }
||	z
  }|dd df   }ddlm}  |        t        j                  d||      }t        j                  d|j                  d      |
j                  d      z  ||j                  ddd            }t        j                  d||
||j                  ddd            }t        j                  d|||
||j                  ddd             t        j                  |      \  }}}t        j                   |j                  d   | j"                        j                  d      }|j%                  |j                  d   dd      }|d d d
d
fxx   t        j&                  t        j(                  |j+                  |j                  ddd                        z  cc<   |j+                  |j+                  |j                  ddd                  }|	 |j*                  |      z
  } |j*                  |       |z   }t        j                   d      d    j-                  | j/                  d      d
d
      j1                  |       }||d d d dd df<   t        j                   d      d    j-                  | j/                  d      d
d
      j1                  |       }|j3                  d
      |d d d dd
f<   t        j                   d      d    j-                  | j/                  d      d
d
      j1                  |       }||z  |z  }||z
  j5                         j7                         |fcd d d        S # 1 sw Y   y xY w)Nr   r   r:   r2   rR   device_typedtypeTư>minr   r"   .)	set_tracezbik,bjk->bijzbpij,bij,bjk->bpikzbik,bpij,bij,bjk->bpikzbik,bjk,bpk,bcp,bcq->bpikrl   rW   )rZ   r   efficient_nonrig_procrustesr   	unflattenr   autocastfloat32permuter   r'   pdbr   r   	unsqueezesvdrX   rm   r   signdetbmmrY   r4   tosqueezesquaremean)S1S2weightsaff_embout
transposedr   weights_normmu1mu2X1X2pdb_tmpr   UsVZrt   tS1_hatR_T_S_rT   s                             r   r   r      s    bhh-/)"**Qq/"**Qq/'//Z[\]J^_f_n_nopqr_st1vc!f&&q"1666 
F%--	@ F2ZZ!AZZ!A!A&
 % Bt <S @A,##Ad#3,##Ad#3!&&3&/#X#X RaR)$&ll>'':
 LL-s}}Q/?Q/OQXZ\ZdZdefhiklZmnLL17BTUWXZ[I\] 	17GRRTR\R\]^`acdRef ))A,1a IIaggaj3==a@HHQWWQZ!$	!B(uzz%))AEE!))Aa2B,C"DEE EE!%%		!Aa()* EAEE#J  rQ 99Q<$$RWWQZ2699"=1RaR799Q<$$RWWQZ2699"=IIbM1RaR799Q<$$RWWQZ2699"=Brr	!!#((*61MF2 F2 F2s   4ORRc                 	   t        | j                        dk(  rht        | j                  dd      |j                  dd      ||j                  dd      nd       }|d   |d   j	                  d| j                  d d       fS t        | j                        dk(  rht        | j                  dd      |j                  dd      ||j                  dd      nd       }|d   |d   j	                  d| j                  d d       fS 	 t        j                  dt
        j                        5  | j                  ddd      } |j                  ddd      }||j                  ddd      }d}|t        j                  | d d d df         }d	}|j                  |
      }||j                  dd      |z   z  }| |z  j                  dd      }||z  j                  dd      }|j                  |
      }| |z
  }	||z
  }
|	|z  j                  |
j                  ddd            }t        j                  |      \  }}}t        j                  |j                  d   | j                        j!                  d      }|j#                  |j                  d   dd      }|d d ddfxx   t        j$                  t        j&                  |j                  |j                  ddd                        z  cc<   |j                  |j                  |j                  ddd                  }| |j                  |      z
  } |j                  |       |z   }t        j                  d      d    j)                  | j+                  d      dd      j-                  |       }||d d d dd df<   t        j                  d      d    j)                  | j+                  d      dd      j-                  |       }|j/                  d      |d d d ddf<   t        j                  d      d    j)                  | j+                  d      dd      j-                  |       }||z  |z  }||z
  j1                         j3                         |fcd d d        S # 1 sw Y   y xY wN   r   r:   r2   rW   rR   r   Tr   r   r   r"   rl   r   )rZ   r   efficient_procrustesr   r   r   r   r   r   r   r   r'   r   r   rX   rm   r   r   r   r   rY   r4   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   rt   r   r   r   r   r   rT   s                          r   r   r      s    288}a"2::a?2::a?[b[n7??STUVCWtxy1vc!f&&q"1666
288}a"2::a?2::a?[b[n7??STUVCWtxy1vc!f&&q"1666 
F%--	@ 72ZZ!AZZ!AOOAa*G
?eoob2A2h&?G% Bt <S @A,##Ad#3,##Ad#3!&&3&/#X#X ZRZZ!A./ ))A,1a IIaggaj3==a@HHQWWQZ!$	!B(uzz%))AEE!))Aa2B,C"DEE EE!%%		!Aa()* EAEE#J  rQ 99Q<$$RWWQZ2699"=1RaR799Q<$$RWWQZ2699"=IIbM1RaR799Q<$$RWWQZ2699"=Brr	!!#((*61o72 72 72s   'M	Q::Rc                 T	   t        | j                        dk(  rht        | j                  dd      |j                  dd      ||j                  dd      nd       }|d   |d   j	                  d| j                  d d       fS t        | j                        dk(  rht        | j                  dd      |j                  dd      ||j                  dd      nd       }|d   |d   j	                  d| j                  d d       fS 	 t        j                  dt
        j                        5  | j                  ddd      } |j                  ddd      }||j                  ddd      }d}|t        j                  | d d d df         }d	}|j                  |
      }||j                  dd      |z   z  }| |z  j                  dd      }||z  j                  dd      }|j                  |
      }| |z
  }	||z
  }
t        j                  |j                  d            }|	|z  j                  |
j                  ddd            }t        j                  |      \  }}}t        j                   |j                  d   | j"                        j%                  d      }|j'                  |j                  d   dd      }|d d ddfxx   t        j(                  t        j*                  |j                  |j                  ddd                        z  cc<   |j                  |j                  |j                  ddd                  }| |j                  |      z
  } |j                  |       |z   }t        j                   d      d    j-                  | j/                  d      dd      j1                  |       }||d d d dd df<   t        j                   d      d    j-                  | j/                  d      dd      j1                  |       }|j                  d      |d d d ddf<   t        j                   d      d    j-                  | j/                  d      dd      j1                  |       }||z  |z  }||z
  j3                         j5                         |fcd d d        S # 1 sw Y   y xY wr   )rZ   r   rL   r   r   r   r   r   r   r   r   r'   
diag_embedr   r   r   rX   rm   r   r   r   r   rY   r4   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   diagsr   r   r   r   r   rt   r   r   r   r   r   rT   s                           r   rL   rL   %  s    288}aAaAaQXQd19Mjno1vc!f&&q"1666
288}aAaAaQXQd19Mjno1vc!f&&q"1666 
F%--	@ 42ZZ!AZZ!AOOAa*G
?eoob2A2h&?G% Bt <S @A,##Ad#3,##Ad#3!&&3&/#X#X  !34 XNN2::a!,- ))A,1a IIaggaj3==a@HHQWWQZ!$	!B(uzz%))AEE!))Aa2B,C"DEE EE!%%		!Aa()* EAEE#J  rQ 99Q<$$RWWQZ2699"=1RaR799Q<$$RWWQZ2699"=IIbM1RaR799Q<$$RWWQZ2699"=Brr	!!#((*61i42 42 42s   'M-RR'pointsc                     t        j                  | dddf   | j                        }t        j                  | |fd      S )zAppends a "1" to the coordinates of a (batch of) points of dimension DIM.

    Args:
        points: points of shape (..., DIM)

    Returns:
        points_hom: points with appended "1" dimension.
    .Nr:   rl   r   r    )r   r   rm   r   )r   r   s     r   homogenize_pointsr   k  s9     ??6#rr'?6==AD99fd^,,r   vectorsc                     t        j                  | dddf   | j                        }t        j                  | |fd      S )zAppends a "0" to the coordinates of a (batch of) vectors of dimension DIM.

    Args:
        vectors: vectors of shape (..., DIM)

    Returns:
        vectors_hom: points with appended "0" dimension.
    .Nr:   rl   r   r    )r   r   rm   r   )r   zeross     r   homogenize_vecsr   x  s=     WS"1"W-gnnEE99gu%2..r   xy_pixz
intrinsicsc                 p    t        |       }t        j                  d|j                         |      }||z  }|S )aw  Unproject (lift) 2D pixel coordinates x_pix and per-pixel z coordinate
    to 3D points in camera coordinates.

    Args:
        xy_pix: 2D pixel coordinates of shape (..., 2)
        z: per-pixel depth, defined as z coordinate of shape (..., 1)
        intrinscis: camera intrinscics of shape (..., 3, 3)

    Returns:
        xyz_cam: points in 3D camera coordinates.
    ...ij,...kj->...ki)r   r   r   r<   )r   r   r   
xy_pix_homxyz_cams        r   	unprojectr     s8     #6*Jll/1C1C1EzRGqLGNr   xyz_world_hom	cam2worldc                 D    t        j                  |      }t        | |      S )a  Transforms points from 3D world coordinates to 3D camera coordinates.

    Args:
        xyz_world_hom: homogenized 3D points of shape (..., 4)
        cam2world: camera pose of shape (..., 4, 4)

    Returns:
        xyz_cam: points in camera coordinates.
    )r   r<   transform_rigid)r   r   	world2cams      r   transform_world2camr     s     i(I=)44r   xyz_cam_homc                     t        | |      S )a  Transforms points from 3D world coordinates to 3D camera coordinates.

    Args:
        xyz_cam_hom: homogenized 3D points of shape (..., 4)
        cam2world: camera pose of shape (..., 4, 4)

    Returns:
        xyz_world: points in camera coordinates.
    )r   )r   r   s     r   transform_cam2worldr     s     ;	22r   xyz_homTc                 0    t        j                  d||       S )zApply a rigid-body transform to a (batch of) points / vectors.

    Args:
        xyz_hom: homogenized 3D points of shape (..., 4)
        T: rigid-body transform matrix of shape (..., 4, 4)

    Returns:
        xyz_trans: transformed points.
    r   )r   r   )r   r  s     r   r   r     s     <<,a99r   c           	      j    t        | t        j                  | dd df   | j                        |      S )N.r:   rl   )r   )r   r   r   rm   )r   r   s     r   #get_unnormalized_cam_ray_directionsr    s5     sBQBw> r   c                 j   |Gt        j                  d      d    j                  | j                  d      dd      j	                  |       }|dd ddf   }t        | |      }||j                  dd      z  }t        |      }t        ||      }t        |d|j                  d	      
      }||dd df   fS )NrW   r   r   .r   T)r!   r#   z... ch -> ... num_rays chr$   )num_rays)
r   rX   rY   r4   r   r  r}   r   r   r   )r   r   r   cam_origin_worldray_dirs_cam
rd_cam_homrd_world_homs          r   get_world_rays_r    s     IIaL&--fkk!nRCFFvN	 !bqb"- 7vzJL,"3"3D"3"IIL !.J 'z9=L/1LWcWhWhikWln \#rr'222r   c           	      2   t        | j                        dk(  rnt        | j                  dd      |j                  dd      ||j                  dd      nd       }|D cg c]!  }|j	                  d| j                  d d       # c}S t        | ||      S c c}w )NrW   r   r:   r2   )rZ   r   r  r   r   )r   r   r   r   r   s        r   get_world_raysr    s    
 6<<!fnnQq1*2D2DQq2Idmdy)J[J[\]^_J`  @D  E9<=AAfll2A./==6*Y77 >s   &Bc                    | j                   \  }}|j                   \  }}| j                  d      }|j                  d      }	| |z
  }
||	z
  }|
dz  j                         }|dz  j                         }t        j                  |      }t        j                  |      }|
|z  }
||z  }||k  r/t        j
                  |t        j                  |||z
        fd      }t        j                  |
j                  |      }t        j                  j                  |d      \  }}}|j                  }t        j                  ||j                        }|dk7  ret        j                  j                  |      dk  }||k7  r>|d d dfxx   dz  cc<   |dxx   dz  cc<   t        j                  ||j                        }|j                         }|r0||z  |z  }d|dz  z
  }||z  t        j                  ||      z  |z   }n2d}d||z  z   d|z  |z  |z  z
  }|t        j                  ||      z  |z   }||k  r|d |d d f   }||t        j                  |	|      z  z
  }|||d	}|||fS )
Nr   g       @F)full_matricesbestr   r:   r2   )rotationscaletranslation)r   r   r'   npsqrtconcatenater   dotr  linalgr   r   )XYscaling
reflectionnmnymymuXmuYX0Y0ssXssYnormXnormYAr   r   Vtr   r  have_reflectiontraceTAbdr   ctforms                                r   numpy_procrustesr1    sF   
''CAaGGEBr
&&)C
&&)C	
SB	
SBr6,,.Cr6,,.C GGCLEGGCLE %KB%KB	Av^^R!QrT!23A6 	rttRAYY]]15]1FAa
A
q!##AV ))--*Q. (adGrMGbERKEq!##AeegG eOe# 
N 'M"&&Q-'#- CK!g+-55"&&Q-#% 
Avcrc!eHasAA 1A6E a;r   )r   F)N)Tr  )6__doc__r   einopsr   r   torch.nnr   r%   rr   r  mathr   r   r   r   	jaxtypingr	   r
   r[   r=   r   r?   r/   r8   rH   sklearn.clusterrI   scipy.spatial.transformrJ   rt   rs   rR   rS   rM   rO   rU   rb   rj   r   r   r   r   r   rL   r   r   r   r   r   r   r  r  r  r1  r   r   r   <module>r9     sT   B  $ $        C2R-ell -u|| -@%,, @5<< @ # 1 5<<+kEFtLQQSYY[9 ech4:(&R2lF2VC2L
-ell 
-
/U\\ 
/LL"\\7<||
\\(5<<5,1LL5
\\5 33*/,,3
\\3
:U\\ 
:ell 
:u|| 
:LL&+ll
\\3LL33 ||3 \\	368LL88 ||8 \\	8Kr   