a d @szddlZddlZddlmZmZddlZddlmmZ ddlm Z m Z ddl m Z ddlmZddlmZgdZGdd d ejZej ej d d d Zej ej d d dZej ej eej ej fdddZdoej ej eeej ej fdddZdpej eej dddZej ej dddZej ej dddZej ej ddd Zej ej dd!d"Zej ej d#d$d%Zej ej d&d'd(Z dej!fej eeej d)d*d+Z"dqej eej d-d.d/Z#ej!fej eej d0d1d2Z$ej!fej eej d0d3d4Z%dej!fej eeej d5d6d7Z&dej!fej eeej d5d8d9Z'ej!fej eej d:d;d<Z(drej e)e)eej d=d>d?Z*dsej e)e)eej d=d@dAZ+dtej e)e)e)eej dBdCdDZ,duej e)e)e)eej dBdEdFZ-ej ej dGdHdIZ.ej ee)e)fee)e)fej dJdKdLZ/dve)e)eeej0eej1ej dNdOdPZ2dwe)e)e)eeej0eej1ej dQdRdSZ3ej ee)e)fee)e)fej dJdTdUZ4ej ee)e)e)fee)e)e)fej dJdVdWZ5e e e dXdYdZZ6e ee e fd[d\d]Z7e e d^d_d`Z8e e ee e fdXdadbZ9e e dcdddeZ:e e ee e fdXdfdgZ;e e ee e fdXdhdiZdS)xN)OptionalTuple)Tensortensor)piKORNIA_CHECK_SHAPE)_torch_inverse_cast)$rad2degdeg2radpol2cartcart2polconvert_points_from_homogeneousconvert_points_to_homogeneous"convert_affinematrix_to_homography$convert_affinematrix_to_homography3dangle_axis_to_rotation_matrixangle_axis_to_quaternionrotation_matrix_to_angle_axisrotation_matrix_to_quaternionquaternion_to_angle_axisquaternion_to_rotation_matrixquaternion_log_to_expquaternion_exp_to_logdenormalize_pixel_coordinatesnormalize_pixel_coordinatesnormalize_quaterniondenormalize_pixel_coordinates3dnormalize_pixel_coordinates3dangle_to_rotation_matrixnormalize_homographydenormalize_homographynormalize_homography3dnormal_transform_pixelnormal_transform_pixel3dworldtocam_to_camtoworld_Rtcamtoworld_to_worldtocam_RtRt_to_matrix4x4matrix4x4_to_Rt!camtoworld_graphics_to_vision_4x4!camtoworld_vision_to_graphics_4x4 camtoworld_graphics_to_vision_Rt camtoworld_vision_to_graphics_RtARKitQTVecs_to_ColmapQTVecsc@seZdZdZdZdS)QuaternionCoeffOrderZxyzwwxyzN)__name__ __module__ __qualname__XYZWWXYZr5r5d/var/www/html/stable-diffusion-webui/venv/lib/python3.9/site-packages/kornia/geometry/conversions.pyr.5sr.)rreturncCs:t|tjstdt|d|t|j|jS)aFunction that converts angles from radians to degrees. Args: tensor: Tensor of arbitrary shape. Returns: Tensor with same shape as input. Example: >>> input = torch.tensor(3.1415926535) >>> rad2deg(input) tensor(180.) &Input type is not a torch.Tensor. Got f@ isinstancetorchr TypeErrortypertodevicedtyperr5r5r6r :s r cCs:t|tjstdt||t|j|jdS)aFunction that converts angles from degrees to radians. Args: tensor: Tensor of arbitrary shape. Returns: tensor with same shape as input. Examples: >>> input = torch.tensor(180.) >>> deg2rad(input) tensor(3.1416) r8r9r:rBr5r5r6r Ns r )rhophir7cCsXt|tjt|tj@s4tdt|dt||t|}|t|}||fS)aFunction that converts polar coordinates to cartesian coordinates. Args: rho: Tensor of arbitrary shape. phi: Tensor of same arbitrary shape. Returns: - x: Tensor with same shape as input. - y: Tensor with same shape as input. Example: >>> rho = torch.rand(1, 3, 3) >>> phi = torch.rand(1, 3, 3) >>> x, y = pol2cart(rho, phi) r8, )r;r<rr=r>cossin)rCrDxyr5r5r6r bs r :0yE>)rHrIepsr7cCsbt|tjt|tj@s4tdt|dt|t|d|d|}t||}||fS)aFunction that converts cartesian coordinates to polar coordinates. Args: x: Tensor of arbitrary shape. y: Tensor of same arbitrary shape. eps: To avoid division by zero. Returns: - rho: Tensor with same shape as input. - phi: Tensor with same shape as input. Example: >>> x = torch.rand(1, 3, 3) >>> y = torch.rand(1, 3, 3) >>> rho, phi = cart2pol(x, y) r8rE)r;r<rr=r>sqrtatan2)rHrIrKrCrDr5r5r6r zs  r )pointsrKr7cCst|tjstdt|t|jdkr>> input = torch.tensor([[0., 0., 1.]]) >>> convert_points_from_homogeneous(input) tensor([[0., 0.]]) r8rL(Input must be at least a 2D tensor. Got .N?) r;r<rr=r>lenshape ValueErrorabswhere ones_like)rOrKZz_vecmaskZscaler5r5r6rs r)rOr7cCsTt|tjstdt|t|jdkr>> input = torch.tensor([[0., 0.]]) >>> convert_points_to_homogeneous(input) tensor([[0., 0., 1.]]) r8rLrPrconstantrR) r;r<rr=r>rSrTrUnn functionalpad)rOr5r5r6rs  r)Ar7cCs.tjjj|gdddd}|dd7<|S)N)rrrrZr[)value).rQrQrR)r<r\r]r^)r_Hr5r5r6(_convert_affinematrix_to_homography_implsrccCsVt|tjstdt|t|jdkr>|jdddksNtd|jt|S)aFunction that converts batch of affine matrices. Args: A: the affine matrix with shape :math:`(B,2,3)`. Returns: the homography matrix with shape of :math:`(B,3,3)`. Examples: >>> A = torch.tensor([[[1., 0., 0.], ... [0., 1., 0.]]]) >>> convert_affinematrix_to_homography(A) tensor([[[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]]) r8N)rLrdz)Input matrix must be a Bx2x3 tensor. Got r;r<rr=r>rSrTrUrcr_r5r5r6rs   rcCsVt|tjstdt|t|jdkr>|jdddksNtd|jt|S)a.Function that converts batch of 3d affine matrices. Args: A: the affine matrix with shape :math:`(B,3,4)`. Returns: the homography matrix with shape of :math:`(B,4,4)`. Examples: >>> A = torch.tensor([[[1., 0., 0., 0.], ... [0., 1., 0., 0.], ... [0., 0., 1., 0.]]]) >>> convert_affinematrix_to_homography3d(A) tensor([[[1., 0., 0., 0.], [0., 1., 0., 0.], [0., 0., 1., 0.], [0., 0., 0., 1.]]]) r8rdreN)rdz)Input matrix must be a Bx3x4 tensor. Got rfrgr5r5r6rs   r) angle_axisr7c Cs$t|tjstdt||jddks>> input = torch.tensor([[0., 0., 0.]]) >>> angle_axis_to_rotation_matrix(input) tensor([[[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]]) >>> input = torch.tensor([[1.5708, 0., 0.]]) >>> angle_axis_to_rotation_matrix(input) tensor([[[ 1.0000e+00, 0.0000e+00, 0.0000e+00], [ 0.0000e+00, -3.6200e-06, -1.0000e+00], [ 0.0000e+00, 1.0000e+00, -3.6200e-06]]]) r8rQrdz(Input size must be a (*, 3) tensor. Got ư>c SsBd}t|}|||}tj|ddd\}}}t|} t|} | |||| } || |||| } | | |||| } |||| || }| |||| }|| |||| }|| |||| }| | |||| }| |||| }tj| ||| ||| ||g dd}|dddS)NrRrdrZdimrQ)r<rMchunkrFrGcatview)ritheta2rKk_onethetar/ZwxZwyZwz cos_theta sin_thetaZr00Zr10Zr20Zr01Zr11Zr21Zr02Zr12Zr22rotation_matrixr5r5r6_compute_rotation_matrix"s"     z?angle_axis_to_rotation_matrix.._compute_rotation_matrixc SsTtj|ddd\}}}t|}tj|| |||| | ||g dd}|dddS)NrdrZrkrQ)r<rmrXrnro)rirxZryZrzrqrur5r5r6_compute_rotation_matrix_taylor9s &zFangle_axis_to_rotation_matrix.._compute_rotation_matrix_taylorrZrkrLr.N)rj)r;r<rr=r>rTrU unsqueezematmul transposesqueezeror?r@Ztype_asZeyerepeat) rirvrxZ _angle_axisrpZrotation_matrix_normalZrotation_matrix_taylorrKrYZmask_posZmask_negZ batch_sizerur5r5r6rs(      "r)rur7cCs\t|tjstdt||jdddks@td|jt|tj d}t |tj dS)aConvert 3x3 rotation matrix to Rodrigues vector in radians. Args: rotation_matrix: rotation matrix of shape :math:`(N, 3, 3)`. Returns: Rodrigues vector transformation of shape :math:`(N, 3)`. Example: >>> input = torch.tensor([[1., 0., 0.], ... [0., 1., 0.], ... [0., 0., 1.]]) >>> rotation_matrix_to_angle_axis(input) tensor([0., 0., 0.]) >>> input = torch.tensor([[1., 0., 0.], ... [0., 0., -1.], ... [0., 1., 0.]]) >>> rotation_matrix_to_angle_axis(input) tensor([1.5708, 0.0000, 0.0000]) r8reNrdrd+Input size must be a (*, 3, 3) tensor. Got order) r;r<rr=r>rTrUrr.r4r)ru quaternionr5r5r6rXs  r)rurKrr7c st|tjstdt||jdddks@td|jtjsn j t j vrntdt j  t j krtdtjtjtjdd d  |jg|jddd R}tj|d d d \     f dd} f dd} f dd} f dd}t k||}tk k@||} t dk|| } | S)aConvert 3x3 rotation matrix to 4d quaternion vector. The quaternion vector has components in (w, x, y, z) or (x, y, z, w) format. .. note:: The (x, y, z, w) order is going to be deprecated in favor of efficiency. Args: rotation_matrix: the rotation matrix to convert with shape :math:`(*, 3, 3)`. eps: small value to avoid zero division. order: quaternion coefficient order. Note: 'xyzw' will be deprecated in favor of 'wxyz'. Return: the rotation in quaternion with shape :math:`(*, 4)`. Example: >>> input = torch.tensor([[1., 0., 0.], ... [0., 1., 0.], ... [0., 0., 1.]]) >>> rotation_matrix_to_quaternion(input, eps=torch.finfo(input.dtype).eps, ... order=QuaternionCoeffOrder.WXYZ) tensor([1., 0., 0., 0.]) r8reNr~rorder must be one of `XYZW` quaternion coefficient order is deprecated and will be removed after > 0.6. Please use `QuaternionCoeffOrder.WXYZ` instead.) numerator denominatorr7cSs t|jj}|tj||dS)Nmin)r<ZfinforAZtinyclamp)rrrKr5r5r6safe_zero_divisionsz9rotation_matrix_to_quaternion..safe_zero_division rQchunksrlcs~t dd}d|}|}|}|}tjkrhtj||||fddStj||||fddSNrR@g?rQrkr<rMr.r3rnsqZqwZqxZqyZqz) rKm01m02m10m12m20m21rrtracer5r6trace_positive_conds z:rotation_matrix_to_quaternion..trace_positive_condcstd d} |}d|} |} |} tjkrptj||||fddStj||||fddSrrr rKm00rrrm11rrrm22rrr5r6cond_1s z-rotation_matrix_to_quaternion..cond_1cstd d} |} |}d|} |} tjkrptj||||fddStj||||fddSrrrrr5r6cond_2s z-rotation_matrix_to_quaternion..cond_2cstd d} |} |} |}d|} tjkrptj||||fddStj||||fddSrrrrr5r6cond_3s z-rotation_matrix_to_quaternion..cond_3r`)r;r<rr=r>rTrUjit is_scriptingnamer. __members__keysr3warningswarnrormrW) rurKrZrotation_matrix_vecrrrrZwhere_2Zwhere_1rr5) rKrrrrrrrrrrrrr6rws.   "  " " " r-q=)rrKr7cCsNt|tjstdt||jddks>> quaternion = torch.tensor((1., 0., 1., 0.)) >>> normalize_quaternion(quaternion) tensor([0.7071, 0.0000, 0.7071, 0.0000]) r8rQrh,Input must be a tensor of shape (*, 4). Got r)prlrK) r;r<rr=r>rTrUF normalize)rrKr5r5r6rs  r)rrr7c Cst|tjstdt||jddks>> quaternion = torch.tensor((0., 0., 0., 1.)) >>> quaternion_to_rotation_matrix(quaternion, order=QuaternionCoeffOrder.WXYZ) tensor([[-1., 0., 0.], [ 0., -1., 0.], [ 0., 0., 1.]]) r8rQrhrrrrrrRrkrdrZr)r;r<rr=r>rTrUrrrr.rrr3rrrrmrstackrorSr|)rrZquaternion_normrHrIzwZtxtytzZtwxZtwyZtwzZtxxZtxyZtxzZtyyZtyzZtzzZoneZmatrixr5r5r6rs\          rc Cst|stdt||jddks:td|jtjsh|jt j vrhtdt j |t j kr|t dtg}tg}tg}tg}|t j kr|d}|d}|d }|d }n |d}|d}|d }|d }||||||}t|}d t|d kt| | t||}||} d t|} t|d k| | } t|d ddf} | d|| 7<| d|| 7<| d || 7<| S)aConvert quaternion vector to angle axis of rotation in radians. The quaternion should be in (x, y, z, w) or (w, x, y, z) format. Adapted from ceres C++ library: ceres-solver/include/ceres/rotation.h Args: quaternion: tensor with quaternions. order: quaternion coefficient order. Note: 'xyzw' will be deprecated in favor of 'wxyz'. Return: tensor with angle axis of rotation. Shape: - Input: :math:`(*, 4)` where `*` means, any number of dimensions - Output: :math:`(*, 3)` Example: >>> quaternion = torch.tensor((1., 0., 0., 0.)) >>> quaternion_to_angle_axis(quaternion) tensor([3.1416, 0.0000, 0.0000]) r8rQrhz.Input must be a tensor of shape Nx4 or 4. Got rr).r).rZ).rL).rdrr`.Nrd)r< is_tensorr=r>rTrUrrrr.rrr3rrrrMrWrNrXZ zeros_like) rrZq1Zq2Zq3rsZsin_squared_thetartZ two_thetak_posk_negkrir5r5r6rMsJ          r)rrKrr7cCst|tjstdt||jddks>> quaternion = torch.tensor((0., 0., 0.)) >>> quaternion_log_to_exp(quaternion, eps=torch.finfo(quaternion.dtype).eps, ... order=QuaternionCoeffOrder.WXYZ) tensor([1., 0., 0., 0.]) r8rQrdz,Input must be a tensor of shape (*, 3). Got rrrLTrrlZkeepdimrrk)r;r<rr=r>rTrUrrrr.rrr3rrnormrrGrFrrn)rrKrnorm_qquaternion_vectorquaternion_scalarZquaternion_expr5r5r6rs&      rcCst|tjstdt||jddks>> quaternion = torch.tensor((1., 0., 0., 0.)) >>> quaternion_exp_to_log(quaternion, eps=torch.finfo(quaternion.dtype).eps, ... order=QuaternionCoeffOrder.WXYZ) tensor([0., 0., 0.]) r8rQrhrrr.rrdrZrLTrrrR)rmax)r;r<rr=r>rTrUrrrr.rrr3rrrrracos)rrKrrrrZquaternion_logr5r5r6rs,      r)rirr7cCst|stdt||jddks:td|jtjsh|jt j vrhtdt j |t j kr|t d|ddd f}|dd d f}|dd df}||||||}t|}|d }|d k}t|} d | } t||} t|| | } t|t|| } tjg|jd ddR|j|jd}|t j kr|| |ddd f<|| |dd d f<|| |dd df<| |dddf<nL|| |dd d f<|| |dd df<|| |dddf<| |ddd f<|S)aConvert an angle axis to a quaternion. The quaternion vector has components in (x, y, z, w) or (w, x, y, z) format. Adapted from ceres C++ library: ceres-solver/include/ceres/rotation.h Args: angle_axis: tensor with angle axis in radians. order: quaternion coefficient order. Note: 'xyzw' will be deprecated in favor of 'wxyz'. Return: tensor with quaternion. Shape: - Input: :math:`(*, 3)` where `*` means, any number of dimensions - Output: :math:`(*, 4)` Example: >>> angle_axis = torch.tensor((0., 1., 0.)) >>> angle_axis_to_quaternion(angle_axis, order=QuaternionCoeffOrder.WXYZ) tensor([0.8776, 0.0000, 0.4794, 0.0000]) r8rQrdz.Input must be a tensor of shape Nx3 or 3. Got rr.rrZrLg?r`Nrh)sizerAr@)r<rr=r>rTrUrrrr.rrr3rrrMrXrGrWrFzerosrAr@)rirZa0Za1Za2Z theta_squaredrrZ half_thetarYZonesrrrrrr5r5r6rsH      r)pixel_coordinatesheightwidthrKr7cCsz|jddkrtd|jttj||j|jdtj||j|jdg}tjd|j|jd|d|}||dS)aRNormalize pixel coordinates between -1 and 1. Normalized, -1 if on extreme left, 1 if on extreme right (x = w-1). Args: pixel_coordinates: the grid with pixel coordinates. Shape can be :math:`(*, 2)`. width: the maximum width in the x-axis. height: the maximum height in the y-axis. eps: safe division by zero. Return: the normalized pixel coordinates with shape :math:`(*, 2)`. Examples: >>> coords = torch.tensor([[50., 100.]]) >>> normalize_pixel_coordinates(coords, 100, 50) tensor([[1.0408, 1.0202]]) rQrL7Input pixel_coordinates must be of shape (*, 2). Got {}r@rArrZ) rTrUformatr<rrr@rArrrrrKZhwfactorr5r5r6rasrcCsv|jddkrtd|jtt|t|g|j|j}td|d |}td||dS)aMDenormalize pixel coordinates. The input is assumed to be -1 if on extreme left, 1 if on extreme right (x = w-1). Args: pixel_coordinates: the normalized grid coordinates. Shape can be :math:`(*, 2)`. width: the maximum width in the x-axis. height: the maximum height in the y-axis. eps: safe division by zero. Return: the denormalized pixel coordinates with shape :math:`(*, 2)`. Examples: >>> coords = torch.tensor([[-1., -1.]]) >>> denormalize_pixel_coordinates(coords, 100, 50) tensor([[0., 0.]]) rQrLrrrZrR rTrUrr<rrr?r@rArrr5r5r6rsr)rdepthrrrKr7cCst|jddkrtd|jtt|t|t|g|j|j}td|d |}||dS)aNormalize pixel coordinates between -1 and 1. Normalized, -1 if on extreme left, 1 if on extreme right (x = w-1). Args: pixel_coordinates: the grid with pixel coordinates. Shape can be :math:`(*, 3)`. depth: the maximum depth in the z-axis. height: the maximum height in the y-axis. width: the maximum width in the x-axis. eps: safe division by zero. Return: the normalized pixel coordinates. rQrd7Input pixel_coordinates must be of shape (*, 3). Got {}rrZrrrrrrKZdhwrr5r5r6rs"rcCs~|jddkrtd|jtt|t|t|g|j|j}td|d |}td||dS)aDenormalize pixel coordinates. The input is assumed to be -1 if on extreme left, 1 if on extreme right (x = w-1). Args: pixel_coordinates: the normalized grid coordinates. Shape can be :math:`(*, 3)`. depth: the maximum depth in the x-axis. height: the maximum height in the y-axis. width: the maximum width in the x-axis. eps: safe division by zero. Return: the denormalized pixel coordinates. rQrdrrrZrRrrr5r5r6rs"r)angler7cCsJt|}t|}t|}tj||| |gddjg|jddRS)aOCreate a rotation matrix out of angles in degrees. Args: angle: tensor of angles in degrees, any shape :math:`(*)`. Returns: tensor of rotation matrices with shape :math:`(*, 2, 2)`. Example: >>> input = torch.rand(1, 3) # Nx3 >>> output = angle_to_rotation_matrix(input) # Nx3x2x2 rQrkrL)r r<rFrGrrorT)rZang_radZcos_aZsin_ar5r5r6rs   r)dst_pix_trans_src_pix dsize_src dsize_dstr7c Cst|tjstdt|t|jdksN|jdddksNtd|j|\}}|\}}t|| |}t |}t|| |} | ||} | S)aNormalize a given homography in pixels to [-1, 1]. Args: dst_pix_trans_src_pix: homography/ies from source to destination to be normalized. :math:`(B, 3, 3)` dsize_src: size of the source image (height, width). dsize_dst: size of the destination image (height, width). Returns: the normalized homography of shape :math:`(B, 3, 3)`. r8rdreNr~8Input dst_pix_trans_src_pix must be a Bx3x3 tensor. Got r;r<rr=r>rSrTrUr#r?r ) rrrsrc_hsrc_wdst_hdst_wsrc_norm_trans_src_pixsrc_pix_trans_src_normdst_norm_trans_dst_pixdst_norm_trans_src_normr5r5r6r s   r +=)rrrKr@rAr7cCs|tjgdgdgdg||d}|dkr.|n|d}|dkrB|n|d}|dd||d<|d d||d <|d S) aCompute the normalization matrix from image size in pixels to [-1, 1]. Args: height image height. width: image width. eps: epsilon to prevent divide-by-zero errors Returns: normalized transform with shape :math:`(1, 3, 3)`. )rRr`r)r`rRr)r`r`rRrrZrRrrrrZrZrr<rry)rrrKr@rAtr_mat width_denom height_denomr5r5r6r#s "r#)rrrrKr@rAr7c Cstjgdgdgdgdg||d}|dkr4|n|d}|dkrH|n|d}|dkr\|n|d} |dd ||d<|d d ||d <|d d | |d <|d S) a+Compute the normalization matrix from image size in pixels to [-1, 1]. Args: depth: image depth. height: image height. width: image width. eps: epsilon to prevent divide-by-zero errors Returns: normalized transform with shape :math:`(1, 4, 4)`. )rRr`r`r)r`rRr`r)r`r`rRr)r`r`r`rRrrZrRrrr)rLrLrr) rrrrKr@rArrrZ depth_denomr5r5r6r$<sr$c Cst|tjstdt|t|jdksN|jdddksNtd|j|\}}|\}}t|| |}t|| |}t |} | ||} | S)aDe-normalize a given homography in pixels from [-1, 1] to actual height and width. Args: dst_pix_trans_src_pix: homography/ies from source to destination to be denormalized. :math:`(B, 3, 3)` dsize_src: size of the source image (height, width). dsize_dst: size of the destination image (height, width). Returns: the denormalized homography of shape :math:`(B, 3, 3)`. r8rdreNr~rr) rrrrrrrrrZdst_denorm_trans_dst_pixrr5r5r6r!as   r!c Cst|tjstdt|t|jdksN|jdddksNtd|j|\}}}|\}}}t||| |} t | } t||| |} | || } | S)aNormalize a given homography in pixels to [-1, 1]. Args: dst_pix_trans_src_pix: homography/ies from source to destination to be normalized. :math:`(B, 4, 4)` dsize_src: size of the source image (depth, height, width). dsize_src: size of the destination image (depth, height, width). Returns: the normalized homography. Shape: Output: :math:`(B, 4, 4)` r8rdreN)rhrhr) r;r<rr=r>rSrTrUr$r?r ) rrrZsrc_drrZdst_drrrrrrr5r5r6r"s     r")Rtr7cCs6t|gdt|gdtj||gdd}t|S)aCombines 3x3 rotation matrix R and 1x3 translation vector t into 4x4 extrinsics. Args: R: Rotation matrix, :math:`(B, 3, 3).` t: Translation matrix :math:`(B, 3, 1)`. Returns: the extrinsics :math:`(B, 4, 4)`. Example: >>> R, t = torch.eye(3)[None], torch.ones(3).reshape(1, 3, 1) >>> Rt_to_matrix4x4(R, t) tensor([[[1., 0., 0., 1.], [0., 1., 0., 1.], [0., 0., 1., 1.], [0., 0., 0., 1.]]]) B3rrr1rLrk)rr<rnr)rrZRtr5r5r6r'sr') extrinsicsr7cCsLt|gd|ddddddf|ddddddf}}||fS)aConverts 4x4 extrinsics into 3x3 rotation matrix R and 1x3 translation vector ts. Args: extrinsics: pose matrix :math:`(B, 4, 4)`. Returns: R: Rotation matrix, :math:`(B, 3, 3).` t: Translation matrix :math:`(B, 3, 1)`. Example: >>> ext = torch.eye(4)[None] >>> matrix4x4_to_Rt(ext) (tensor([[[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]]), tensor([[[0.], [0.], [0.]]])) r4rNrdr)rrrr5r5r6r(s6r()extrinsics_graphicsr7cCsBt|gdtgdgdgdgdgg|j|jd}||S)aConverts graphics coordinate frame (e.g. OpenGL) to vision coordinate frame (e.g. OpenCV.), , i.e. flips y and z axis. Graphics convention: [+x, +y, +z] == [right, up, backwards]. Vision convention: [+x, +y, +z] == [right, down, forwards] Args: extrinsics: pose matrix :math:`(B, 4, 4)`. Returns: extrinsics: pose matrix :math:`(B, 4, 4)`. Example: >>> ext = torch.eye(4)[None] >>> camtoworld_graphics_to_vision_4x4(ext) tensor([[[ 1., 0., 0., 0.], [ 0., -1., 0., 0.], [ 0., 0., -1., 0.], [ 0., 0., 0., 1.]]]) rrZrrrrrQrrrrrQrrrrrRrAr@)rrrAr@)r invert_yzr5r5r6r)sr)cCs2t|gdt|gdtt||}t|S)aConverts graphics coordinate frame (e.g. OpenGL) to vision coordinate frame (e.g. OpenCV.), , i.e. flips y and z axis. Graphics convention: [+x, +y, +z] == [right, up, backwards]. Vision convention: [+x, +y, +z] == [right, down, forwards] Args: R: Rotation matrix, :math:`(B, 3, 3).` t: Translation matrix :math:`(B, 3, 1)`. Returns: R: Rotation matrix, :math:`(B, 3, 3).` t: Translation matrix :math:`(B, 3, 1)`. Example: >>> R, t = torch.eye(3)[None], torch.ones(3).reshape(1, 3, 1) >>> camtoworld_graphics_to_vision_Rt(R, t) (tensor([[[ 1., 0., 0.], [ 0., -1., 0.], [ 0., 0., -1.]]]), tensor([[[1.], [1.], [1.]]])) rr)rr)r'r(rrZmat4x4r5r5r6r+sr+)extrinsics_visionr7cCsDt|gdtjgdgdgdgdgg|j|jd}||S)a{Converts vision coordinate frame (e.g. OpenCV) to graphics coordinate frame (e.g. OpenGK.), i.e. flips y and z axis Graphics convention: [+x, +y, +z] == [right, up, backwards]. Vision convention: [+x, +y, +z] == [right, down, forwards] Args: extrinsics: pose matrix :math:`(B, 4, 4)`. Returns: extrinsics: pose matrix :math:`(B, 4, 4)`. Example: >>> ext = torch.eye(4)[None] >>> camtoworld_vision_to_graphics_4x4(ext) tensor([[[ 1., 0., 0., 0.], [ 0., -1., 0., 0.], [ 0., 0., -1., 0.], [ 0., 0., 0., 1.]]]) rrrrrr)rr<rrAr@)rrr5r5r6r*sr*cCs2t|gdt|gdtt||}t|S)aConverts graphics coordinate frame (e.g. OpenGL) to vision coordinate frame (e.g. OpenCV.), , i.e. flips y and z axis. Graphics convention: [+x, +y, +z] == [right, up, backwards]. Vision convention: [+x, +y, +z] == [right, down, forwards] Args: R: Rotation matrix, :math:`(B, 3, 3).` t: Translation matrix :math:`(B, 3, 1)`. Returns: R: Rotation matrix, :math:`(B, 3, 3).` t: Translation matrix :math:`(B, 3, 1)`. Example: >>> R, t = torch.eye(3)[None], torch.ones(3).reshape(1, 3, 1) >>> camtoworld_vision_to_graphics_Rt(R, t) (tensor([[[ 1., 0., 0.], [ 0., -1., 0.], [ 0., 0., -1.]]]), tensor([[[1.], [1.], [1.]]])) rr)rr*r'r(rr5r5r6r,-sr,cCs:t|gdt|gd|dd}| |}||fS)aConverts camtoworld, i.e. projection from camera coordinate system to world coordinate system, to worldtocam frame i.e. projection from world to the camera coordinate system (used in Colmap). See long-url: https://colmap.github.io/format.html#output-format Args: R: Rotation matrix, :math:`(B, 3, 3).` t: Translation matrix :math:`(B, 3, 1)`. Returns: Rinv: Rotation matrix, :math:`(B, 3, 3).` tinv: Translation matrix :math:`(B, 3, 1)`. Example: >>> R, t = torch.eye(3)[None], torch.ones(3).reshape(1, 3, 1) >>> camtoworld_to_worldtocam_Rt(R, t) (tensor([[[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]]), tensor([[[-1.], [-1.], [-1.]]])) rrrZrLrr{rrZR_invZnew_tr5r5r6r&Js   r&cCs:t|gdt|gd|dd}| |}||fS)aConverts worldtocam frame i.e. projection from world to the camera coordinate system (used in Colmap) to camtoworld, i.e. projection from camera coordinate system to world coordinate system. Args: R: Rotation matrix, :math:`(B, 3, 3).` t: Translation matrix :math:`(B, 3, 1)`. Returns: Rinv: Rotation matrix, :math:`(B, 3, 3).` tinv: Translation matrix :math:`(B, 3, 1)`. Example: >>> R, t = torch.eye(3)[None], torch.ones(3).reshape(1, 3, 1) >>> worldtocam_to_camtoworld_Rt(R, t) (tensor([[[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]]), tensor([[[-1.], [-1.], [-1.]]])) rrrZrLrrr5r5r6r%js   r%)qvectvecr7cCsRt|tjd}t||\}}t||\}}|ddd}t|tjd}||fS)aConverts output of Apple ARKit screen pose (in quaternion representation) to the camera-to-world transformation, expected by Colmap, also in quaternion representation. Args: qvec: ARKit rotation quaternion :math:`(B, 4)`, [x, y, z, w] format. tvec: translation vector :math:`(B, 3, 1)`, [x, y, z] Returns: qvec: Colmap rotation quaternion :math:`(B, 4)`, [w, x, y, z] format. tvec: translation vector :math:`(B, 3, 1)`, [x, y, z] Example: >>> q, t = torch.tensor([0, 1, 0, 1.])[None], torch.ones(3).reshape(1, 3, 1) >>> ARKitQTVecs_to_ColmapQTVecs(q, t) (tensor([[0.7071, 0.0000, 0.7071, 0.0000]]), tensor([[[-1.0000], [-1.0000], [ 1.0000]]])) rrQrdrZ)rr.r4r+r&Zreshaper contiguous)rrZRcgZRcvZTcvZR_colmapZt_colmapZq_colmapr5r5r6r-s r-)rJ)rJ)r)rJ)rJ)rJ)rJ)rNN)rNN)?enumrtypingrrr<Ztorch.nn.functionalr\r]rrrZkornia.constantsrZkornia.testingrZkornia.utils.helpersr __all__Enumr.r r r floatr rrrcrrrrr3rrrrrrrintrrrrrr r@rAr#r$r!r"r'r(r)r+r*r,r&r%r-r5r5r5r6s   ("&!R  d  T M 9 B P  (  $     & ! & # $