3jSSKJr SSKJr SSKrSSKJs Jr SSK J r SSK J r SSK JrJr SSKJr /SQrS=S jrS=S jrS>S jrS?S@S jjrS?SAS jjrSBSjrSCSjrSCSjrSCSjrSDSjr\ "SSS9SDSj5rSESjr\ "SSS9SESj5rS?SFSjjr SGSHSjjr!SISjr"SISjr#\ "SSS9SISj5r$S?SHS jjr%S?SHS!jjr&SDS"jr'\ "S#SS9SDS$j5r(SJS%jr)SKS&jr*S?SLS'jjr+S?SLS(jjr,S?SMS)jjr-S?SMS*jjr.SNS+jr/SOS,jr0SPSQS-jjr1SPSRS.jjr2SOS/jr3SSS0jr4STS1jr5SUS2jr6SVS3jr7SWS4jr8SXS5jr9SYS6jr:SZS7jr;SYS8jrS[S;jr?S\S<jr@g)]) annotations)OptionalN)pi) deprecated) KORNIA_CHECKKORNIA_CHECK_SHAPE)_torch_inverse_cast)-ARKitQTVecs_to_ColmapQTVecsRt_to_matrix4x4angle_axis_to_quaternionangle_axis_to_rotation_matrixangle_to_rotation_matrixaxis_angle_to_quaternionaxis_angle_to_rotation_matrix!camtoworld_graphics_to_vision_4x4 camtoworld_graphics_to_vision_Rtcamtoworld_to_worldtocam_Rt!camtoworld_vision_to_graphics_4x4 camtoworld_vision_to_graphics_Rtcart2pol"convert_affinematrix_to_homography$convert_affinematrix_to_homography3dconvert_points_from_homogeneousconvert_points_to_homogeneousdeg2raddenormalize_homographydenormalize_pixel_coordinatesdenormalize_pixel_coordinates3d"denormalize_points_with_intrinsicseuler_from_quaternionmatrix4x4_to_Rtnormal_transform_pixelnormal_transform_pixel3dnormalize_homographynormalize_homography3dnormalize_pixel_coordinatesnormalize_pixel_coordinates3d normalize_points_with_intrinsicsnormalize_quaternionpol2cartquaternion_exp_to_logquaternion_from_eulerquaternion_log_to_expquaternion_to_angle_axisquaternion_to_axis_anglequaternion_to_rotation_matrixrad2degrotation_matrix_to_angle_axisrotation_matrix_to_axis_anglerotation_matrix_to_quaternionvector_to_skew_symmetric_matrixworldtocam_to_camtoworld_Rtc[U[R5(d[S[ U535eSU-[ R "UR5R UR5- $)zConvert angles from radians to degrees. Args: tensor: torch.Tensor of arbitrary shape. Returns: torch.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@ isinstancetorchTensor TypeErrortypertodevicedtypetensors U/home/wildlama/miniconda3/lib/python3.13/site-packages/kornia/geometry/conversions.pyr1r1OsW fell + +@fOPP 6>BEE&--055fllC CCc[U[R5(d[S[ U535eU[ R "UR5R UR5-S- $)zConvert angles from degrees to radians. Args: tensor: torch.Tensor of arbitrary shape. Returns: tensor with same shape as input. Examples: >>> input = torch.tensor(180.) >>> deg2rad(input) tensor(3.1416) r8r9r:rCs rErrdsX fell + +@fOPP BEE&--(--fll; ;e CCrFc&[U[R5[U[R5-(d#[S[ U5S[ U535eU[R "U5-nU[R "U5-nX#4$)aoConvert polar coordinates to cartesian coordinates. Args: rho: torch.Tensor of arbitrary shape. phi: torch.Tensor of same arbitrary shape. Returns: - x: torch.Tensor with same shape as input. - y: torch.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<r=r>r?cossin)rhophixys rEr*r*yso" sELL )JsELL,I I@c 2dSVi[YZZ eiinA eiinA 4KrFc2[U[R5[U[R5-(d#[S[ U5S[ U535e[R "US-US--U-5n[R "X5nX44$)aConvert cartesian coordinates to polar coordinates. Args: x: torch.Tensor of arbitrary shape. y: torch.Tensor of same arbitrary shape. eps: To avoid division by zero. Returns: - rho: torch.Tensor with same shape as input. - phi: torch.Tensor with same shape as input. Example: >>> x = torch.rand(1, 3, 3) >>> y = torch.rand(1, 3, 3) >>> rho, phi = cart2pol(x, y) r8rI)r;r<r=r>r?sqrtatan2)rNrOepsrLrMs rErrsx$ q%,, '*Q *E E@a DQRG9UVV **QTAqD[3& 'C ++a C 8OrFc[U[R5(d[S[ U535e[ UR 5S:a[SUR 35eUSSS24n[R"U5U:n[R"USX!-- [R"U55nX@SSS24-$)adConvert points from homogeneous to Euclidean space. Args: points: the points to be transformed of shape :math:`(B, N, D)`. eps: to avoid division by zero. Returns: the points in Euclidean space :math:`(B, N, D-1)`. Examples: >>> input = torch.tensor([[0., 0., 1.]]) >>> convert_points_from_homogeneous(input) tensor([[0., 0.]]) r8rQ(Input must be at least a 2D tensor. Got .N?) r;r<r=r>r?lenshape ValueErrorabswhere ones_like)pointsrTz_vecmaskscales rErrs fell + +@fOPP 6<<1CFLL>RSS!bc*E 5)C/D KKcU[15??53I JE #ss(# ##rFc[U[R5(d[S[ U535e[ UR 5S:a[SUR 35e[R"USS/SS5$)aHConvert points from Euclidean to homogeneous space. Args: points: the points to be transformed with shape :math:`(*, N, D)`. Returns: the points in homogeneous coordinates :math:`(*, N, D+1)`. Examples: >>> input = torch.tensor([[0., 0.]]) >>> convert_points_to_homogeneous(input) tensor([[0., 0., 1.]]) r8rQrVrconstantrX) r;r<r=r>r?rYrZr[Fpad)r_s rErrsm fell + +@fOPP 6<<1CFLL>RSS 55!QS 11rFcR[R"U/SQSSS9nUS==S- ss'U$)N)rrrrdre)value).rWrWrX)rfrg)AHs rE(_convert_affinematrix_to_homography_implrms)eeA|ZsCAkNcN HrFc [U[R5(d[S[ U535e[ UR 5S:XaUR SSS:Xd[SUR 35e[U5$)aConvert 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)rQroz)Input matrix must be a Bx2x3 tensor. Got r;r<r=r>r?rYrZr[rmrks rErrso$ a & &@a JKK LA !''"#,&"8DQWWINOO 3A 66rFc [U[R5(d[S[ U535e[ UR 5S:XaUR SSS:Xd[SUR 35e[U5$)aConvert batch of 3d affine matrices. Args: A: the affine matrix with shape :math:`(B,3,4)`. Returns: the homography matrix with shape of :math:`(B,4,4)`. Examples: >>> A = torch.tensor([[[1., 0., 0., 0.], ... [0., 1., 0., 0.], ... [0., 0., 1., 0.]]]) >>> convert_affinematrix_to_homography3d(A) tensor([[[1., 0., 0., 0.], [0., 1., 0., 0.], [0., 0., 1., 0.], [0., 0., 0., 1.]]]) r8rorpN)roz)Input matrix must be a Bx3x4 tensor. Got rqrrs rErrso( a & &@a JKK LA !''"#,&"8DQWWINOO 3A 66rFc|[U[R5(d[S[ U535eUR SS:Xd[ SUR 35eS S SjjnS SjnX-RSS9nU"X5nU"U5nUS:RSS S 5n[R"XdU5nU$) aConvert 3d vector of axis-angle rotation to 3x3 rotation matrix. Args: axis_angle: tensor of 3d vector of axis-angle rotations in radians with shape :math:`(N, 3)`. Returns: tensor of rotation matrices of shape :math:`(N, 3, 3)`. Example: >>> input = torch.tensor([[0., 0., 0.]]) >>> axis_angle_to_rotation_matrix(input) # doctest: +ELLIPSIS tensor([[[1., ...0., 0.], [0., 1., ...0.], [...0., 0., 1.]]]) >>> input = torch.tensor([[1.5708, 0., 0.]]) >>> axis_angle_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]]]) r8rWroz(Input size must be a (*, 3) tensor. Got ư>c x[R"URSS95nXRS5U-- nUR SS9upVn[R "U5n[R "U5n SU- n XV-n XW-n Xg-n XU-U --nX-Xy-- nXi-X--nXy-X--nXU-U --nU*U -X--nU*U -X--nXY-X--nXU-U --n[R"[R"XU/SS9[R"UUU/SS9[R"UUU/SS9/SS9nU$)N-q=minrWrddimrX)r<rRclamp unsqueezeunbindrJrKstack) axis_angletheta2rTthetawxyzwxwywz cos_theta sin_theta one_minus_coswxwywxwzwywzr00r01r02r10r11r12r20r21r22rots rE_compute_rotation_matrix?axis_angle_to_rotation_matrix.._compute_rotation_matrix@sm 6<._compute_rotation_matrix_taylordsv&&r* #kk    $r1a.  rFr{rd)rv)r torch.TensorrrrTfloatreturnrrrrr) r;r<r=r>r?rZr[sumrr])rrrr rot_normal rot_taylorrarotation_matrixs rErr#s. j%,, / /@jAQ@RSTT   B 1 $CJDTDTCUVWW"H*% * *r * 2F)*=J0>> input = torch.tensor([[1., 0., 0.], ... [0., 1., 0.], ... [0., 0., 1.]]) >>> rotation_matrix_to_axis_angle(input) tensor([0., 0., 0.]) >>> input = torch.tensor([[1., 0., 0.], ... [0., 0., -1.], ... [0., 1., 0.]]) >>> rotation_matrix_to_axis_angle(input) tensor([1.5708, 0.0000, 0.0000]) r8rpNroro+Input size must be a (*, 3, 3) tensor. Got ) r;r<r=r>r?rZr[r4r/)r quaternions rEr3r3sr. ou|| 4 4@oAV@WXYY   % /FG\G\F]^__<_MJ #J //rFr3c[U5$r)r3)rs rEr2r2s ( 99rFc ^^ ^ ^ ^ ^^^^^^^[U[R5(d[S[ U535eUR SSS:Xd[ SUR 35eSSjmUR"/UR SSQSP76n[R"USSS 9u m m m m mmmmmT T-T-mSUU U U UUUUU4 S jjnSUU U U U UUUUUU4 S jjnSUU U U U UUUUUU4 S jjnSUU U U U UUUUUU4 S jjn[R"TT:U"5U"55n[R"T T:T T:-U"5U5n[R"TS:U"5U5n U $)a8Convert 3x3 rotation matrix to 4d quaternion vector. The quaternion vector has components in (w, x, y, z) format. Args: rotation_matrix: the rotation matrix to convert with shape :math:`(*, 3, 3)`. eps: small value to avoid zero division. 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) tensor([1., 0., 0., 0.]) r8rpNrrc[R"UR5RnU[R"XS9- $)Nry)r<finforBtinyr}) numerator denominatorrTs rEsafe_zero_division9rotation_matrix_to_quaternion..safe_zero_divisions.[[1665;;{<< [R"T S-T-5S-nSU-nT "T T - U5nT "TT - U5nT "TT- U5n[R"XX44SS9$NrX@g?rWr{r<rRcat)sqqwqxqyqzrTm01m02m10m12m20m21rtraces rEtrace_positive_cond:rotation_matrix_to_quaternion..trace_positive_condsn ZZ c) *S 0 BY c 2 . c 2 . c 2 .yy"")r22rFc> [R"ST-T - T- T-5S-nT"T T - U5nSU-nT"TT -U5nT"TT -U5n[R"XX44SS9$rrrrrrrrTm00rrrm11rrrm22rs rEcond_1-rotation_matrix_to_quaternion..cond_1sw ZZc C#-3 4s : c 2 . BY c 2 . c 2 .yy"")r22rFc> [R"ST -T- T- T-5S-nT"TT - U5nT"TT -U5nSU-nT"T T -U5n[R"XX44SS9$rrrs rEcond_2-rotation_matrix_to_quaternion..cond_2sw ZZc C#-3 4s : c 2 . c 2 . BY c 2 .yy"")r22rFc> [R"ST-T- T - T-5S-nT"T T- U5nT"TT -U5nT"T T -U5nSU-n[R"XX44SS9$rrrs rEcond_3-rotation_matrix_to_quaternion..cond_3sw ZZc C#-3 4s : c 2 . c 2 . c 2 . BYyy"")r22rFri)rrrrrr)rr) r;r<r=r>r?rZr[reshapechunkr])rrTrotation_matrix_vecrrrrwhere_2where_1rrrrrrrrrrrrs ` @@@@@@@@@@@rEr4r4sX( ou|| 4 4@oAV@WXYY   % /FG\G\F]^__=)8(?(?(_AVAVWZXZA[(_]^(_27++>QZ[ac2d/Cc3S#sC)c/E33333333333kk#)VXvx8Gkk39s3VXwGG${{53;8K8MwWJ rFc[U[R5(d[S[ U535eUR SS:Xd[ SUR 35e[R"USSUS9$)aNormalize a quaternion. The quaternion should be in (x, y, z, w) or (w, x, y, z) format. Args: quaternion: a tensor containing a quaternion to be normalized. The tensor can be of shape :math:`(*, 4)`. eps: small value to avoid division by zero. Return: the normalized quaternion of shape :math:`(*, 4)`. Example: >>> quaternion = torch.tensor((1., 0., 1., 0.)) >>> normalize_quaternion(quaternion) tensor([0.7071, 0.0000, 0.7071, 0.0000]) r8rWrt,Input must be a tensor of shape (*, 4). Got r)pr|rT) r;r<r=r>r?rZr[rf normalize)rrTs rEr)r)sp& j%,, / /@jAQ@RSTT   B 1 $G HXHXGYZ[[ ;;zSbc ::rFc p[U[R5(d[S[ U535eUR SS:Xd[ SUR 35e[U5nUSnUSnUSnUSnS U-nS U-nS U-nXb-n Xr-n X-n Xc-n Xs-n X-nXt-nX-nX-n[R"S 5n[R"UUU-- X- X-X-UU U-- UU - X- UU -UX-- 4 SS 9n/[UR S S5QS PS PnURU5nU$)aConvert a quaternion to a rotation matrix. The quaternion should be in (w, x, y, z) format. Args: quaternion: a tensor containing a quaternion to be converted. The tensor can be of shape :math:`(*, 4)`. Return: the rotation matrix of shape :math:`(*, 3, 3)`. Example: >>> quaternion = torch.tensor((0., 0., 0., 1.)) >>> quaternion_to_rotation_matrix(quaternion) tensor([[-1., 0., 0.], [ 0., -1., 0.], [ 0., 0., 1.]]) r8rWrtr.r.rd.rQ.rorrXr{Nro) r;r<r=r>r?rZr[r)rDrlistr)rquaternion_normwrNrOztxtytztwxtwytwztxxtxytxztyytyztzzone matrix_flat output_shapematrixs rEr0r0s( j%,, / /@jAQ@RSTT   B 1 $G HXHXGYZ[[%9$DO AAAAQwBQwBQwBCCCCCCCCC S)C % 39  I I I 39  #I I #I 39    !K 8T***3B/07!7Q7L   .F MrFc |[U[R5(d[S[ U535eUR SS:Xd[ SUR 35e[R"/5n[R"/5n[R"/5n[R"/5nUSnUSnUSnUSnX-X"--X3--n[R"U5nS [R"US :[R"U*U*5[R"Xd55-nXv- nS [R"U5-n [R"US :X5n [R"U5S S S 24n U S==X-- ss'U S==X*-- ss'U S==X:-- ss'U $)a Convert quaternion vector to axis angle of rotation in radians. The quaternion should be in (w, x, y, z) format. Adapted from ceres C++ library: ceres-solver/include/ceres/rotation.h Args: quaternion: tensor with quaternions. Return: tensor with axis angle 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_axis_angle(quaternion) tensor([0., 0., 0.]) r8rWrtz.Input must be a tensor of shape Nx4 or 4. Got rrrrrri.Nro) r;r<r=r>r?rZr[rDrRr]rSr^ zeros_like) rq1q2q3rsin_squared_thetar two_thetak_posk_negkrs rEr/r/bs. j%,, / /@jAQ@RSTT   B 1 $I*JZJZI[\]]||B'B||B'B||B'B#ll2.I6"I F B F B F B&(g&7"'&A#jj):;I!EKKCiZ)_%I$/E ::Ekk"3c"95HA$// ;C!GDJv"& v"& v"&  rFr/c[U5$r)r/)rs rEr.r. #J //rFc[U[R5(d[S[ U535eUR SS:Xd[ SUR 35e[R"USSSS9RUS9nU[R"U5-U- n[R"U5n[R"/5n[R"XC4SS 9nU$) aApply exponential map to log quaternion. The quaternion should be in (w, x, y, z) format. Args: quaternion: a tensor containing a quaternion to be converted. The tensor can be of shape :math:`(*, 3)`. eps: a small number for clamping. Return: the quaternion exponential map of shape :math:`(*, 4)`. Example: >>> quaternion = torch.tensor((0., 0., 0.)) >>> quaternion_log_to_exp(quaternion, eps=torch.finfo(quaternion.dtype).eps) tensor([1., 0., 0., 0.]) r8rWroz,Input must be a tensor of shape (*, 3). Got rQTrr|keepdimryr{) r;r<r=r>r?rZr[normr}rKrJrDr)rrTnorm_qquaternion_vectorquaternion_scalarquaternion_exps rEr-r-s& j%,, / /@jAQ@RSTT   B 1 $G HXHXGYZ[[!::jA2tLRRWZR'1599V3D&Dv&M&+ii&7$)<<#3NYY 1E2NN rFc [U[R5(d[S[ U535eUR SS:Xd[ SUR 35e[R"/5n[R"/5nUSSS24nUSSS24n[R"USSS S 9RUS 9nU[R"[R"US S S95-U- nU$)aApply the log map to a quaternion. The quaternion should be in (w, x, y, z) format. Args: quaternion: a tensor containing a quaternion to be converted. The tensor can be of shape :math:`(*, 4)`. eps: a small number for clamping. Return: the quaternion log map of shape :math:`(*, 3)`. Example: >>> quaternion = torch.tensor((1., 0., 0., 0.)) >>> quaternion_exp_to_log(quaternion, eps=torch.finfo(quaternion.dtype).eps) tensor([0., 0., 0.]) r8rWrtr.rrdrQTr ryrXrzmax) r;r<r=r>r?rZr[rDrr}acos)rrTrrrquaternion_logs rEr+r+s& j%,, / /@jAQ@RSTT   B 1 $G HXHXGYZ[[',ll2&6&+ll2&6"3!8,"3!8,!::&71"dSYY^aYbF EJJu{{3D$TW'XYY\bb rFc[U[R5(d[S[ U535eUR SS:Xd[ SUR 35eUSSS24nUSSS24nUSSS24nX-X"--X3--n[R"U5nUS -nUS :n[R"U5nS U-n [R"U5U- n [R"XzU 5n [R"U[R"U5U5n [R"/UR S SQS P7URURS 9n X-U SSS24'X+-U SSS24'X;-U SSS 24'XSSS24'U $)a Convert an axis angle to a quaternion. The quaternion vector has components in (w, x, y, z) format. Adapted from ceres C++ library: ceres-solver/include/ceres/rotation.h Args: axis_angle: tensor with axis angle in radians. Return: tensor with quaternion. Shape: - Input: :math:`(*, 3)` where `*` means, any number of dimensions - Output: :math:`(*, 4)` Example: >>> axis_angle = torch.tensor((0., 1., 0.)) >>> axis_angle_to_quaternion(axis_angle) tensor([0.8776, 0.0000, 0.4794, 0.0000]) r8rWroz.Input must be a tensor of shape Nx3 or 3. Got .rrdrQ?riNrt)sizerBrA)r;r<r=r>r?rZr[rRr^rKr]rJzerosrBrA)ra0a1a2 theta_squaredr half_thetaraonesrrr rrs rErrs. j%,, / /@jAQ@RSTT   B 1 $I*JZJZI[\]]"#qs(+B!#qs(+B!#qs(+B"$'BG"3bg"=M**]3E$s{J&,D4D*E))J/%7Ekk$u5Akk$ *(=tDA${{ (z$ (a ( 0@0@IZIZ J6JsAaCx6JsAaCx6JsAaCxsAaCx rFrc[U5$r)rrs rEr r /r rFc[URUR:H5 [URUR:H5 [URUR:H5 X"-nSX-X#---nSSX-U--- nURU5nSX-X1-- -nURSSS9nUR 5n SX-X---n SSXCU---- n U RU 5n XyU 4$)aXConvert a quaternion coefficients to Euler angles. Returned angles are in radians in XYZ convention. Args: w: quaternion :math:`q_w` coefficient. x: quaternion :math:`q_x` coefficient. y: quaternion :math:`q_y` coefficient. z: quaternion :math:`q_z` coefficient. Return: A tuple with euler angles`roll`, `pitch`, `yaw`. rrXrr)rrZrSr}asin) rrNrOryy sinr_cosp cosr_cosprollsinppitch siny_cosp cosy_cospyaws rEr r 7s"AGG#$AGG#$AGG#$ Bququ}%IcQURZ((I ??9 %D !%!%- D ::$C: (D IIKEququ}%IcRa%Z((I //) $C  rFc[URUR:H5 [URUR:H5 US-nUS-nUS-nUR5nUR5nUR5nUR5n UR5n UR5n Xh-U -Xy-U --n Xh-U -Xy-U -- n Xx-U -Xi-U --nXx-U -Xi-U -- nXX4$)aConvert Euler angles to quaternion coefficients. Euler angles are assumed to be in radians in XYZ convention. Args: roll: the roll euler angle. pitch: the pitch euler angle. yaw: the yaw euler angle. Return: A tuple with quaternion coefficients in order of `wxyz`. r)rrZrJrK)r*r,r/ roll_half pitch_halfyaw_halfcysycpspcrsrrrrrs rEr,r,]s u{{*+ )*s IJSyH B B  B  B B B 2" $B 2" $B 2" $B 2" $B 2>rFc URSS:wa[SUR35e[R"[R"X R UR S9[R"XR UR S9/5n[R"SUR UR S9US- RU5- nXP-S- $)aNormalize pixel coordinates between -1 and 1. Normalized, -1 if on extreme left, 1 if on extreme right (x = w-1). Args: pixel_coordinates: the grid with pixel coordinates. Shape can be :math:`(*, 2)`. width: the maximum width in the x-axis. height: the maximum height in the y-axis. eps: safe division by zero. Return: the normalized pixel coordinates with shape :math:`(*, 2)`. Examples: >>> coords = torch.tensor([[50., 100.]]) >>> normalize_pixel_coordinates(coords, 100, 50) tensor([[1.0408, 1.0202]]) rWrQ5Input pixel_coordinates must be of shape (*, 2). Got rArBrrd)rZr[r<rrDrArBr}pixel_coordinatesheightwidthrThwfactors rEr&r&s,r"a'PQbQhQhPijkk{{ LL'?'?GXG^G^ _ LL(@(@HYH_H_ ` B!<<4E4L4LTeTkTkl Q eCjF  % ))rFcURSS:wa[SUR35e[R"[R"U5[R"U5/5R UR 5R UR5n[R"S5US- RU5- n[R"S5U- US--$)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:`(*, 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.]]) rWrQr;rrdrX rZr[r<rrDr@rArBr}r=s rErrs,r"a'PQbQhQhPijkk  U\\%(%,,v*>?@   $ $ %   # # $ !<<,Q~~c/BBF << v %):Q)> ??rFcURSS:wa[SUR35e[R"[R"U5[R"U5[R"U5/5R UR 5R UR5n[R"S5US- RU5- nX`-S- $)aNormalize pixel coordinates between -1 and 1. Normalized, -1 if on extreme left, 1 if on extreme right (x = w-1). Args: pixel_coordinates: the grid with pixel coordinates. Shape can be :math:`(*, 3)`. depth: the maximum depth in the z-axis. height: the maximum height in the y-axis. width: the maximum width in the x-axis. eps: safe division by zero. Return: the normalized pixel coordinates. rWro5Input pixel_coordinates must be of shape (*, 3). Got rrdrDr>depthr?r@rTdhwrBs rEr'r's$r"a'PQbQhQhPijkk  U\\%(%,,u*=u||F?STU   $ $ %   # # $ !<<,as/CCF  % ))rFcURSS:wa[SUR35e[R"[R"U5[R"U5[R"U5/5R UR 5R UR5n[R"S5US- RU5- n[R"S5U- US--$)aDenormalize pixel coordinates. The input is assumed to be -1 if on extreme left, 1 if on extreme right (x = w-1). Args: pixel_coordinates: the normalized grid coordinates. Shape can be :math:`(*, 3)`. depth: the maximum depth in the x-axis. height: the maximum height in the y-axis. width: the maximum width in the x-axis. eps: safe division by zero. Return: the denormalized pixel coordinates. rWrorFrrdrXrDrGs rErrs$r"a'PQbQhQhPijkk  U\\%(%,,u*=u||F?STU   $ $ %   # # $ !<<,as/CCF << v %):Q)> ??rFc[U5n[R"U5n[R"U5n[R"X#U*U/SS9R "/UR QSPSP76$)a0Create 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 rWr{rQ)rr<rJrKrrrZ)angleang_radcos_asin_as rErrsaenG))G,E))G,E ;;ufe4" = B B VEKK VQR VTU VVrFc[U[R5(d[S[ U535e[ UR 5S:Xd+UR SSS:Xd[SUR 35eUup4UupV[X45RU5n[U5n[XV5RU5n XU--n U $)aeNormalize a given homography in pixels to [-1, 1]. Args: dst_pix_trans_src_pix: homography/ies from source to destination to be normalized. :math:`(B, 3, 3)` dsize_src: size of the source image (height, width). dsize_dst: size of the destination image (height, width). Returns: the normalized homography of shape :math:`(B, 3, 3)`. r8rorpNr8Input dst_pix_trans_src_pix must be a Bx3x3 tensor. Got r;r<r=r>r?rYrZr[r"r@r ) dst_pix_trans_src_pix dsize_src dsize_dstsrc_hsrc_wdst_hdst_wsrc_norm_trans_src_pixsrc_pix_trans_src_normdst_norm_trans_dst_pixdst_norm_trans_src_norms rEr$r$'s +U\\ : :@F[A\@]^__ %++ , 15J5P5PQSQT5UY_5_STiToToSpqrrLELE,B%+O+R+RSh+i01GH+A%+O+R+RSh+i-C^tFt,u ""rFc[R"/SQ/SQ/SQ/X4S9nUS:XaUOUS- nUS:XaUOUS- nUSS-U- US'US S-U- US 'URS 5$) a?Compute 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 device: device to place the result on. dtype: dtype of the result. Returns: normalized transform with shape :math:`(1, 3, 3)`. )rXrir)rirXr)ririrXr<rdrXrrrrdrdrr<rDr~)r?r@rTrArBtr_mat width_denom height_denoms rEr"r"Ks(\\+-=OX^ lF!&  K!'1#&3,L$<#% 3F4L$<#% 4F4L   A rFc [R"/SQ/SQ/SQ/SQ/UUS9nUS:XaUOUS- nUS:XaUOUS- nUS:XaUOUS- n USS -U- US'US S -U- US 'US S -U - US 'URS 5$) aWCompute the normalization matrix from image size in pixels to [-1, 1]. Args: depth: image depth. height: image height. width: image width. eps: epsilon to prevent divide-by-zero errors device: device to place the result on. dtype: dtype of the result. Returns: normalized transform with shape :math:`(1, 4, 4)`. )rXririr)rirXrir)ririrXr)riririrXr<rdrXr_rr`)rQrQrra) rHr?r@rTrArBrbrcrd depth_denoms rEr#r#ks,\\  57LNbcF!&  K!'1#&3,L %  K$<#% 3F4L$<#% 4F4L$<#% 3F4L   A rFc[U[R5(d[S[ U535e[ UR 5S:Xd+UR SSS:Xd[SUR 35eUup4UupV[X45RU5n[XV5RU5n[U5n XU--n U $)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)`. r8rorpNrrQrR) rSrTrUrVrWrXrYrZr\dst_denorm_trans_dst_pixr]s rErrs +U\\ : :@F[A\@]^__ %++ , 15J5P5PQSQT5UY_5_STiToToSpqrrLELE,B%+O+R+RSh+i+A%+O+R+RSh+i23IJ,D`vHv,w ""rFc[U[R5(d[S[ U535e[ UR 5S:Xd+UR SSS:Xd[SUR 35eUup4nUupgn[X4U5RU5n [U 5n [XgU5RU5n XU --n U $)a~Normalize a given homography in pixels to [-1, 1]. Args: dst_pix_trans_src_pix: homography/ies from source to destination to be normalized. :math:`(B, 4, 4)` dsize_src: size of the source image (depth, height, width). dsize_dst: size of the destination image (depth, height, width). Returns: the normalized homography. Shape: Output: :math:`(B, 4, 4)` r8rorpN)rtrtrQ) r;r<r=r>r?rYrZr[r#r@r ) rSrTrUsrc_drVrWdst_drXrYrZr[r\r]s rEr%r%s$ +U\\ : :@F[A\@]^__ %++ , 15J5P5PQSQT5UY_5_STiToToSpqrr$E%#E%+CERW+X+[+[\q+r01GH+CERW+X+[+[\q+r,B^tFt,u ""rFc.[USS/5 [U/SQ5 USSS2S4nUSSS2SS24RSSS 9n[UR5[UR5:a!UR S5UR S5p2X- U- nU$) ahNormalize points with intrinsics. Useful for conversion of keypoints to be used with essential matrix. Args: point_2d: tensor containing the 2d points in the image pixel coordinates. The shape of the tensor can be :math:`(*, 2)`. camera_matrix: tensor containing the intrinsics camera matrix. The tensor shape must be :math:`(*, 3, 3)`. Returns: tensor of (u, v) cam coordinates with shape :math:`(*, 2)`. Example: >>> _ = torch.manual_seed(0) >>> X = torch.rand(1, 2) >>> K = torch.eye(3)[None] >>> normalize_points_with_intrinsics(X, K) tensor([[0.4963, 0.7682]]) *2rm3rp.NrQrprWdim1dim2rdiagonalrYrZr~)point_2d camera_matrixcxcyfxfyxys rEr(r(s&x#s,}o6 bqb! $D bqb"1" % . .BR . @D 4::X^^,,^^B');d /T !B IrFc*[USS/5 [U/SQ5 USSS2SS24RSSS 9nUSSS2S4n[UR5[UR5:a!UR S5UR S5p2X-U-$) atNormalize points with intrinsics. Useful for conversion of keypoints to be used with essential matrix. Args: point_2d_norm: tensor containing the 2d points in the image pixel coordinates. The shape of the tensor can be :math:`(*, 2)`. camera_matrix: tensor containing the intrinsics camera matrix. The tensor shape must be :math:`(*, 3, 3)`. Returns: tensor of (u, v) cam coordinates with shape :math:`(*, 2)`. Example: >>> _ = torch.manual_seed(0) >>> X = torch.rand(1, 2) >>> K = torch.eye(3)[None] >>> denormalize_points_with_intrinsics(X, K) tensor([[0.4963, 0.7682]]) rmrnro.NrQrprWrqrt) point_2d_normrwryrxs rErrs&}sCj1}o6 bqb"1" % . .BR . @D bqb! $D 4::]0011^^B');d  $ &&rFc|[U/SQ5 [U/SQ5 [R"X/SS9n[U5$)aCombine 3x3 rotation matrix R and 1x3 translation vector t into 4x4 extrinsics. Args: R: Rotation matrix, :math:`(B, 3, 3).` t: Translation matrix :math:`(B, 3, 1)`. Returns: the extrinsics :math:`(B, 4, 4)`. Example: >>> R, t = torch.eye(3)[None], torch.ones(3).reshape(1, 3, 1) >>> Rt_to_matrix4x4(R, t) tensor([[[1., 0., 0., 1.], [0., 1., 0., 1.], [0., 0., 1., 1.], [0., 0., 0., 1.]]]) Brprprrp1rQr{)rr<rr)RtRts rEr r s5&q/*q/* A6q !B / 33rFcZ[U/SQ5 USS2SS2SS24USS2SS2SS24p!X4$)aConvert 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.]]])) r4rNro)r) extrinsicsrrs rEr!r!6s@(z?3 a!RaRi *QABY"7q 4KrFc[U/SQ5 [R"/SQ/SQ/SQ/SQ//URURS9nX-$)aOConvert graphics coordinate frame (e.g. OpenGL) to vision coordinate frame (e.g. OpenCV.). I.e. flips y and z axis. Graphics convention: [+x, +y, +z] == [right, up, backwards]. Vision convention: [+x, +y, +z] == [right, down, forwards]. Args: extrinsics_graphics: pose matrix :math:`(B, 4, 4)`. Returns: extrinsics: pose matrix :math:`(B, 4, 4)`. Example: >>> ext = torch.eye(4)[None] >>> camtoworld_graphics_to_vision_4x4(ext) tensor([[[ 1., 0., 0., 0.], [ 0., -1., 0., 0.], [ 0., 0., -1., 0.], [ 0., 0., 0., 1.]]]) rrdrrrrrWrrrrrWrrrrrXrBrArr<rDrBrA)extrinsics_graphics invert_yzs rErrOsI**O<  }n EF!''"))I  **rFcx[U/SQ5 [U/SQ5 [[X55n[U5$)aConvert 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.]]])) r~r)rrr r!rrmat4x4s rErrm20q/*q/* .q/D EF 6 ""rFc[U/SQ5 [R"/SQ/SQ/SQ/SQ//URURS9nX-$)aLConvert vision coordinate frame (e.g. OpenCV) to graphics coordinate frame (e.g. OpenGK.). I.e. flips y and z axis Graphics convention: [+x, +y, +z] == [right, up, backwards]. Vision convention: [+x, +y, +z] == [right, down, forwards]. Args: extrinsics_vision: pose matrix :math:`(B, 4, 4)`. Returns: extrinsics: pose matrix :math:`(B, 4, 4)`. Example: >>> ext = torch.eye(4)[None] >>> camtoworld_vision_to_graphics_4x4(ext) tensor([[[ 1., 0., 0., 0.], [ 0., -1., 0., 0.], [ 0., 0., -1., 0.], [ 0., 0., 0., 1.]]]) rrrrrrr)extrinsics_visionrs rErrsI*(/:  }n EF%% ''I  ((rFcx[U/SQ5 [U/SQ5 [[X55n[U5$)aConvert 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.]]])) r~r)rrr r!rs rErrrrFcp[U/SQ5 [U/SQ5 URSS5nU*U-nX#4$)aGConvert camtoworld to worldtocam frame used in Colmap. See long-url: https://colmap.github.io/format.html#output-format Args: R: Rotation matrix, :math:`(B, 3, 3).` t: Translation matrix :math:`(B, 3, 1)`. Returns: Rinv: Rotation matrix, :math:`(B, 3, 3).` tinv: Translation matrix :math:`(B, 3, 1)`. Example: >>> R, t = torch.eye(3)[None], torch.ones(3).reshape(1, 3, 1) >>> camtoworld_to_worldtocam_Rt(R, t) (tensor([[[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]]), tensor([[[-1.], [-1.], [-1.]]])) r~rrdrQr transposerrR_invnew_ts rErrs;0q/*q/* KK1 E &1*E >rFcp[U/SQ5 [U/SQ5 URSS5nU*U-nX#4$)aConvert worldtocam frame used in Colmap to camtoworld. 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.]]])) r~rrdrQrrs rEr6r6s;*q/*q/* KK1 E &1*E >rFc[U5n[X!5up4[X45upVURSSS5n[ UR 55nXv4$)aConvert output of Apple ARKit screen pose to the camera-to-world transformation, expected by Colmap. Both poses in quaternion representation. Args: qvec: ARKit rotation quaternion :math:`(B, 4)`, [w, x, y, z] format. tvec: translation vector :math:`(B, 3, 1)`, [x, y, z] Returns: qvec: Colmap rotation quaternion :math:`(B, 4)`, [w, x, y, z] format. tvec: translation vector :math:`(B, 3, 1)`, [x, y, z] Example: >>> q, t = torch.tensor([0, 1, 0, 1.])[None], torch.ones(3).reshape(1, 3, 1) >>> ARKitQTVecs_to_ColmapQTVecs(q, t) (tensor([[0.7071, 0.0000, 0.7071, 0.0000]]), tensor([[[-1.0000], [-1.0000], [ 1.0000]]])) rWrord)r0rrrr4 contiguous)qvectvecRcgRcvTcvR_colmapt_colmapq_colmaps rEr r sW. ( -C/:HC4S>HAq)H,X-@-@-BCH  rFc URSS:wd[UR5S:a[SUR35eUSUSUSp2n[R"U5n[R "[R "XC*U/SS9[R "X4U*/SS9[R "U*X/SS9/S S9nU$) a Convert a vector to a skew symmetric matrix. A vector :math:`(v1, v2, v3)` has a corresponding skew-symmetric matrix, which is of the form: .. math:: \begin{bmatrix} 0 & -v3 & v2 \\ v3 & 0 & -v1 \\ -v2 & v1 & 0\end{bmatrix} Args: vec: tensor of shape :math:`(B, 3)`. Returns: tensor of shape :math:`(B, 3, 3)`. Example: >>> vec = torch.tensor([1.0, 2.0, 3.0]) >>> vector_to_skew_symmetric_matrix(vec) tensor([[ 0., -3., 2.], [ 3., 0., -1.], [-2., 1., 0.]]) rWrorQz2Input vector must be of shape (B, 3) or (3,). Got rrrr{rp)rZrYr[r<rr)vecv1v2v3rskew_symmetric_matrixs rEr5r5%s2 yy}S^a/Mcii[YZZVc&k3v;BB   R E!KK KKR(b 1 KKRC(b 1 KK"b(b 1   ! rF)rDrrr)rLrrMrr!tuple[torch.Tensor, torch.Tensor])g:0yE>)rNrrOrrTrrr)r_rrTrrr)r_rrr)rkrrrr)rrrr)rrrTrrr)rx)rrrTrrr)rrrr) rrrNrrOrrrrz/tuple[torch.Tensor, torch.Tensor, torch.Tensor])r*rr,rr/rrz=tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]) r>rr?intr@rrTrrr) r>rrHrr?rr@rrTrrr)rLrrr)rSrrTtuple[int, int]rUrrr)g+=NN) r?rr@rrTrrAOptional[torch.device]rBOptional[torch.dtype]rr)rHrr?rr@rrTrrArrBrrr)rSrrTtuple[int, int, int]rUrrr)rvrrwrrr)r|rrwrrr)rrrrrr)rrrr)rrrr)rrrrrr)rrrr)rrrrrr)rrrr)A __future__rtypingrr<torch.nn.functionalnn functionalrfkornia.constantsrkornia.core._compatrkornia.core.checkrrkornia.core.utilsr __all__r1rr*rrrrmrrrr r3r2r4r)r0r/r.r-r+rr r r,r&rr'rrr$r"r#rr%r(rr r!rrrrrr6r r5rFrErs$# *>1. bD*D*24$D2. 767:_D 8'J5K50@ 8'J:K:HV;@EP7t 3WE0F0$N(^5p 3WE0F0##$#)5#:F#4#L# #+#2>#B#VLP%*#%*-0%*9<%*CH%*%*RLP!@#!@-0!@9<!@CH!@!@JX\*#*,/*9<*EH*OT**BX\@#@,/@9<@EH@OT@@@W(!#'!#4C!#P_!#!#N%)#'     #  !   H%)#' % % % %  % # % ! %%P #' #4C #P_ # #F"#'"#4H"#Ui"#"#JD'@422+<#<)<#<B<>%!rF