a d"*@sddlmZddlmZmZddlmZmZmZm Z m Z m Z m Z ddl mZmZmZmZddlmZmZmZGdddeZdS) )pi)TupleUnion)Module ParameterTensor as_tensor concatenaterandstack)QuaternionCoeffOrdernormalize_quaternionquaternion_to_rotation_matrixrotation_matrix_to_quaternion) KORNIA_CHECKKORNIA_CHECK_SHAPEKORNIA_CHECK_TYPEcs@eZdZdZeddfdd ZedddZd d Zddd d Z ddd ddZ ddd ddZ ddd ddZ e edfdd ddZddd ddZeedddZeedddZeedddZeedddZeedd d!Zeedd"d#Zeedd$d%Zeedd&d'Zeedd(d)Zeedd*d+Zeeed,fdd-d.Zeedd/d0Zedd1d2Ze edd3d4d5Z!e edd6d7d8Z"e e#e#e#e#dd9d:d;Z$e edd6dd?Z&ddd@dAZ'dddBdCZ(dddDdEZ)eddFdGZ*dLdHdIZ+dJdKZ,Z-S)M Quaterniona`Base class to represent a Quaternion. A quaternion is a four dimensional vector representation of a rotation transformation in 3d. See more: https://en.wikipedia.org/wiki/Quaternion The general definition of a quaternion is given by: .. math :: Q = a + b \cdot \mathbf{i} + c \cdot \mathbf{j} + d \cdot \mathbf{k} Thus, we represent a rotation quaternion as a contiguous tensor structure to perform rigid bodies transformations: .. math :: Q = \begin{bmatrix} q_w & q_x & q_y & q_z \end{bmatrix} Example: >>> q = Quaternion.identity(batch_size=4) >>> q.data Parameter containing: tensor([[1., 0., 0., 0.], [1., 0., 0., 0.], [1., 0., 0., 0.], [1., 0., 0., 0.]], requires_grad=True) >>> q.real tensor([[1.], [1.], [1.], [1.]], grad_fn=) >>> q.vec tensor([[0., 0., 0.], [0., 0., 0.], [0., 0., 0.], [0., 0., 0.]], grad_fn=) N)datareturncs&tt|ddgt||_dS)aConstructor for the base class. Args: data: tensor containing the quaternion data with the sape of :math:`(B, 4)`. Example: >>> data = torch.rand(2, 4) >>> q = Quaternion(data) >>> q.shape (2, 4) B4N)super__init__rr_data)selfr __class__c/var/www/html/stable-diffusion-webui/venv/lib/python3.9/site-packages/kornia/geometry/quaternion.pyr9s zQuaternion.__init__)rcCsd|jd|jS)Nzreal: z vec: )realvecrrrr__repr__IszQuaternion.__repr__cCs |j|SNr)ridxrrr __getitem__LszQuaternion.__getitem__cCs t|j S)zInverts the sign of the quaternion data. Example: >>> q = Quaternion.identity(batch_size=1) >>> -q.data tensor([[-1., -0., -0., -0.]], grad_fn=) )rrr"rrr__neg__OszQuaternion.__neg__)rightrcCst|tt|j|jS)apAdd a given quaternion. Args: right: the quaternion to add. Example: >>> q1 = Quaternion.identity(batch_size=1) >>> q2 = Quaternion(Tensor([[2., 0., 1., 1.]])) >>> q3 = q1 + q2 >>> q3.data Parameter containing: tensor([[3., 0., 1., 1.]], requires_grad=True) rrrrr)rrr__add__Ys zQuaternion.__add__cCst|tt|j|jS)azSubtract a given quaternion. Args: right: the quaternion to subtract. Example: >>> q1 = Quaternion(Tensor([[2., 0., 1., 1.]])) >>> q2 = Quaternion.identity(batch_size=1) >>> q3 = q1 - q2 >>> q3.data Parameter containing: tensor([[1., 0., 1., 1.]], requires_grad=True) r*r+rrr__sub__js zQuaternion.__sub__cCs^t|t|j|j||j|j}|j|j|j|j|j|j}tt||fdSN)rrr _batched_squared_normr!Zcrossr )rr)Znew_realZnew_vecrrr__mul__{s &zQuaternion.__mul__cCs.t|trt|j|St|t||Sr$) isinstancerrrrinvr+rrr__div__s  zQuaternion.__div__cCs ||Sr$)r4r+rrr __truediv__szQuaternion.__truediv__cCs|jS)z4Return the underlying data with shape :math:`(B,4).`rr"rrrrszQuaternion.datacCs|jSzReturn the underlying data with shape :math:`(B,4)`. Alias for :func:`~kornia.geometry.quaternion.Quaternion.data` r6r"rrrcoeffsszQuaternion.coeffscCs|jS)z{Return the real part with shape :math:`(B,1)`. Alias for :func:`~kornia.geometry.quaternion.Quaternion.w` )wr"rrrr szQuaternion.realcCs|jdddfS)zCReturn the vector with the imaginary part with shape :math:`(B,3)`..Nr%r"rrrr!szQuaternion.veccCs|jSr7r%r"rrrqsz Quaternion.qcCs|jS)zReturn a scalar with the real with shape :math:`(B,1)`. Alias for :func:`~kornia.geometry.quaternion.Quaternion.w` )r r"rrrscalarszQuaternion.scalarcCs|jdddfS)z0Return the :math:`q_w` with shape :math:`(B,1)`..rr:r%r"rrrr9sz Quaternion.wcCs|jdddfS)z0Return the :math:`q_x` with shape :math:`(B,1)`..r:r%r"rrrxsz Quaternion.xcCs|jdddfS)z0Return the :math:`q_y` with shape :math:`(B,1)`..r=r%r"rrrysz Quaternion.ycCs|jdddfS)z0Return the :math:`q_z` with shape :math:`(B,1)`..r?r%r"rrrzsz Quaternion.z.cCs t|jjS)zAReturn the shape of the underlying data with shape :math:`(B,4)`.)tuplershaper"rrrrDszQuaternion.shapecCs|j|S)zReturn the polar angle with shape :math:`(B,1)`. Example: >>> q = Quaternion.identity(batch_size=1) >>> q.polar_angle tensor([[0.]], grad_fn=) )r<normacosr"rrr polar_angles zQuaternion.polar_anglecCst|jtjdS)aKConvert the quaternion to a rotation matrix of shape :math:`(B,3,3)`. Example: >>> q = Quaternion.identity(batch_size=1) >>> m = q.matrix() >>> m tensor([[[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]], grad_fn=) order)rrr WXYZr"rrrmatrixs zQuaternion.matrix)rKrcCs|t|tjdS)akCreate a quaternion from a rotation matrix. Args: matrix: the rotation matrix to convert of shape :math:`(B,3,3)`. Example: >>> m = torch.eye(3)[None] >>> q = Quaternion.from_matrix(m) >>> q.data Parameter containing: tensor([[1., 0., 0., 0.]], requires_grad=True) rH)rr rJ)clsrKrrr from_matrixszQuaternion.from_matrix) batch_sizercCs tgd}||d}||S)aoCreate a quaternion representing an identity rotation. Args: batch_size: the batch size of the underlying data. Example: >>> q = Quaternion.identity(batch_size=2) >>> q.data Parameter containing: tensor([[1., 0., 0., 0.], [1., 0., 0., 0.]], requires_grad=True) )?rPrPr:)rrepeat)rLrNrrrridentitys  zQuaternion.identity)r9r>r@rBrcCs|t||||ggS)aCreate a quaternion from the data coefficients. Args: w: a float representing the :math:`q_w` component. x: a float representing the :math:`q_x` component. y: a float representing the :math:`q_y` component. z: a float representing the :math:`q_z` component. Example: >>> q = Quaternion.from_coeffs(1., 0., 0., 0.) >>> q.data Parameter containing: tensor([[1., 0., 0., 0.]], requires_grad=True) )r)rLr9r>r@rBrrr from_coeffs szQuaternion.from_coeffsc Cstd|\}}}d|dt|}d|dt|}|dt|}|dt|}|t||||fdS)aCreate a random unit quaternion of shape :math:`(B,4)`. Uniformly distributed across the rotation space as per: http://planning.cs.uiuc.edu/node198.html Args: batch_size: the batch size of the underlying data. Example: >>> q = Quaternion.random(batch_size=2) >>> q.norm() tensor([1.0000, 1.0000], grad_fn=) r?rOr=r/)r sqrtrsincosr ) rLrNZr1Zr2Zr3Zq1Zq2Zq3Zq4rrrrandoms zQuaternion.randomcCs|jjdddS)Nr=r/)pZdim)rrEr"rrrrE0szQuaternion.normcCstt|jSr$)rr rr"rrr normalize3szQuaternion.normalizecCstt|j|j fdSr.)rr r r!r"rrrconj6szQuaternion.conjcCs||Sr$)rZ squared_normr"rrrr39szQuaternion.invcCs||j|jdS)Nr=)r0r!r r"rrrr[<szQuaternion.squared_normcCsD|dur |}t|j|jk|ddddf|ddddfdS)N.).r)rrD)rr>r@rrrr0?sz Quaternion._batched_squared_normcCstdSr$)NotImplementedErrorr"rrrslerpFszQuaternion.slerp)N).__name__ __module__ __qualname____doc__rrstrr#r'r(r,r-r1rr4r5propertyrr8r r!r;r<r9r>r@rBrintrDrGrK classmethodrMrRfloatrSrWrErYrZr3r[r0r] __classcell__rrrrrsd&    rN)mathrtypingrrZ kornia.corerrrrr r r Zkornia.geometry.conversionsr r rrZkornia.testingrrrrrrrrs $