Source code for torchgeometry.core.conversions

import torch
import torch.nn as nn

import torchgeometry as tgm

__all__ = [
    # functional api
    "pi",
    "rad2deg",
    "deg2rad",
    "convert_points_from_homogeneous",
    "convert_points_to_homogeneous",
    "angle_axis_to_rotation_matrix",
    "rotation_matrix_to_angle_axis",
    "rotation_matrix_to_quaternion",
    "quaternion_to_angle_axis",
    "angle_axis_to_quaternion",
    "rtvec_to_pose",
    # layer api
    "RadToDeg",
    "DegToRad",
    "ConvertPointsFromHomogeneous",
    "ConvertPointsToHomogeneous",
]


"""Constant with number pi
"""
pi = torch.Tensor([3.14159265358979323846])


[docs]def rad2deg(tensor): r"""Function that converts angles from radians to degrees. See :class:`~torchgeometry.RadToDeg` for details. Args: tensor (Tensor): Tensor of arbitrary shape. Returns: Tensor: Tensor with same shape as input. Example: >>> input = tgm.pi * torch.rand(1, 3, 3) >>> output = tgm.rad2deg(input) """ if not torch.is_tensor(tensor): raise TypeError("Input type is not a torch.Tensor. Got {}" .format(type(tensor))) return 180. * tensor / pi.to(tensor.device).type(tensor.dtype)
[docs]def deg2rad(tensor): r"""Function that converts angles from degrees to radians. See :class:`~torchgeometry.DegToRad` for details. Args: tensor (Tensor): Tensor of arbitrary shape. Returns: Tensor: Tensor with same shape as input. Examples:: >>> input = 360. * torch.rand(1, 3, 3) >>> output = tgm.deg2rad(input) """ if not torch.is_tensor(tensor): raise TypeError("Input type is not a torch.Tensor. Got {}" .format(type(tensor))) return tensor * pi.to(tensor.device).type(tensor.dtype) / 180.
[docs]def convert_points_from_homogeneous(points): r"""Function that converts points from homogeneous to Euclidean space. See :class:`~torchgeometry.ConvertPointsFromHomogeneous` for details. Examples:: >>> input = torch.rand(2, 4, 3) # BxNx3 >>> output = tgm.convert_points_from_homogeneous(input) # BxNx2 """ if not torch.is_tensor(points): raise TypeError("Input type is not a torch.Tensor. Got {}".format( type(points))) if len(points.shape) < 2: raise ValueError("Input must be at least a 2D tensor. Got {}".format( points.shape)) return points[..., :-1] / points[..., -1:]
[docs]def convert_points_to_homogeneous(points): r"""Function that converts points from Euclidean to homogeneous space. See :class:`~torchgeometry.ConvertPointsToHomogeneous` for details. Examples:: >>> input = torch.rand(2, 4, 3) # BxNx3 >>> output = tgm.convert_points_to_homogeneous(input) # BxNx4 """ if not torch.is_tensor(points): raise TypeError("Input type is not a torch.Tensor. Got {}".format( type(points))) if len(points.shape) < 2: raise ValueError("Input must be at least a 2D tensor. Got {}".format( points.shape)) return nn.functional.pad(points, (0, 1), "constant", 1.0)
[docs]def angle_axis_to_rotation_matrix(angle_axis): """Convert 3d vector of axis-angle rotation to 4x4 rotation matrix Args: angle_axis (Tensor): tensor of 3d vector of axis-angle rotations. Returns: Tensor: tensor of 4x4 rotation matrices. Shape: - Input: :math:`(N, 3)` - Output: :math:`(N, 4, 4)` Example: >>> input = torch.rand(1, 3) # Nx3 >>> output = tgm.angle_axis_to_rotation_matrix(input) # Nx4x4 """ def _compute_rotation_matrix(angle_axis, theta2, eps=1e-6): # We want to be careful to only evaluate the square root if the # norm of the angle_axis vector is greater than zero. Otherwise # we get a division by zero. k_one = 1.0 theta = torch.sqrt(theta2) wxyz = angle_axis / (theta + eps) wx, wy, wz = torch.chunk(wxyz, 3, dim=1) cos_theta = torch.cos(theta) sin_theta = torch.sin(theta) r00 = cos_theta + wx * wx * (k_one - cos_theta) r10 = wz * sin_theta + wx * wy * (k_one - cos_theta) r20 = -wy * sin_theta + wx * wz * (k_one - cos_theta) r01 = wx * wy * (k_one - cos_theta) - wz * sin_theta r11 = cos_theta + wy * wy * (k_one - cos_theta) r21 = wx * sin_theta + wy * wz * (k_one - cos_theta) r02 = wy * sin_theta + wx * wz * (k_one - cos_theta) r12 = -wx * sin_theta + wy * wz * (k_one - cos_theta) r22 = cos_theta + wz * wz * (k_one - cos_theta) rotation_matrix = torch.cat( [r00, r01, r02, r10, r11, r12, r20, r21, r22], dim=1) return rotation_matrix.view(-1, 3, 3) def _compute_rotation_matrix_taylor(angle_axis): rx, ry, rz = torch.chunk(angle_axis, 3, dim=1) k_one = torch.ones_like(rx) rotation_matrix = torch.cat( [k_one, -rz, ry, rz, k_one, -rx, -ry, rx, k_one], dim=1) return rotation_matrix.view(-1, 3, 3) # stolen from ceres/rotation.h _angle_axis = torch.unsqueeze(angle_axis, dim=1) theta2 = torch.matmul(_angle_axis, _angle_axis.transpose(1, 2)) theta2 = torch.squeeze(theta2, dim=1) # compute rotation matrices rotation_matrix_normal = _compute_rotation_matrix(angle_axis, theta2) rotation_matrix_taylor = _compute_rotation_matrix_taylor(angle_axis) # create mask to handle both cases eps = 1e-6 mask = (theta2 > eps).view(-1, 1, 1).to(theta2.device) mask_pos = (mask).type_as(theta2) mask_neg = (mask == False).type_as(theta2) # noqa # create output pose matrix batch_size = angle_axis.shape[0] rotation_matrix = torch.eye(4).to(angle_axis.device).type_as(angle_axis) rotation_matrix = rotation_matrix.view(1, 4, 4).repeat(batch_size, 1, 1) # fill output matrix with masked values rotation_matrix[..., :3, :3] = \ mask_pos * rotation_matrix_normal + mask_neg * rotation_matrix_taylor return rotation_matrix # Nx4x4
[docs]def rtvec_to_pose(rtvec): """ Convert axis-angle rotation and translation vector to 4x4 pose matrix Args: rtvec (Tensor): Rodrigues vector transformations Returns: Tensor: transformation matrices Shape: - Input: :math:`(N, 6)` - Output: :math:`(N, 4, 4)` Example: >>> input = torch.rand(3, 6) # Nx6 >>> output = tgm.rtvec_to_pose(input) # Nx4x4 """ assert rtvec.shape[-1] == 6, 'rtvec=[rx, ry, rz, tx, ty, tz]' pose = angle_axis_to_rotation_matrix(rtvec[..., :3]) pose[..., :3, 3] = rtvec[..., 3:] return pose
[docs]def rotation_matrix_to_angle_axis(rotation_matrix): """Convert 3x4 rotation matrix to Rodrigues vector Args: rotation_matrix (Tensor): rotation matrix. Returns: Tensor: Rodrigues vector transformation. Shape: - Input: :math:`(N, 3, 4)` - Output: :math:`(N, 3)` Example: >>> input = torch.rand(2, 3, 4) # Nx4x4 >>> output = tgm.rotation_matrix_to_angle_axis(input) # Nx3 """ # todo add check that matrix is a valid rotation matrix quaternion = rotation_matrix_to_quaternion(rotation_matrix) return quaternion_to_angle_axis(quaternion)
[docs]def rotation_matrix_to_quaternion(rotation_matrix, eps=1e-6): """Convert 3x4 rotation matrix to 4d quaternion vector This algorithm is based on algorithm described in https://github.com/KieranWynn/pyquaternion/blob/master/pyquaternion/quaternion.py#L201 Args: rotation_matrix (Tensor): the rotation matrix to convert. Return: Tensor: the rotation in quaternion Shape: - Input: :math:`(N, 3, 4)` - Output: :math:`(N, 4)` Example: >>> input = torch.rand(4, 3, 4) # Nx3x4 >>> output = tgm.rotation_matrix_to_quaternion(input) # Nx4 """ if not torch.is_tensor(rotation_matrix): raise TypeError("Input type is not a torch.Tensor. Got {}".format( type(rotation_matrix))) if len(rotation_matrix.shape) > 3: raise ValueError( "Input size must be a three dimensional tensor. Got {}".format( rotation_matrix.shape)) if not rotation_matrix.shape[-2:] == (3, 4): raise ValueError( "Input size must be a N x 3 x 4 tensor. Got {}".format( rotation_matrix.shape)) rmat_t = torch.transpose(rotation_matrix, 1, 2) mask_d2 = rmat_t[:, 2, 2] < eps mask_d0_d1 = rmat_t[:, 0, 0] > rmat_t[:, 1, 1] mask_d0_nd1 = rmat_t[:, 0, 0] < -rmat_t[:, 1, 1] t0 = 1 + rmat_t[:, 0, 0] - rmat_t[:, 1, 1] - rmat_t[:, 2, 2] q0 = torch.stack([rmat_t[:, 1, 2] - rmat_t[:, 2, 1], t0, rmat_t[:, 0, 1] + rmat_t[:, 1, 0], rmat_t[:, 2, 0] + rmat_t[:, 0, 2]], -1) t0_rep = t0.repeat(4, 1).t() t1 = 1 - rmat_t[:, 0, 0] + rmat_t[:, 1, 1] - rmat_t[:, 2, 2] q1 = torch.stack([rmat_t[:, 2, 0] - rmat_t[:, 0, 2], rmat_t[:, 0, 1] + rmat_t[:, 1, 0], t1, rmat_t[:, 1, 2] + rmat_t[:, 2, 1]], -1) t1_rep = t1.repeat(4, 1).t() t2 = 1 - rmat_t[:, 0, 0] - rmat_t[:, 1, 1] + rmat_t[:, 2, 2] q2 = torch.stack([rmat_t[:, 0, 1] - rmat_t[:, 1, 0], rmat_t[:, 2, 0] + rmat_t[:, 0, 2], rmat_t[:, 1, 2] + rmat_t[:, 2, 1], t2], -1) t2_rep = t2.repeat(4, 1).t() t3 = 1 + rmat_t[:, 0, 0] + rmat_t[:, 1, 1] + rmat_t[:, 2, 2] q3 = torch.stack([t3, rmat_t[:, 1, 2] - rmat_t[:, 2, 1], rmat_t[:, 2, 0] - rmat_t[:, 0, 2], rmat_t[:, 0, 1] - rmat_t[:, 1, 0]], -1) t3_rep = t3.repeat(4, 1).t() mask_c0 = mask_d2 * mask_d0_d1 mask_c1 = mask_d2 * (1 - mask_d0_d1) mask_c2 = (1 - mask_d2) * mask_d0_nd1 mask_c3 = (1 - mask_d2) * (1 - mask_d0_nd1) mask_c0 = mask_c0.view(-1, 1).type_as(q0) mask_c1 = mask_c1.view(-1, 1).type_as(q1) mask_c2 = mask_c2.view(-1, 1).type_as(q2) mask_c3 = mask_c3.view(-1, 1).type_as(q3) q = q0 * mask_c0 + q1 * mask_c1 + q2 * mask_c2 + q3 * mask_c3 q /= torch.sqrt(t0_rep * mask_c0 + t1_rep * mask_c1 + # noqa t2_rep * mask_c2 + t3_rep * mask_c3) # noqa q *= 0.5 return q
[docs]def quaternion_to_angle_axis(quaternion: torch.Tensor) -> torch.Tensor: """Convert quaternion vector to angle axis of rotation. Adapted from ceres C++ library: ceres-solver/include/ceres/rotation.h Args: quaternion (torch.Tensor): tensor with quaternions. Return: torch.Tensor: tensor with angle axis of rotation. Shape: - Input: :math:`(*, 4)` where `*` means, any number of dimensions - Output: :math:`(*, 3)` Example: >>> quaternion = torch.rand(2, 4) # Nx4 >>> angle_axis = tgm.quaternion_to_angle_axis(quaternion) # Nx3 """ if not torch.is_tensor(quaternion): raise TypeError("Input type is not a torch.Tensor. Got {}".format( type(quaternion))) if not quaternion.shape[-1] == 4: raise ValueError("Input must be a tensor of shape Nx4 or 4. Got {}" .format(quaternion.shape)) # unpack input and compute conversion q1: torch.Tensor = quaternion[..., 1] q2: torch.Tensor = quaternion[..., 2] q3: torch.Tensor = quaternion[..., 3] sin_squared_theta: torch.Tensor = q1 * q1 + q2 * q2 + q3 * q3 sin_theta: torch.Tensor = torch.sqrt(sin_squared_theta) cos_theta: torch.Tensor = quaternion[..., 0] two_theta: torch.Tensor = 2.0 * torch.where( cos_theta < 0.0, torch.atan2(-sin_theta, -cos_theta), torch.atan2(sin_theta, cos_theta)) k_pos: torch.Tensor = two_theta / sin_theta k_neg: torch.Tensor = 2.0 * torch.ones_like(sin_theta) k: torch.Tensor = torch.where(sin_squared_theta > 0.0, k_pos, k_neg) angle_axis: torch.Tensor = torch.zeros_like(quaternion)[..., :3] angle_axis[..., 0] += q1 * k angle_axis[..., 1] += q2 * k angle_axis[..., 2] += q3 * k return angle_axis
# based on: # https://github.com/facebookresearch/QuaterNet/blob/master/common/quaternion.py#L138
[docs]def angle_axis_to_quaternion(angle_axis: torch.Tensor) -> torch.Tensor: """Convert an angle axis to a quaternion. Adapted from ceres C++ library: ceres-solver/include/ceres/rotation.h Args: angle_axis (torch.Tensor): tensor with angle axis. Return: torch.Tensor: tensor with quaternion. Shape: - Input: :math:`(*, 3)` where `*` means, any number of dimensions - Output: :math:`(*, 4)` Example: >>> angle_axis = torch.rand(2, 4) # Nx4 >>> quaternion = tgm.angle_axis_to_quaternion(angle_axis) # Nx3 """ if not torch.is_tensor(angle_axis): raise TypeError("Input type is not a torch.Tensor. Got {}".format( type(angle_axis))) if not angle_axis.shape[-1] == 3: raise ValueError("Input must be a tensor of shape Nx3 or 3. Got {}" .format(angle_axis.shape)) # unpack input and compute conversion a0: torch.Tensor = angle_axis[..., 0:1] a1: torch.Tensor = angle_axis[..., 1:2] a2: torch.Tensor = angle_axis[..., 2:3] theta_squared: torch.Tensor = a0 * a0 + a1 * a1 + a2 * a2 theta: torch.Tensor = torch.sqrt(theta_squared) half_theta: torch.Tensor = theta * 0.5 mask: torch.Tensor = theta_squared > 0.0 ones: torch.Tensor = torch.ones_like(half_theta) k_neg: torch.Tensor = 0.5 * ones k_pos: torch.Tensor = torch.sin(half_theta) / theta k: torch.Tensor = torch.where(mask, k_pos, k_neg) w: torch.Tensor = torch.where(mask, torch.cos(half_theta), ones) quaternion: torch.Tensor = torch.zeros_like(angle_axis) quaternion[..., 0:1] += a0 * k quaternion[..., 1:2] += a1 * k quaternion[..., 2:3] += a2 * k return torch.cat([w, quaternion], dim=-1)
# TODO: add below funtionalities # - pose_to_rtvec # layer api
[docs]class RadToDeg(nn.Module): r"""Creates an object that converts angles from radians to degrees. Args: tensor (Tensor): Tensor of arbitrary shape. Returns: Tensor: Tensor with same shape as input. Examples:: >>> input = tgm.pi * torch.rand(1, 3, 3) >>> output = tgm.RadToDeg()(input) """ def __init__(self): super(RadToDeg, self).__init__() def forward(self, input): return rad2deg(input)
[docs]class DegToRad(nn.Module): r"""Function that converts angles from degrees to radians. Args: tensor (Tensor): Tensor of arbitrary shape. Returns: Tensor: Tensor with same shape as input. Examples:: >>> input = 360. * torch.rand(1, 3, 3) >>> output = tgm.DegToRad()(input) """ def __init__(self): super(DegToRad, self).__init__() def forward(self, input): return deg2rad(input)
[docs]class ConvertPointsFromHomogeneous(nn.Module): r"""Creates a transformation that converts points from homogeneous to Euclidean space. Args: points (Tensor): tensor of N-dimensional points. Returns: Tensor: tensor of N-1-dimensional points. Shape: - Input: :math:`(B, D, N)` or :math:`(D, N)` - Output: :math:`(B, D, N + 1)` or :math:`(D, N + 1)` Examples:: >>> input = torch.rand(2, 4, 3) # BxNx3 >>> transform = tgm.ConvertPointsFromHomogeneous() >>> output = transform(input) # BxNx2 """ def __init__(self): super(ConvertPointsFromHomogeneous, self).__init__() def forward(self, input): return convert_points_from_homogeneous(input)
[docs]class ConvertPointsToHomogeneous(nn.Module): r"""Creates a transformation to convert points from Euclidean to homogeneous space. Args: points (Tensor): tensor of N-dimensional points. Returns: Tensor: tensor of N+1-dimensional points. Shape: - Input: :math:`(B, D, N)` or :math:`(D, N)` - Output: :math:`(B, D, N + 1)` or :math:`(D, N + 1)` Examples:: >>> input = torch.rand(2, 4, 3) # BxNx3 >>> transform = tgm.ConvertPointsToHomogeneous() >>> output = transform(input) # BxNx4 """ def __init__(self): super(ConvertPointsToHomogeneous, self).__init__() def forward(self, input): return convert_points_to_homogeneous(input)