# Copyright (c) Meta Platforms, Inc. and affiliates. # All rights reserved. # # This source code is licensed under the BSD-style license found in the # LICENSE file in the root directory of this source tree. import sys import math import warnings from typing import List, Optional, Sequence, Tuple, Union, Any import numpy as np import torch import torch.nn.functional as F import copy import inspect import torch.nn as nn Device = Union[str, torch.device] # Default values for rotation and translation matrices. _R = torch.eye(3)[None] # (1, 3, 3) _T = torch.zeros(1, 3) # (1, 3) # Provide get_origin and get_args even in Python 3.7. if sys.version_info >= (3, 8, 0): from typing import get_args, get_origin elif sys.version_info >= (3, 7, 0): def get_origin(cls): # pragma: no cover return getattr(cls, "__origin__", None) def get_args(cls): # pragma: no cover return getattr(cls, "__args__", None) else: raise ImportError("This module requires Python 3.7+") ################################################################ ## ██████╗██╗ █████╗ ███████╗███████╗███████╗███████╗ ## ## ██╔════╝██║ ██╔══██╗██╔════╝██╔════╝██╔════╝██╔════╝ ## ## ██║ ██║ ███████║███████╗███████╗█████╗ ███████╗ ## ## ██║ ██║ ██╔══██║╚════██║╚════██║██╔══╝ ╚════██║ ## ## ╚██████╗███████╗██║ ██║███████║███████║███████╗███████║ ## ## ╚═════╝╚══════╝╚═╝ ╚═╝╚══════╝╚══════╝╚══════╝╚══════╝ ## ################################################################ class Transform3d: """ A Transform3d object encapsulates a batch of N 3D transformations, and knows how to transform points and normal vectors. Suppose that t is a Transform3d; then we can do the following: .. code-block:: python N = len(t) points = torch.randn(N, P, 3) normals = torch.randn(N, P, 3) points_transformed = t.transform_points(points) # => (N, P, 3) normals_transformed = t.transform_normals(normals) # => (N, P, 3) BROADCASTING Transform3d objects supports broadcasting. Suppose that t1 and tN are Transform3d objects with len(t1) == 1 and len(tN) == N respectively. Then we can broadcast transforms like this: .. code-block:: python t1.transform_points(torch.randn(P, 3)) # => (P, 3) t1.transform_points(torch.randn(1, P, 3)) # => (1, P, 3) t1.transform_points(torch.randn(M, P, 3)) # => (M, P, 3) tN.transform_points(torch.randn(P, 3)) # => (N, P, 3) tN.transform_points(torch.randn(1, P, 3)) # => (N, P, 3) COMBINING TRANSFORMS Transform3d objects can be combined in two ways: composing and stacking. Composing is function composition. Given Transform3d objects t1, t2, t3, the following all compute the same thing: .. code-block:: python y1 = t3.transform_points(t2.transform_points(t1.transform_points(x))) y2 = t1.compose(t2).compose(t3).transform_points(x) y3 = t1.compose(t2, t3).transform_points(x) Composing transforms should broadcast. .. code-block:: python if len(t1) == 1 and len(t2) == N, then len(t1.compose(t2)) == N. We can also stack a sequence of Transform3d objects, which represents composition along the batch dimension; then the following should compute the same thing. .. code-block:: python N, M = len(tN), len(tM) xN = torch.randn(N, P, 3) xM = torch.randn(M, P, 3) y1 = torch.cat([tN.transform_points(xN), tM.transform_points(xM)], dim=0) y2 = tN.stack(tM).transform_points(torch.cat([xN, xM], dim=0)) BUILDING TRANSFORMS We provide convenience methods for easily building Transform3d objects as compositions of basic transforms. .. code-block:: python # Scale by 0.5, then translate by (1, 2, 3) t1 = Transform3d().scale(0.5).translate(1, 2, 3) # Scale each axis by a different amount, then translate, then scale t2 = Transform3d().scale(1, 3, 3).translate(2, 3, 1).scale(2.0) t3 = t1.compose(t2) tN = t1.stack(t3, t3) BACKPROP THROUGH TRANSFORMS When building transforms, we can also parameterize them by Torch tensors; in this case we can backprop through the construction and application of Transform objects, so they could be learned via gradient descent or predicted by a neural network. .. code-block:: python s1_params = torch.randn(N, requires_grad=True) t_params = torch.randn(N, 3, requires_grad=True) s2_params = torch.randn(N, 3, requires_grad=True) t = Transform3d().scale(s1_params).translate(t_params).scale(s2_params) x = torch.randn(N, 3) y = t.transform_points(x) loss = compute_loss(y) loss.backward() with torch.no_grad(): s1_params -= lr * s1_params.grad t_params -= lr * t_params.grad s2_params -= lr * s2_params.grad CONVENTIONS We adopt a right-hand coordinate system, meaning that rotation about an axis with a positive angle results in a counter clockwise rotation. This class assumes that transformations are applied on inputs which are row vectors. The internal representation of the Nx4x4 transformation matrix is of the form: .. code-block:: python M = [ [Rxx, Ryx, Rzx, 0], [Rxy, Ryy, Rzy, 0], [Rxz, Ryz, Rzz, 0], [Tx, Ty, Tz, 1], ] To apply the transformation to points which are row vectors, the M matrix can be pre multiplied by the points: .. code-block:: python points = [[0, 1, 2]] # (1 x 3) xyz coordinates of a point transformed_points = points * M """ def __init__( self, dtype: torch.dtype = torch.float32, device: Device = "cpu", matrix: Optional[torch.Tensor] = None, ) -> None: """ Args: dtype: The data type of the transformation matrix. to be used if `matrix = None`. device: The device for storing the implemented transformation. If `matrix != None`, uses the device of input `matrix`. matrix: A tensor of shape (4, 4) or of shape (minibatch, 4, 4) representing the 4x4 3D transformation matrix. If `None`, initializes with identity using the specified `device` and `dtype`. """ if matrix is None: self._matrix = torch.eye(4, dtype=dtype, device=device).view(1, 4, 4) else: if matrix.ndim not in (2, 3): raise ValueError('"matrix" has to be a 2- or a 3-dimensional tensor.') if matrix.shape[-2] != 4 or matrix.shape[-1] != 4: raise ValueError( '"matrix" has to be a tensor of shape (minibatch, 4, 4)' ) # set dtype and device from matrix dtype = matrix.dtype device = matrix.device self._matrix = matrix.view(-1, 4, 4) self._transforms = [] # store transforms to compose self._lu = None self.device = make_device(device) self.dtype = dtype def __len__(self) -> int: return self.get_matrix().shape[0] def __getitem__( self, index: Union[int, List[int], slice, torch.Tensor] ) -> "Transform3d": """ Args: index: Specifying the index of the transform to retrieve. Can be an int, slice, list of ints, boolean, long tensor. Supports negative indices. Returns: Transform3d object with selected transforms. The tensors are not cloned. """ if isinstance(index, int): index = [index] return self.__class__(matrix=self.get_matrix()[index]) def compose(self, *others: "Transform3d") -> "Transform3d": """ Return a new Transform3d representing the composition of self with the given other transforms, which will be stored as an internal list. Args: *others: Any number of Transform3d objects Returns: A new Transform3d with the stored transforms """ out = Transform3d(dtype=self.dtype, device=self.device) out._matrix = self._matrix.clone() for other in others: if not isinstance(other, Transform3d): msg = "Only possible to compose Transform3d objects; got %s" raise ValueError(msg % type(other)) out._transforms = self._transforms + list(others) return out def get_matrix(self) -> torch.Tensor: """ Return a matrix which is the result of composing this transform with others stored in self.transforms. Where necessary transforms are broadcast against each other. For example, if self.transforms contains transforms t1, t2, and t3, and given a set of points x, the following should be true: .. code-block:: python y1 = t1.compose(t2, t3).transform(x) y2 = t3.transform(t2.transform(t1.transform(x))) y1.get_matrix() == y2.get_matrix() Returns: A transformation matrix representing the composed inputs. """ composed_matrix = self._matrix.clone() if len(self._transforms) > 0: for other in self._transforms: other_matrix = other.get_matrix() composed_matrix = _broadcast_bmm(composed_matrix, other_matrix) return composed_matrix def _get_matrix_inverse(self) -> torch.Tensor: """ Return the inverse of self._matrix. """ return torch.inverse(self._matrix) def inverse(self, invert_composed: bool = False) -> "Transform3d": """ Returns a new Transform3d object that represents an inverse of the current transformation. Args: invert_composed: - True: First compose the list of stored transformations and then apply inverse to the result. This is potentially slower for classes of transformations with inverses that can be computed efficiently (e.g. rotations and translations). - False: Invert the individual stored transformations independently without composing them. Returns: A new Transform3d object containing the inverse of the original transformation. """ tinv = Transform3d(dtype=self.dtype, device=self.device) if invert_composed: # first compose then invert tinv._matrix = torch.inverse(self.get_matrix()) else: # self._get_matrix_inverse() implements efficient inverse # of self._matrix i_matrix = self._get_matrix_inverse() # 2 cases: if len(self._transforms) > 0: # a) Either we have a non-empty list of transforms: # Here we take self._matrix and append its inverse at the # end of the reverted _transforms list. After composing # the transformations with get_matrix(), this correctly # right-multiplies by the inverse of self._matrix # at the end of the composition. tinv._transforms = [t.inverse() for t in reversed(self._transforms)] last = Transform3d(dtype=self.dtype, device=self.device) last._matrix = i_matrix tinv._transforms.append(last) else: # b) Or there are no stored transformations # we just set inverted matrix tinv._matrix = i_matrix return tinv def stack(self, *others: "Transform3d") -> "Transform3d": """ Return a new batched Transform3d representing the batch elements from self and all the given other transforms all batched together. Args: *others: Any number of Transform3d objects Returns: A new Transform3d. """ transforms = [self] + list(others) matrix = torch.cat([t.get_matrix() for t in transforms], dim=0) out = Transform3d(dtype=self.dtype, device=self.device) out._matrix = matrix return out def transform_points(self, points, eps: Optional[float] = None) -> torch.Tensor: """ Use this transform to transform a set of 3D points. Assumes row major ordering of the input points. Args: points: Tensor of shape (P, 3) or (N, P, 3) eps: If eps!=None, the argument is used to clamp the last coordinate before performing the final division. The clamping corresponds to: last_coord := (last_coord.sign() + (last_coord==0)) * torch.clamp(last_coord.abs(), eps), i.e. the last coordinates that are exactly 0 will be clamped to +eps. Returns: points_out: points of shape (N, P, 3) or (P, 3) depending on the dimensions of the transform """ points_batch = points.clone() if points_batch.dim() == 2: points_batch = points_batch[None] # (P, 3) -> (1, P, 3) if points_batch.dim() != 3: msg = "Expected points to have dim = 2 or dim = 3: got shape %r" raise ValueError(msg % repr(points.shape)) N, P, _3 = points_batch.shape ones = torch.ones(N, P, 1, dtype=points.dtype, device=points.device) points_batch = torch.cat([points_batch, ones], dim=2) composed_matrix = self.get_matrix() points_out = _broadcast_bmm(points_batch, composed_matrix) denom = points_out[..., 3:] # denominator if eps is not None: denom_sign = denom.sign() + (denom == 0.0).type_as(denom) denom = denom_sign * torch.clamp(denom.abs(), eps) points_out = points_out[..., :3] / denom # When transform is (1, 4, 4) and points is (P, 3) return # points_out of shape (P, 3) if points_out.shape[0] == 1 and points.dim() == 2: points_out = points_out.reshape(points.shape) return points_out def transform_normals(self, normals) -> torch.Tensor: """ Use this transform to transform a set of normal vectors. Args: normals: Tensor of shape (P, 3) or (N, P, 3) Returns: normals_out: Tensor of shape (P, 3) or (N, P, 3) depending on the dimensions of the transform """ if normals.dim() not in [2, 3]: msg = "Expected normals to have dim = 2 or dim = 3: got shape %r" raise ValueError(msg % (normals.shape,)) composed_matrix = self.get_matrix() # TODO: inverse is bad! Solve a linear system instead mat = composed_matrix[:, :3, :3] normals_out = _broadcast_bmm(normals, mat.transpose(1, 2).inverse()) # This doesn't pass unit tests. TODO investigate further # if self._lu is None: # self._lu = self._matrix[:, :3, :3].transpose(1, 2).lu() # normals_out = normals.lu_solve(*self._lu) # When transform is (1, 4, 4) and normals is (P, 3) return # normals_out of shape (P, 3) if normals_out.shape[0] == 1 and normals.dim() == 2: normals_out = normals_out.reshape(normals.shape) return normals_out def translate(self, *args, **kwargs) -> "Transform3d": return self.compose( Translate(device=self.device, dtype=self.dtype, *args, **kwargs) ) def scale(self, *args, **kwargs) -> "Transform3d": return self.compose( Scale(device=self.device, dtype=self.dtype, *args, **kwargs) ) def rotate(self, *args, **kwargs) -> "Transform3d": return self.compose( Rotate(device=self.device, dtype=self.dtype, *args, **kwargs) ) def rotate_axis_angle(self, *args, **kwargs) -> "Transform3d": return self.compose( RotateAxisAngle(device=self.device, dtype=self.dtype, *args, **kwargs) ) def clone(self) -> "Transform3d": """ Deep copy of Transforms object. All internal tensors are cloned individually. Returns: new Transforms object. """ other = Transform3d(dtype=self.dtype, device=self.device) if self._lu is not None: other._lu = [elem.clone() for elem in self._lu] other._matrix = self._matrix.clone() other._transforms = [t.clone() for t in self._transforms] return other def to( self, device: Device, copy: bool = False, dtype: Optional[torch.dtype] = None, ) -> "Transform3d": """ Match functionality of torch.Tensor.to() If copy = True or the self Tensor is on a different device, the returned tensor is a copy of self with the desired torch.device. If copy = False and the self Tensor already has the correct torch.device, then self is returned. Args: device: Device (as str or torch.device) for the new tensor. copy: Boolean indicator whether or not to clone self. Default False. dtype: If not None, casts the internal tensor variables to a given torch.dtype. Returns: Transform3d object. """ device_ = make_device(device) dtype_ = self.dtype if dtype is None else dtype skip_to = self.device == device_ and self.dtype == dtype_ if not copy and skip_to: return self other = self.clone() if skip_to: return other other.device = device_ other.dtype = dtype_ other._matrix = other._matrix.to(device=device_, dtype=dtype_) other._transforms = [ t.to(device_, copy=copy, dtype=dtype_) for t in other._transforms ] return other def cpu(self) -> "Transform3d": return self.to("cpu") def cuda(self) -> "Transform3d": return self.to("cuda") class Translate(Transform3d): def __init__( self, x, y=None, z=None, dtype: torch.dtype = torch.float32, device: Optional[Device] = None, ) -> None: """ Create a new Transform3d representing 3D translations. Option I: Translate(xyz, dtype=torch.float32, device='cpu') xyz should be a tensor of shape (N, 3) Option II: Translate(x, y, z, dtype=torch.float32, device='cpu') Here x, y, and z will be broadcast against each other and concatenated to form the translation. Each can be: - A python scalar - A torch scalar - A 1D torch tensor """ xyz = _handle_input(x, y, z, dtype, device, "Translate") super().__init__(device=xyz.device, dtype=dtype) N = xyz.shape[0] mat = torch.eye(4, dtype=dtype, device=self.device) mat = mat.view(1, 4, 4).repeat(N, 1, 1) mat[:, 3, :3] = xyz self._matrix = mat def _get_matrix_inverse(self) -> torch.Tensor: """ Return the inverse of self._matrix. """ inv_mask = self._matrix.new_ones([1, 4, 4]) inv_mask[0, 3, :3] = -1.0 i_matrix = self._matrix * inv_mask return i_matrix class Rotate(Transform3d): def __init__( self, R: torch.Tensor, dtype: torch.dtype = torch.float32, device: Optional[Device] = None, orthogonal_tol: float = 1e-5, ) -> None: """ Create a new Transform3d representing 3D rotation using a rotation matrix as the input. Args: R: a tensor of shape (3, 3) or (N, 3, 3) orthogonal_tol: tolerance for the test of the orthogonality of R """ device_ = get_device(R, device) super().__init__(device=device_, dtype=dtype) if R.dim() == 2: R = R[None] if R.shape[-2:] != (3, 3): msg = "R must have shape (3, 3) or (N, 3, 3); got %s" raise ValueError(msg % repr(R.shape)) R = R.to(device=device_, dtype=dtype) _check_valid_rotation_matrix(R, tol=orthogonal_tol) N = R.shape[0] mat = torch.eye(4, dtype=dtype, device=device_) mat = mat.view(1, 4, 4).repeat(N, 1, 1) mat[:, :3, :3] = R self._matrix = mat def _get_matrix_inverse(self) -> torch.Tensor: """ Return the inverse of self._matrix. """ return self._matrix.permute(0, 2, 1).contiguous() class TensorAccessor(nn.Module): """ A helper class to be used with the __getitem__ method. This can be used for getting/setting the values for an attribute of a class at one particular index. This is useful when the attributes of a class are batched tensors and one element in the batch needs to be modified. """ def __init__(self, class_object, index: Union[int, slice]) -> None: """ Args: class_object: this should be an instance of a class which has attributes which are tensors representing a batch of values. index: int/slice, an index indicating the position in the batch. In __setattr__ and __getattr__ only the value of class attributes at this index will be accessed. """ self.__dict__["class_object"] = class_object self.__dict__["index"] = index def __setattr__(self, name: str, value: Any): """ Update the attribute given by `name` to the value given by `value` at the index specified by `self.index`. Args: name: str, name of the attribute. value: value to set the attribute to. """ v = getattr(self.class_object, name) if not torch.is_tensor(v): msg = "Can only set values on attributes which are tensors; got %r" raise AttributeError(msg % type(v)) # Convert the attribute to a tensor if it is not a tensor. if not torch.is_tensor(value): value = torch.tensor( value, device=v.device, dtype=v.dtype, requires_grad=v.requires_grad ) # Check the shapes match the existing shape and the shape of the index. if v.dim() > 1 and value.dim() > 1 and value.shape[1:] != v.shape[1:]: msg = "Expected value to have shape %r; got %r" raise ValueError(msg % (v.shape, value.shape)) if ( v.dim() == 0 and isinstance(self.index, slice) and len(value) != len(self.index) ): msg = "Expected value to have len %r; got %r" raise ValueError(msg % (len(self.index), len(value))) self.class_object.__dict__[name][self.index] = value def __getattr__(self, name: str): """ Return the value of the attribute given by "name" on self.class_object at the index specified in self.index. Args: name: string of the attribute name """ if hasattr(self.class_object, name): return self.class_object.__dict__[name][self.index] else: msg = "Attribute %s not found on %r" return AttributeError(msg % (name, self.class_object.__name__)) BROADCAST_TYPES = (float, int, list, tuple, torch.Tensor, np.ndarray) class TensorProperties(nn.Module): """ A mix-in class for storing tensors as properties with helper methods. """ def __init__( self, dtype: torch.dtype = torch.float32, device: Device = "cpu", **kwargs, ) -> None: """ Args: dtype: data type to set for the inputs device: Device (as str or torch.device) kwargs: any number of keyword arguments. Any arguments which are of type (float/int/list/tuple/tensor/array) are broadcasted and other keyword arguments are set as attributes. """ super().__init__() self.device = make_device(device) self._N = 0 if kwargs is not None: # broadcast all inputs which are float/int/list/tuple/tensor/array # set as attributes anything else e.g. strings, bools args_to_broadcast = {} for k, v in kwargs.items(): if v is None or isinstance(v, (str, bool)): setattr(self, k, v) elif isinstance(v, BROADCAST_TYPES): args_to_broadcast[k] = v else: msg = "Arg %s with type %r is not broadcastable" warnings.warn(msg % (k, type(v))) names = args_to_broadcast.keys() # convert from type dict.values to tuple values = tuple(v for v in args_to_broadcast.values()) if len(values) > 0: broadcasted_values = convert_to_tensors_and_broadcast( *values, device=device ) # Set broadcasted values as attributes on self. for i, n in enumerate(names): setattr(self, n, broadcasted_values[i]) if self._N == 0: self._N = broadcasted_values[i].shape[0] def __len__(self) -> int: return self._N def isempty(self) -> bool: return self._N == 0 def __getitem__(self, index: Union[int, slice]) -> TensorAccessor: """ Args: index: an int or slice used to index all the fields. Returns: if `index` is an index int/slice return a TensorAccessor class with getattribute/setattribute methods which return/update the value at the index in the original class. """ if isinstance(index, (int, slice)): return TensorAccessor(class_object=self, index=index) msg = "Expected index of type int or slice; got %r" raise ValueError(msg % type(index)) # pyre-fixme[14]: `to` overrides method defined in `Module` inconsistently. def to(self, device: Device = "cpu") -> "TensorProperties": """ In place operation to move class properties which are tensors to a specified device. If self has a property "device", update this as well. """ device_ = make_device(device) for k in dir(self): v = getattr(self, k) if k == "device": setattr(self, k, device_) if torch.is_tensor(v) and v.device != device_: setattr(self, k, v.to(device_)) return self def cpu(self) -> "TensorProperties": return self.to("cpu") # pyre-fixme[14]: `cuda` overrides method defined in `Module` inconsistently. def cuda(self, device: Optional[int] = None) -> "TensorProperties": return self.to(f"cuda:{device}" if device is not None else "cuda") def clone(self, other) -> "TensorProperties": """ Update the tensor properties of other with the cloned properties of self. """ for k in dir(self): v = getattr(self, k) if inspect.ismethod(v) or k.startswith("__"): continue if torch.is_tensor(v): v_clone = v.clone() else: v_clone = copy.deepcopy(v) setattr(other, k, v_clone) return other def gather_props(self, batch_idx) -> "TensorProperties": """ This is an in place operation to reformat all tensor class attributes based on a set of given indices using torch.gather. This is useful when attributes which are batched tensors e.g. shape (N, 3) need to be multiplied with another tensor which has a different first dimension e.g. packed vertices of shape (V, 3). Example .. code-block:: python self.specular_color = (N, 3) tensor of specular colors for each mesh A lighting calculation may use .. code-block:: python verts_packed = meshes.verts_packed() # (V, 3) To multiply these two tensors the batch dimension needs to be the same. To achieve this we can do .. code-block:: python batch_idx = meshes.verts_packed_to_mesh_idx() # (V) This gives index of the mesh for each vertex in verts_packed. .. code-block:: python self.gather_props(batch_idx) self.specular_color = (V, 3) tensor with the specular color for each packed vertex. torch.gather requires the index tensor to have the same shape as the input tensor so this method takes care of the reshaping of the index tensor to use with class attributes with arbitrary dimensions. Args: batch_idx: shape (B, ...) where `...` represents an arbitrary number of dimensions Returns: self with all properties reshaped. e.g. a property with shape (N, 3) is transformed to shape (B, 3). """ # Iterate through the attributes of the class which are tensors. for k in dir(self): v = getattr(self, k) if torch.is_tensor(v): if v.shape[0] > 1: # There are different values for each batch element # so gather these using the batch_idx. # First clone the input batch_idx tensor before # modifying it. _batch_idx = batch_idx.clone() idx_dims = _batch_idx.shape tensor_dims = v.shape if len(idx_dims) > len(tensor_dims): msg = "batch_idx cannot have more dimensions than %s. " msg += "got shape %r and %s has shape %r" raise ValueError(msg % (k, idx_dims, k, tensor_dims)) if idx_dims != tensor_dims: # To use torch.gather the index tensor (_batch_idx) has # to have the same shape as the input tensor. new_dims = len(tensor_dims) - len(idx_dims) new_shape = idx_dims + (1,) * new_dims expand_dims = (-1,) + tensor_dims[1:] _batch_idx = _batch_idx.view(*new_shape) _batch_idx = _batch_idx.expand(*expand_dims) v = v.gather(0, _batch_idx) setattr(self, k, v) return self class CamerasBase(TensorProperties): """ `CamerasBase` implements a base class for all cameras. For cameras, there are four different coordinate systems (or spaces) - World coordinate system: This is the system the object lives - the world. - Camera view coordinate system: This is the system that has its origin on the camera and the and the Z-axis perpendicular to the image plane. In PyTorch3D, we assume that +X points left, and +Y points up and +Z points out from the image plane. The transformation from world --> view happens after applying a rotation (R) and translation (T) - NDC coordinate system: This is the normalized coordinate system that confines in a volume the rendered part of the object or scene. Also known as view volume. For square images, given the PyTorch3D convention, (+1, +1, znear) is the top left near corner, and (-1, -1, zfar) is the bottom right far corner of the volume. The transformation from view --> NDC happens after applying the camera projection matrix (P) if defined in NDC space. For non square images, we scale the points such that smallest side has range [-1, 1] and the largest side has range [-u, u], with u > 1. - Screen coordinate system: This is another representation of the view volume with the XY coordinates defined in image space instead of a normalized space. A better illustration of the coordinate systems can be found in pytorch3d/docs/notes/cameras.md. It defines methods that are common to all camera models: - `get_camera_center` that returns the optical center of the camera in world coordinates - `get_world_to_view_transform` which returns a 3D transform from world coordinates to the camera view coordinates (R, T) - `get_full_projection_transform` which composes the projection transform (P) with the world-to-view transform (R, T) - `transform_points` which takes a set of input points in world coordinates and projects to the space the camera is defined in (NDC or screen) - `get_ndc_camera_transform` which defines the transform from screen/NDC to PyTorch3D's NDC space - `transform_points_ndc` which takes a set of points in world coordinates and projects them to PyTorch3D's NDC space - `transform_points_screen` which takes a set of points in world coordinates and projects them to screen space For each new camera, one should implement the `get_projection_transform` routine that returns the mapping from camera view coordinates to camera coordinates (NDC or screen). Another useful function that is specific to each camera model is `unproject_points` which sends points from camera coordinates (NDC or screen) back to camera view or world coordinates depending on the `world_coordinates` boolean argument of the function. """ # Used in __getitem__ to index the relevant fields # When creating a new camera, this should be set in the __init__ _FIELDS: Tuple[str, ...] = () # Names of fields which are a constant property of the whole batch, rather # than themselves a batch of data. # When joining objects into a batch, they will have to agree. _SHARED_FIELDS: Tuple[str, ...] = () def get_projection_transform(self): """ Calculate the projective transformation matrix. Args: **kwargs: parameters for the projection can be passed in as keyword arguments to override the default values set in `__init__`. Return: a `Transform3d` object which represents a batch of projection matrices of shape (N, 3, 3) """ raise NotImplementedError() def unproject_points(self, xy_depth: torch.Tensor, **kwargs): """ Transform input points from camera coodinates (NDC or screen) to the world / camera coordinates. Each of the input points `xy_depth` of shape (..., 3) is a concatenation of the x, y location and its depth. For instance, for an input 2D tensor of shape `(num_points, 3)` `xy_depth` takes the following form: `xy_depth[i] = [x[i], y[i], depth[i]]`, for a each point at an index `i`. The following example demonstrates the relationship between `transform_points` and `unproject_points`: .. code-block:: python cameras = # camera object derived from CamerasBase xyz = # 3D points of shape (batch_size, num_points, 3) # transform xyz to the camera view coordinates xyz_cam = cameras.get_world_to_view_transform().transform_points(xyz) # extract the depth of each point as the 3rd coord of xyz_cam depth = xyz_cam[:, :, 2:] # project the points xyz to the camera xy = cameras.transform_points(xyz)[:, :, :2] # append depth to xy xy_depth = torch.cat((xy, depth), dim=2) # unproject to the world coordinates xyz_unproj_world = cameras.unproject_points(xy_depth, world_coordinates=True) print(torch.allclose(xyz, xyz_unproj_world)) # True # unproject to the camera coordinates xyz_unproj = cameras.unproject_points(xy_depth, world_coordinates=False) print(torch.allclose(xyz_cam, xyz_unproj)) # True Args: xy_depth: torch tensor of shape (..., 3). world_coordinates: If `True`, unprojects the points back to world coordinates using the camera extrinsics `R` and `T`. `False` ignores `R` and `T` and unprojects to the camera view coordinates. from_ndc: If `False` (default), assumes xy part of input is in NDC space if self.in_ndc(), otherwise in screen space. If `True`, assumes xy is in NDC space even if the camera is defined in screen space. Returns new_points: unprojected points with the same shape as `xy_depth`. """ raise NotImplementedError() def get_camera_center(self, **kwargs) -> torch.Tensor: """ Return the 3D location of the camera optical center in the world coordinates. Args: **kwargs: parameters for the camera extrinsics can be passed in as keyword arguments to override the default values set in __init__. Setting T here will update the values set in init as this value may be needed later on in the rendering pipeline e.g. for lighting calculations. Returns: C: a batch of 3D locations of shape (N, 3) denoting the locations of the center of each camera in the batch. """ w2v_trans = self.get_world_to_view_transform(**kwargs) P = w2v_trans.inverse().get_matrix() # the camera center is the translation component (the first 3 elements # of the last row) of the inverted world-to-view # transform (4x4 RT matrix) C = P[:, 3, :3] return C def get_world_to_view_transform(self, **kwargs) -> Transform3d: """ Return the world-to-view transform. Args: **kwargs: parameters for the camera extrinsics can be passed in as keyword arguments to override the default values set in __init__. Setting R and T here will update the values set in init as these values may be needed later on in the rendering pipeline e.g. for lighting calculations. Returns: A Transform3d object which represents a batch of transforms of shape (N, 3, 3) """ R: torch.Tensor = kwargs.get("R", self.R) T: torch.Tensor = kwargs.get("T", self.T) self.R = R # pyre-ignore[16] self.T = T # pyre-ignore[16] world_to_view_transform = get_world_to_view_transform(R=R, T=T) return world_to_view_transform def get_full_projection_transform(self, **kwargs) -> Transform3d: """ Return the full world-to-camera transform composing the world-to-view and view-to-camera transforms. If camera is defined in NDC space, the projected points are in NDC space. If camera is defined in screen space, the projected points are in screen space. Args: **kwargs: parameters for the projection transforms can be passed in as keyword arguments to override the default values set in __init__. Setting R and T here will update the values set in init as these values may be needed later on in the rendering pipeline e.g. for lighting calculations. Returns: a Transform3d object which represents a batch of transforms of shape (N, 3, 3) """ self.R: torch.Tensor = kwargs.get("R", self.R) # pyre-ignore[16] self.T: torch.Tensor = kwargs.get("T", self.T) # pyre-ignore[16] world_to_view_transform = self.get_world_to_view_transform(R=self.R, T=self.T) view_to_proj_transform = self.get_projection_transform(**kwargs) return world_to_view_transform.compose(view_to_proj_transform) def transform_points( self, points, eps: Optional[float] = None, **kwargs ) -> torch.Tensor: """ Transform input points from world to camera space with the projection matrix defined by the camera. For `CamerasBase.transform_points`, setting `eps > 0` stabilizes gradients since it leads to avoiding division by excessively low numbers for points close to the camera plane. Args: points: torch tensor of shape (..., 3). eps: If eps!=None, the argument is used to clamp the divisor in the homogeneous normalization of the points transformed to the ndc space. Please see `transforms.Transform3d.transform_points` for details. For `CamerasBase.transform_points`, setting `eps > 0` stabilizes gradients since it leads to avoiding division by excessively low numbers for points close to the camera plane. Returns new_points: transformed points with the same shape as the input. """ world_to_proj_transform = self.get_full_projection_transform(**kwargs) return world_to_proj_transform.transform_points(points, eps=eps) def get_ndc_camera_transform(self, **kwargs) -> Transform3d: """ Returns the transform from camera projection space (screen or NDC) to NDC space. For cameras that can be specified in screen space, this transform allows points to be converted from screen to NDC space. The default transform scales the points from [0, W]x[0, H] to [-1, 1]x[-u, u] or [-u, u]x[-1, 1] where u > 1 is the aspect ratio of the image. This function should be modified per camera definitions if need be, e.g. for Perspective/Orthographic cameras we provide a custom implementation. This transform assumes PyTorch3D coordinate system conventions for both the NDC space and the input points. This transform interfaces with the PyTorch3D renderer which assumes input points to the renderer to be in NDC space. """ if self.in_ndc(): return Transform3d(device=self.device, dtype=torch.float32) else: # For custom cameras which can be defined in screen space, # users might might have to implement the screen to NDC transform based # on the definition of the camera parameters. # See PerspectiveCameras/OrthographicCameras for an example. # We don't flip xy because we assume that world points are in # PyTorch3D coordinates, and thus conversion from screen to ndc # is a mere scaling from image to [-1, 1] scale. image_size = kwargs.get("image_size", self.get_image_size()) return get_screen_to_ndc_transform( self, with_xyflip=False, image_size=image_size ) def transform_points_ndc( self, points, eps: Optional[float] = None, **kwargs ) -> torch.Tensor: """ Transforms points from PyTorch3D world/camera space to NDC space. Input points follow the PyTorch3D coordinate system conventions: +X left, +Y up. Output points are in NDC space: +X left, +Y up, origin at image center. Args: points: torch tensor of shape (..., 3). eps: If eps!=None, the argument is used to clamp the divisor in the homogeneous normalization of the points transformed to the ndc space. Please see `transforms.Transform3d.transform_points` for details. For `CamerasBase.transform_points`, setting `eps > 0` stabilizes gradients since it leads to avoiding division by excessively low numbers for points close to the camera plane. Returns new_points: transformed points with the same shape as the input. """ world_to_ndc_transform = self.get_full_projection_transform(**kwargs) if not self.in_ndc(): to_ndc_transform = self.get_ndc_camera_transform(**kwargs) world_to_ndc_transform = world_to_ndc_transform.compose(to_ndc_transform) return world_to_ndc_transform.transform_points(points, eps=eps) def transform_points_screen( self, points, eps: Optional[float] = None, **kwargs ) -> torch.Tensor: """ Transforms points from PyTorch3D world/camera space to screen space. Input points follow the PyTorch3D coordinate system conventions: +X left, +Y up. Output points are in screen space: +X right, +Y down, origin at top left corner. Args: points: torch tensor of shape (..., 3). eps: If eps!=None, the argument is used to clamp the divisor in the homogeneous normalization of the points transformed to the ndc space. Please see `transforms.Transform3d.transform_points` for details. For `CamerasBase.transform_points`, setting `eps > 0` stabilizes gradients since it leads to avoiding division by excessively low numbers for points close to the camera plane. Returns new_points: transformed points with the same shape as the input. """ points_ndc = self.transform_points_ndc(points, eps=eps, **kwargs) image_size = kwargs.get("image_size", self.get_image_size()) return get_ndc_to_screen_transform( self, with_xyflip=True, image_size=image_size ).transform_points(points_ndc, eps=eps) def clone(self): """ Returns a copy of `self`. """ cam_type = type(self) other = cam_type(device=self.device) return super().clone(other) def is_perspective(self): raise NotImplementedError() def in_ndc(self): """ Specifies whether the camera is defined in NDC space or in screen (image) space """ raise NotImplementedError() def get_znear(self): return self.znear if hasattr(self, "znear") else None def get_image_size(self): """ Returns the image size, if provided, expected in the form of (height, width) The image size is used for conversion of projected points to screen coordinates. """ return self.image_size if hasattr(self, "image_size") else None def __getitem__( self, index: Union[int, List[int], torch.LongTensor] ) -> "CamerasBase": """ Override for the __getitem__ method in TensorProperties which needs to be refactored. Args: index: an int/list/long tensor used to index all the fields in the cameras given by self._FIELDS. Returns: if `index` is an index int/list/long tensor return an instance of the current cameras class with only the values at the selected index. """ kwargs = {} if not isinstance(index, (int, list, torch.LongTensor, torch.cuda.LongTensor)): msg = "Invalid index type, expected int, List[int] or torch.LongTensor; got %r" raise ValueError(msg % type(index)) if isinstance(index, int): index = [index] if max(index) >= len(self): raise ValueError(f"Index {max(index)} is out of bounds for select cameras") for field in self._FIELDS: val = getattr(self, field, None) if val is None: continue # e.g. "in_ndc" is set as attribute "_in_ndc" on the class # but provided as "in_ndc" on initialization if field.startswith("_"): field = field[1:] if isinstance(val, (str, bool)): kwargs[field] = val elif isinstance(val, torch.Tensor): # In the init, all inputs will be converted to # tensors before setting as attributes kwargs[field] = val[index] else: raise ValueError(f"Field {field} type is not supported for indexing") kwargs["device"] = self.device return self.__class__(**kwargs) class FoVPerspectiveCameras(CamerasBase): """ A class which stores a batch of parameters to generate a batch of projection matrices by specifying the field of view. The definition of the parameters follow the OpenGL perspective camera. The extrinsics of the camera (R and T matrices) can also be set in the initializer or passed in to `get_full_projection_transform` to get the full transformation from world -> ndc. The `transform_points` method calculates the full world -> ndc transform and then applies it to the input points. The transforms can also be returned separately as Transform3d objects. * Setting the Aspect Ratio for Non Square Images * If the desired output image size is non square (i.e. a tuple of (H, W) where H != W) the aspect ratio needs special consideration: There are two aspect ratios to be aware of: - the aspect ratio of each pixel - the aspect ratio of the output image The `aspect_ratio` setting in the FoVPerspectiveCameras sets the pixel aspect ratio. When using this camera with the differentiable rasterizer be aware that in the rasterizer we assume square pixels, but allow variable image aspect ratio (i.e rectangle images). In most cases you will want to set the camera `aspect_ratio=1.0` (i.e. square pixels) and only vary the output image dimensions in pixels for rasterization. """ # For __getitem__ _FIELDS = ( "K", "znear", "zfar", "aspect_ratio", "fov", "R", "T", "degrees", ) _SHARED_FIELDS = ("degrees",) def __init__( self, znear=1.0, zfar=100.0, aspect_ratio=1.0, fov=60.0, degrees: bool = True, R: torch.Tensor = _R, T: torch.Tensor = _T, K: Optional[torch.Tensor] = None, device: Device = "cpu", ) -> None: """ Args: znear: near clipping plane of the view frustrum. zfar: far clipping plane of the view frustrum. aspect_ratio: aspect ratio of the image pixels. 1.0 indicates square pixels. fov: field of view angle of the camera. degrees: bool, set to True if fov is specified in degrees. R: Rotation matrix of shape (N, 3, 3) T: Translation matrix of shape (N, 3) K: (optional) A calibration matrix of shape (N, 4, 4) If provided, don't need znear, zfar, fov, aspect_ratio, degrees device: Device (as str or torch.device) """ # The initializer formats all inputs to torch tensors and broadcasts # all the inputs to have the same batch dimension where necessary. super().__init__( device=device, znear=znear, zfar=zfar, aspect_ratio=aspect_ratio, fov=fov, R=R, T=T, K=K, ) # No need to convert to tensor or broadcast. self.degrees = degrees def compute_projection_matrix( self, znear, zfar, fov, aspect_ratio, degrees: bool ) -> torch.Tensor: """ Compute the calibration matrix K of shape (N, 4, 4) Args: znear: near clipping plane of the view frustrum. zfar: far clipping plane of the view frustrum. fov: field of view angle of the camera. aspect_ratio: aspect ratio of the image pixels. 1.0 indicates square pixels. degrees: bool, set to True if fov is specified in degrees. Returns: torch.FloatTensor of the calibration matrix with shape (N, 4, 4) """ K = torch.zeros((self._N, 4, 4), device=self.device, dtype=torch.float32) ones = torch.ones((self._N), dtype=torch.float32, device=self.device) if degrees: fov = (np.pi / 180) * fov if not torch.is_tensor(fov): fov = torch.tensor(fov, device=self.device) tanHalfFov = torch.tan((fov / 2)) max_y = tanHalfFov * znear min_y = -max_y max_x = max_y * aspect_ratio min_x = -max_x # NOTE: In OpenGL the projection matrix changes the handedness of the # coordinate frame. i.e the NDC space positive z direction is the # camera space negative z direction. This is because the sign of the z # in the projection matrix is set to -1.0. # In pytorch3d we maintain a right handed coordinate system throughout # so the so the z sign is 1.0. z_sign = 1.0 K[:, 0, 0] = 2.0 * znear / (max_x - min_x) K[:, 1, 1] = 2.0 * znear / (max_y - min_y) K[:, 0, 2] = (max_x + min_x) / (max_x - min_x) K[:, 1, 2] = (max_y + min_y) / (max_y - min_y) K[:, 3, 2] = z_sign * ones # NOTE: This maps the z coordinate from [0, 1] where z = 0 if the point # is at the near clipping plane and z = 1 when the point is at the far # clipping plane. K[:, 2, 2] = z_sign * zfar / (zfar - znear) K[:, 2, 3] = -(zfar * znear) / (zfar - znear) return K def get_projection_transform(self, **kwargs) -> Transform3d: """ Calculate the perspective projection matrix with a symmetric viewing frustrum. Use column major order. The viewing frustrum will be projected into ndc, s.t. (max_x, max_y) -> (+1, +1) (min_x, min_y) -> (-1, -1) Args: **kwargs: parameters for the projection can be passed in as keyword arguments to override the default values set in `__init__`. Return: a Transform3d object which represents a batch of projection matrices of shape (N, 4, 4) .. code-block:: python h1 = (max_y + min_y)/(max_y - min_y) w1 = (max_x + min_x)/(max_x - min_x) tanhalffov = tan((fov/2)) s1 = 1/tanhalffov s2 = 1/(tanhalffov * (aspect_ratio)) # To map z to the range [0, 1] use: f1 = far / (far - near) f2 = -(far * near) / (far - near) # Projection matrix K = [ [s1, 0, w1, 0], [0, s2, h1, 0], [0, 0, f1, f2], [0, 0, 1, 0], ] """ K = kwargs.get("K", self.K) if K is not None: if K.shape != (self._N, 4, 4): msg = "Expected K to have shape of (%r, 4, 4)" raise ValueError(msg % (self._N)) else: K = self.compute_projection_matrix( kwargs.get("znear", self.znear), kwargs.get("zfar", self.zfar), kwargs.get("fov", self.fov), kwargs.get("aspect_ratio", self.aspect_ratio), kwargs.get("degrees", self.degrees), ) # Transpose the projection matrix as PyTorch3D transforms use row vectors. transform = Transform3d( matrix=K.transpose(1, 2).contiguous(), device=self.device ) return transform def unproject_points( self, xy_depth: torch.Tensor, world_coordinates: bool = True, scaled_depth_input: bool = False, **kwargs, ) -> torch.Tensor: """>! FoV cameras further allow for passing depth in world units (`scaled_depth_input=False`) or in the [0, 1]-normalized units (`scaled_depth_input=True`) Args: scaled_depth_input: If `True`, assumes the input depth is in the [0, 1]-normalized units. If `False` the input depth is in the world units. """ # obtain the relevant transformation to ndc if world_coordinates: to_ndc_transform = self.get_full_projection_transform() else: to_ndc_transform = self.get_projection_transform() if scaled_depth_input: # the input is scaled depth, so we don't have to do anything xy_sdepth = xy_depth else: # parse out important values from the projection matrix K_matrix = self.get_projection_transform(**kwargs.copy()).get_matrix() # parse out f1, f2 from K_matrix unsqueeze_shape = [1] * xy_depth.dim() unsqueeze_shape[0] = K_matrix.shape[0] f1 = K_matrix[:, 2, 2].reshape(unsqueeze_shape) f2 = K_matrix[:, 3, 2].reshape(unsqueeze_shape) # get the scaled depth sdepth = (f1 * xy_depth[..., 2:3] + f2) / xy_depth[..., 2:3] # concatenate xy + scaled depth xy_sdepth = torch.cat((xy_depth[..., 0:2], sdepth), dim=-1) # unproject with inverse of the projection unprojection_transform = to_ndc_transform.inverse() return unprojection_transform.transform_points(xy_sdepth) def is_perspective(self): return True def in_ndc(self): return True ####################################################################################### ## ██████╗ ███████╗███████╗██╗███╗ ██╗██╗████████╗██╗ ██████╗ ███╗ ██╗███████╗ ## ## ██╔══██╗██╔════╝██╔════╝██║████╗ ██║██║╚══██╔══╝██║██╔═══██╗████╗ ██║██╔════╝ ## ## ██║ ██║█████╗ █████╗ ██║██╔██╗ ██║██║ ██║ ██║██║ ██║██╔██╗ ██║███████╗ ## ## ██║ ██║██╔══╝ ██╔══╝ ██║██║╚██╗██║██║ ██║ ██║██║ ██║██║╚██╗██║╚════██║ ## ## ██████╔╝███████╗██║ ██║██║ ╚████║██║ ██║ ██║╚██████╔╝██║ ╚████║███████║ ## ## ╚═════╝ ╚══════╝╚═╝ ╚═╝╚═╝ ╚═══╝╚═╝ ╚═╝ ╚═╝ ╚═════╝ ╚═╝ ╚═══╝╚══════╝ ## ####################################################################################### def make_device(device: Device) -> torch.device: """ Makes an actual torch.device object from the device specified as either a string or torch.device object. If the device is `cuda` without a specific index, the index of the current device is assigned. Args: device: Device (as str or torch.device) Returns: A matching torch.device object """ device = torch.device(device) if isinstance(device, str) else device if device.type == "cuda" and device.index is None: # pyre-ignore[16] # If cuda but with no index, then the current cuda device is indicated. # In that case, we fix to that device device = torch.device(f"cuda:{torch.cuda.current_device()}") return device def get_device(x, device: Optional[Device] = None) -> torch.device: """ Gets the device of the specified variable x if it is a tensor, or falls back to a default CPU device otherwise. Allows overriding by providing an explicit device. Args: x: a torch.Tensor to get the device from or another type device: Device (as str or torch.device) to fall back to Returns: A matching torch.device object """ # User overrides device if device is not None: return make_device(device) # Set device based on input tensor if torch.is_tensor(x): return x.device # Default device is cpu return torch.device("cpu") def _axis_angle_rotation(axis: str, angle: torch.Tensor) -> torch.Tensor: """ Return the rotation matrices for one of the rotations about an axis of which Euler angles describe, for each value of the angle given. Args: axis: Axis label "X" or "Y or "Z". angle: any shape tensor of Euler angles in radians Returns: Rotation matrices as tensor of shape (..., 3, 3). """ cos = torch.cos(angle) sin = torch.sin(angle) one = torch.ones_like(angle) zero = torch.zeros_like(angle) if axis == "X": R_flat = (one, zero, zero, zero, cos, -sin, zero, sin, cos) elif axis == "Y": R_flat = (cos, zero, sin, zero, one, zero, -sin, zero, cos) elif axis == "Z": R_flat = (cos, -sin, zero, sin, cos, zero, zero, zero, one) else: raise ValueError("letter must be either X, Y or Z.") return torch.stack(R_flat, -1).reshape(angle.shape + (3, 3)) def euler_angles_to_matrix(euler_angles: torch.Tensor, convention: str) -> torch.Tensor: """ Convert rotations given as Euler angles in radians to rotation matrices. Args: euler_angles: Euler angles in radians as tensor of shape (..., 3). convention: Convention string of three uppercase letters from {"X", "Y", and "Z"}. Returns: Rotation matrices as tensor of shape (..., 3, 3). """ if euler_angles.dim() == 0 or euler_angles.shape[-1] != 3: raise ValueError("Invalid input euler angles.") if len(convention) != 3: raise ValueError("Convention must have 3 letters.") if convention[1] in (convention[0], convention[2]): raise ValueError(f"Invalid convention {convention}.") for letter in convention: if letter not in ("X", "Y", "Z"): raise ValueError(f"Invalid letter {letter} in convention string.") matrices = [ _axis_angle_rotation(c, e) for c, e in zip(convention, torch.unbind(euler_angles, -1)) ] # return functools.reduce(torch.matmul, matrices) return torch.matmul(torch.matmul(matrices[0], matrices[1]), matrices[2]) def _broadcast_bmm(a, b) -> torch.Tensor: """ Batch multiply two matrices and broadcast if necessary. Args: a: torch tensor of shape (P, K) or (M, P, K) b: torch tensor of shape (N, K, K) Returns: a and b broadcast multiplied. The output batch dimension is max(N, M). To broadcast transforms across a batch dimension if M != N then expect that either M = 1 or N = 1. The tensor with batch dimension 1 is expanded to have shape N or M. """ if a.dim() == 2: a = a[None] if len(a) != len(b): if not ((len(a) == 1) or (len(b) == 1)): msg = "Expected batch dim for bmm to be equal or 1; got %r, %r" raise ValueError(msg % (a.shape, b.shape)) if len(a) == 1: a = a.expand(len(b), -1, -1) if len(b) == 1: b = b.expand(len(a), -1, -1) return a.bmm(b) def _safe_det_3x3(t: torch.Tensor): """ Fast determinant calculation for a batch of 3x3 matrices. Note, result of this function might not be the same as `torch.det()`. The differences might be in the last significant digit. Args: t: Tensor of shape (N, 3, 3). Returns: Tensor of shape (N) with determinants. """ det = ( t[..., 0, 0] * (t[..., 1, 1] * t[..., 2, 2] - t[..., 1, 2] * t[..., 2, 1]) - t[..., 0, 1] * (t[..., 1, 0] * t[..., 2, 2] - t[..., 2, 0] * t[..., 1, 2]) + t[..., 0, 2] * (t[..., 1, 0] * t[..., 2, 1] - t[..., 2, 0] * t[..., 1, 1]) ) return det def get_world_to_view_transform( R: torch.Tensor = _R, T: torch.Tensor = _T ) -> Transform3d: """ This function returns a Transform3d representing the transformation matrix to go from world space to view space by applying a rotation and a translation. PyTorch3D uses the same convention as Hartley & Zisserman. I.e., for camera extrinsic parameters R (rotation) and T (translation), we map a 3D point `X_world` in world coordinates to a point `X_cam` in camera coordinates with: `X_cam = X_world R + T` Args: R: (N, 3, 3) matrix representing the rotation. T: (N, 3) matrix representing the translation. Returns: a Transform3d object which represents the composed RT transformation. """ # TODO: also support the case where RT is specified as one matrix # of shape (N, 4, 4). if T.shape[0] != R.shape[0]: msg = "Expected R, T to have the same batch dimension; got %r, %r" raise ValueError(msg % (R.shape[0], T.shape[0])) if T.dim() != 2 or T.shape[1:] != (3,): msg = "Expected T to have shape (N, 3); got %r" raise ValueError(msg % repr(T.shape)) if R.dim() != 3 or R.shape[1:] != (3, 3): msg = "Expected R to have shape (N, 3, 3); got %r" raise ValueError(msg % repr(R.shape)) # Create a Transform3d object T_ = Translate(T, device=T.device) R_ = Rotate(R, device=R.device) return R_.compose(T_) def _check_valid_rotation_matrix(R, tol: float = 1e-7) -> None: """ Determine if R is a valid rotation matrix by checking it satisfies the following conditions: ``RR^T = I and det(R) = 1`` Args: R: an (N, 3, 3) matrix Returns: None Emits a warning if R is an invalid rotation matrix. """ N = R.shape[0] eye = torch.eye(3, dtype=R.dtype, device=R.device) eye = eye.view(1, 3, 3).expand(N, -1, -1) orthogonal = torch.allclose(R.bmm(R.transpose(1, 2)), eye, atol=tol) det_R = _safe_det_3x3(R) no_distortion = torch.allclose(det_R, torch.ones_like(det_R)) if not (orthogonal and no_distortion): msg = "R is not a valid rotation matrix" warnings.warn(msg) return def format_tensor( input, dtype: torch.dtype = torch.float32, device: Device = "cpu", ) -> torch.Tensor: """ Helper function for converting a scalar value to a tensor. Args: input: Python scalar, Python list/tuple, torch scalar, 1D torch tensor dtype: data type for the input device: Device (as str or torch.device) on which the tensor should be placed. Returns: input_vec: torch tensor with optional added batch dimension. """ device_ = make_device(device) if not torch.is_tensor(input): input = torch.tensor(input, dtype=dtype, device=device_) if input.dim() == 0: input = input.view(1) if input.device == device_: return input input = input.to(device=device) return input def convert_to_tensors_and_broadcast( *args, dtype: torch.dtype = torch.float32, device: Device = "cpu", ): """ Helper function to handle parsing an arbitrary number of inputs (*args) which all need to have the same batch dimension. The output is a list of tensors. Args: *args: an arbitrary number of inputs Each of the values in `args` can be one of the following - Python scalar - Torch scalar - Torch tensor of shape (N, K_i) or (1, K_i) where K_i are an arbitrary number of dimensions which can vary for each value in args. In this case each input is broadcast to a tensor of shape (N, K_i) dtype: data type to use when creating new tensors. device: torch device on which the tensors should be placed. Output: args: A list of tensors of shape (N, K_i) """ # Convert all inputs to tensors with a batch dimension args_1d = [format_tensor(c, dtype, device) for c in args] # Find broadcast size sizes = [c.shape[0] for c in args_1d] N = max(sizes) args_Nd = [] for c in args_1d: if c.shape[0] != 1 and c.shape[0] != N: msg = "Got non-broadcastable sizes %r" % sizes raise ValueError(msg) # Expand broadcast dim and keep non broadcast dims the same size expand_sizes = (N,) + (-1,) * len(c.shape[1:]) args_Nd.append(c.expand(*expand_sizes)) return args_Nd def _handle_coord(c, dtype: torch.dtype, device: torch.device) -> torch.Tensor: """ Helper function for _handle_input. Args: c: Python scalar, torch scalar, or 1D torch tensor Returns: c_vec: 1D torch tensor """ if not torch.is_tensor(c): c = torch.tensor(c, dtype=dtype, device=device) if c.dim() == 0: c = c.view(1) if c.device != device or c.dtype != dtype: c = c.to(device=device, dtype=dtype) return c def _handle_input( x, y, z, dtype: torch.dtype, device: Optional[Device], name: str, allow_singleton: bool = False, ) -> torch.Tensor: """ Helper function to handle parsing logic for building transforms. The output is always a tensor of shape (N, 3), but there are several types of allowed input. Case I: Single Matrix In this case x is a tensor of shape (N, 3), and y and z are None. Here just return x. Case II: Vectors and Scalars In this case each of x, y, and z can be one of the following - Python scalar - Torch scalar - Torch tensor of shape (N, 1) or (1, 1) In this case x, y and z are broadcast to tensors of shape (N, 1) and concatenated to a tensor of shape (N, 3) Case III: Singleton (only if allow_singleton=True) In this case y and z are None, and x can be one of the following: - Python scalar - Torch scalar - Torch tensor of shape (N, 1) or (1, 1) Here x will be duplicated 3 times, and we return a tensor of shape (N, 3) Returns: xyz: Tensor of shape (N, 3) """ device_ = get_device(x, device) # If x is actually a tensor of shape (N, 3) then just return it if torch.is_tensor(x) and x.dim() == 2: if x.shape[1] != 3: msg = "Expected tensor of shape (N, 3); got %r (in %s)" raise ValueError(msg % (x.shape, name)) if y is not None or z is not None: msg = "Expected y and z to be None (in %s)" % name raise ValueError(msg) return x.to(device=device_, dtype=dtype) if allow_singleton and y is None and z is None: y = x z = x # Convert all to 1D tensors xyz = [_handle_coord(c, dtype, device_) for c in [x, y, z]] # Broadcast and concatenate sizes = [c.shape[0] for c in xyz] N = max(sizes) for c in xyz: if c.shape[0] != 1 and c.shape[0] != N: msg = "Got non-broadcastable sizes %r (in %s)" % (sizes, name) raise ValueError(msg) xyz = [c.expand(N) for c in xyz] xyz = torch.stack(xyz, dim=1) return xyz