(eye, at, up) extraction function

Summary:
Plotly viewing from a specific camera location requires converting that location in to an (eye, at, up) specification. There may be other reasons to want to do this as well. I create a separate utility function for it.

I envisage more such utility functions for manipulating camera information, so I create a separate camera_utils.py file for such things.

Reviewed By: nikhilaravi

Differential Revision: D25981184

fbshipit-source-id: 0947bf98b212676c021f2fddf775bf436dee3487

pytorch3d/renderer/camera_utils.py

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+# Copyright (c) Facebook, Inc. and its affiliates. All rights reserved.
+
+from typing import Tuple
+
+import torch
+from pytorch3d.transforms import Transform3d
+
+
+def camera_to_eye_at_up(
+    world_to_view_transform: Transform3d,
+) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
+    """
+    Given a world to view transform, return the eye, at and up vectors which
+    represent its position.
+
+    For example, if cam is a camera object, then after running
+
+    .. code-block::
+
+        from cameras import look_at_view_transform
+        eye, at, up = camera_to_eye_at_up(cam.get_world_to_view_transform())
+        R, T = look_at_view_transform(eye=eye, at=at, up=up)
+
+    any other camera created from R and T will have the same world to view
+    transform as cam.
+
+    Also, given a camera position R and T, then after running:
+
+    .. code-block::
+
+        from cameras import get_world_to_view_transform, look_at_view_transform
+        eye, at, up = camera_to_eye_at_up(get_world_to_view_transform(R=R, T=T))
+        R2, T2 = look_at_view_transform(eye=eye, at=at, up=up)
+
+    R2 will equal R and T2 will equal T.
+
+    Args:
+        world_to_view_transform: Transform3d representing the extrinsic
+            transformation of N cameras.
+
+    Returns:
+        eye: FloatTensor of shape [N, 3] representing the camera centers in world space.
+        at: FloatTensor of shape [N, 3] representing points in world space directly in
+            front of the cameras e.g. the positions of objects to be viewed by the
+            cameras.
+        up: FloatTensor of shape [N, 3] representing vectors in world space which
+            when projected on to the camera plane point upwards.
+    """
+    cam_trans = world_to_view_transform.inverse()
+    # In the PyTorch3D right handed coordinate system, the camera in view space
+    # is always at the origin looking along the +z axis.
+
+    # The up vector is not a position so cannot be transformed with
+    # transform_points. However the position eye+up above the camera
+    # (whose position vector in the camera coordinate frame is an up vector)
+    # can be transformed with transform_points.
+    eye_at_up_view = torch.tensor(
+        [[0, 0, 0], [0, 0, 1], [0, 1, 0]], dtype=torch.float32, device=cam_trans.device
+    )
+    eye_at_up_world = cam_trans.transform_points(eye_at_up_view).reshape(-1, 3, 3)
+
+    eye, at, up_plus_eye = eye_at_up_world.unbind(1)
+    up = up_plus_eye - eye
+    return eye, at, up