rotate_on_spot

Summary: Function to relatively rotate a camera position. Also document how to relatively translate a camera position.

Reviewed By: theschnitz

Differential Revision: D25900166

fbshipit-source-id: 2ddaf06ee7c5e2a2e973c04d7dee6ccb61c6ff84

Author: bottler

pytorch3d/renderer/__init__.py

@@ -6,6 +6,7 @@
     sigmoid_alpha_blend,
     softmax_rgb_blend,
 )
+from .camera_utils import rotate_on_spot
 from .cameras import OpenGLOrthographicCameras  # deprecated
 from .cameras import OpenGLPerspectiveCameras  # deprecated
 from .cameras import SfMOrthographicCameras  # deprecated

pytorch3d/renderer/camera_utils.py

@@ -62,3 +62,78 @@ def camera_to_eye_at_up(
     eye, at, up_plus_eye = eye_at_up_world.unbind(1)
     up = up_plus_eye - eye
     return eye, at, up
+
+
+def rotate_on_spot(
+    R: torch.Tensor, T: torch.Tensor, rotation: torch.Tensor
+) -> Tuple[torch.Tensor, torch.Tensor]:
+    """
+    Given a camera position as R and T (batched or not),
+    and a rotation matrix (batched or not)
+    return a new R and T representing camera position(s)
+    in the same location but rotated on the spot by the
+    given rotation. In particular the new world to view
+    rotation will be the previous one followed by the inverse
+    of the given rotation.
+
+    For example, adding the following lines before constructing a camera
+    will make the camera point a little to the right of where it
+    otherwise would have been.
+
+    .. code-block::
+
+        from math import radians
+        from pytorch3d.transforms import axis_angle_to_matrix
+        angles = [0, radians(10), 0]
+        rotation = axis_angle_to_matrix(torch.FloatTensor(angles))
+        R, T = rotate_on_spot(R, T, rotation)
+
+    Note here that if you have a column vector, then when you
+    premultiply it by this `rotation` (see the rotation_conversions doc),
+    then it will be rotated anticlockwise if facing the -y axis.
+    In our context, where we postmultiply row vectors to transform them,
+    `rotation` will rotate the camera clockwise around the -y axis
+    (i.e. when looking down), which is a turn to the right.
+
+    If angles was [radians(10), 0, 0], the camera would get pointed
+    up a bit instead.
+
+    If angles was [0, 0, radians(10)], the camera would be rotated anticlockwise
+    a bit, so the image would appear rotated clockwise from how it
+    otherwise would have been.
+
+    If you want to translate the camera from the origin in camera
+    coordinates, this is simple and does not need a separate function.
+    In particular, a translation by X = [a, b, c] would cause
+    the camera to move a units left, b units up, and c units
+    forward. This is achieved by using T-X in place of T.
+
+    Args:
+        R: FloatTensor of shape [3, 3] or [N, 3, 3]
+        T: FloatTensor of shape [3] or [N, 3]
+        rotation: FloatTensor of shape [3, 3] or [n, 3, 3]
+        where if neither n nor N is 1, then n and N must be equal.
+
+    Returns:
+        R: FloatTensor of shape [max(N, n), 3, 3]
+        T: FloatTensor of shape [max(N, n), 3]
+    """
+    if R.ndim == 2:
+        R = R[None]
+    if T.ndim == 1:
+        T = T[None]
+    if rotation.ndim == 2:
+        rotation = rotation[None]
+
+    if R.ndim != 3 or R.shape[1:] != (3, 3):
+        raise ValueError("Invalid R")
+    if T.ndim != 2 or T.shape[1] != 3:
+        raise ValueError("Invalid T")
+    if rotation.ndim != 3 or rotation.shape[1:] != (3, 3):
+        raise ValueError("Invalid rotation")
+
+    new_R = R @ rotation.transpose(1, 2)
+    old_RT = torch.bmm(R, T[:, :, None])
+    new_T = torch.matmul(new_R.transpose(1, 2), old_RT)[:, :, 0]
+
+    return new_R, new_T

pytorch3d/renderer/cameras.py

@@ -38,7 +38,8 @@ class CamerasBase(TensorProperties):
     - Screen coordinate system: This is another representation of the view volume with
         the XY coordinates defined in pixel space instead of a normalized space.
 
-    A better illustration of the coordinate systems can be found in pytorch3d/docs/notes/cameras.md.
+    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

tests/test_camera_utils.py

@@ -1,14 +1,29 @@
 # Copyright (c) Facebook, Inc. and its affiliates. All rights reserved.
 
 import unittest
+from math import radians
 
 import torch
 from common_testing import TestCaseMixin
-from pytorch3d.renderer.camera_utils import camera_to_eye_at_up
-from pytorch3d.renderer.cameras import PerspectiveCameras, look_at_view_transform
+from pytorch3d.renderer.camera_utils import camera_to_eye_at_up, rotate_on_spot
+from pytorch3d.renderer.cameras import (
+    PerspectiveCameras,
+    get_world_to_view_transform,
+    look_at_view_transform,
+)
+from pytorch3d.transforms import axis_angle_to_matrix
 from torch.nn.functional import normalize
 
 
+def _batched_dotprod(x: torch.Tensor, y: torch.Tensor):
+    """
+    Takes two tensors of shape (N,3) and returns their batched
+    dot product along the last dimension as a tensor of shape
+    (N,).
+    """
+    return torch.einsum("ij,ij->i", x, y)
+
+
 class TestCameraUtils(TestCaseMixin, unittest.TestCase):
     def setUp(self) -> None:
         torch.manual_seed(42)
@@ -28,6 +43,7 @@ def test_invert_eye_at_up(self):
 
         # The retrieved eye matches
         self.assertClose(eye, eye2, atol=1e-5)
+        self.assertClose(cameras.get_camera_center(), eye)
 
         # at-eye as retrieved must be a vector in the same direction as
         # the original.
@@ -49,3 +65,99 @@ def test_invert_eye_at_up(self):
         cam_trans2 = cameras2.get_world_to_view_transform()
 
         self.assertClose(cam_trans.get_matrix(), cam_trans2.get_matrix(), atol=1e-5)
+
+    def test_rotate_on_spot_yaw(self):
+        N = 14
+        eye = torch.rand(N, 3)
+        at = torch.rand(N, 3)
+        up = torch.rand(N, 3)
+
+        R, T = look_at_view_transform(eye=eye, at=at, up=up)
+
+        # Moving around the y axis looks left.
+        angles = torch.FloatTensor([0, -radians(10), 0])
+        rotation = axis_angle_to_matrix(angles)
+        R_rot, T_rot = rotate_on_spot(R, T, rotation)
+
+        eye_rot, at_rot, up_rot = camera_to_eye_at_up(
+            get_world_to_view_transform(R=R_rot, T=T_rot)
+        )
+        self.assertClose(eye, eye_rot, atol=1e-5)
+
+        # Make vectors pointing exactly left and up
+        left = torch.cross(up, at - eye, dim=-1)
+        left_rot = torch.cross(up_rot, at_rot - eye_rot, dim=-1)
+        fully_up = torch.cross(at - eye, left, dim=-1)
+        fully_up_rot = torch.cross(at_rot - eye_rot, left_rot, dim=-1)
+
+        # The up direction is unchanged
+        self.assertClose(normalize(fully_up), normalize(fully_up_rot), atol=1e-5)
+
+        # The camera has moved left
+        agree = _batched_dotprod(torch.cross(left, left_rot, dim=1), fully_up)
+        self.assertGreater(agree.min(), 0)
+
+        # Batch dimension for rotation
+        R_rot2, T_rot2 = rotate_on_spot(R, T, rotation.expand(N, 3, 3))
+        self.assertClose(R_rot, R_rot2)
+        self.assertClose(T_rot, T_rot2)
+
+        # No batch dimension for either
+        R_rot3, T_rot3 = rotate_on_spot(R[0], T[0], rotation)
+        self.assertClose(R_rot[:1], R_rot3)
+        self.assertClose(T_rot[:1], T_rot3)
+
+        # No batch dimension for R, T
+        R_rot4, T_rot4 = rotate_on_spot(R[0], T[0], rotation.expand(N, 3, 3))
+        self.assertClose(R_rot[:1].expand(N, 3, 3), R_rot4)
+        self.assertClose(T_rot[:1].expand(N, 3), T_rot4)
+
+    def test_rotate_on_spot_pitch(self):
+        N = 14
+        eye = torch.rand(N, 3)
+        at = torch.rand(N, 3)
+        up = torch.rand(N, 3)
+
+        R, T = look_at_view_transform(eye=eye, at=at, up=up)
+
+        # Moving around the x axis looks down.
+        angles = torch.FloatTensor([-radians(10), 0, 0])
+        rotation = axis_angle_to_matrix(angles)
+        R_rot, T_rot = rotate_on_spot(R, T, rotation)
+        eye_rot, at_rot, up_rot = camera_to_eye_at_up(
+            get_world_to_view_transform(R=R_rot, T=T_rot)
+        )
+        self.assertClose(eye, eye_rot, atol=1e-5)
+
+        # A vector pointing left is unchanged
+        left = torch.cross(up, at - eye, dim=-1)
+        left_rot = torch.cross(up_rot, at_rot - eye_rot, dim=-1)
+        self.assertClose(normalize(left), normalize(left_rot), atol=1e-5)
+
+        # The camera has moved down
+        fully_up = torch.cross(at - eye, left, dim=-1)
+        fully_up_rot = torch.cross(at_rot - eye_rot, left_rot, dim=-1)
+        agree = _batched_dotprod(torch.cross(fully_up, fully_up_rot, dim=1), left)
+        self.assertGreater(agree.min(), 0)
+
+    def test_rotate_on_spot_roll(self):
+        N = 14
+        eye = torch.rand(N, 3)
+        at = torch.rand(N, 3)
+        up = torch.rand(N, 3)
+
+        R, T = look_at_view_transform(eye=eye, at=at, up=up)
+
+        # Moving around the z axis rotates the image.
+        angles = torch.FloatTensor([0, 0, -radians(10)])
+        rotation = axis_angle_to_matrix(angles)
+        R_rot, T_rot = rotate_on_spot(R, T, rotation)
+        eye_rot, at_rot, up_rot = camera_to_eye_at_up(
+            get_world_to_view_transform(R=R_rot, T=T_rot)
+        )
+        self.assertClose(eye, eye_rot, atol=1e-5)
+        self.assertClose(normalize(at - eye), normalize(at_rot - eye), atol=1e-5)
+
+        # The camera has moved clockwise
+        agree = _batched_dotprod(torch.cross(up, up_rot, dim=1), at - eye)
+        self.assertGreater(agree.min(), 0)