create extrinsic from eye point (#65)

Summary:
Create extrinsic parameters from eye point.
Create the rotation and translation from an eye point, look-at point and up vector.
see:
https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluLookAt.xml

It is arguably easier to initialise a camera position as a point in the world rather than an angle.
Pull Request resolved: https://github.com/facebookresearch/pytorch3d/pull/65

Reviewed By: bottler

Differential Revision: D20419652

Pulled By: nikhilaravi

fbshipit-source-id: 9caa1330860bb8bde1fb5c3864ed4cde836a5d19

pytorch3d/renderer/cameras.py

@@ -2,7 +2,7 @@
 
 import math
 import numpy as np
-from typing import Tuple
+from typing import Tuple, Optional, Sequence
 import torch
 import torch.nn.functional as F
 
@@ -997,10 +997,11 @@ def look_at_rotation(
 
 
 def look_at_view_transform(
-    dist,
-    elev,
-    azim,
+    dist=1.0,
+    elev=0.0,
+    azim=0.0,
     degrees: bool = True,
+    eye: Optional[Sequence] = None,
     at=((0, 0, 0),),  # (1, 3)
     up=((0, 1, 0),),  # (1, 3)
     device="cpu",
@@ -1019,10 +1020,12 @@ def look_at_view_transform(
             reference vector at (1, 0, 0) on the reference plane.
         dist, elem and azim can be of shape (1), (N).
         degrees: boolean flag to indicate if the elevation and azimuth
-            angles are specified in degrees or raidans.
+            angles are specified in degrees or radians.
+        eye: the position of the camera(s) in world coordinates. If eye is not
+            None, it will overide the camera position derived from dist, elev, azim.
         up: the direction of the x axis in the world coordinate system.
         at: the position of the object(s) in world coordinates.
-        up and at can be of shape (1, 3) or (N, 3).
+        eye, up and at can be of shape (1, 3) or (N, 3).
 
     Returns:
         2-element tuple containing
@@ -1033,11 +1036,19 @@ def look_at_view_transform(
     References:
     [0] https://www.scratchapixel.com
     """
-    broadcasted_args = convert_to_tensors_and_broadcast(
-        dist, elev, azim, at, up, device=device
-    )
-    dist, elev, azim, at, up = broadcasted_args
-    C = camera_position_from_spherical_angles(dist, elev, azim, device=device)
+
+    if eye is not None:
+        broadcasted_args = convert_to_tensors_and_broadcast(
+            eye, at, up, device=device)
+        eye, at, up = broadcasted_args
+        C = eye
+    else:
+        broadcasted_args = convert_to_tensors_and_broadcast(
+            dist, elev, azim, at, up, device=device)
+        dist, elev, azim, at, up = broadcasted_args
+        C = camera_position_from_spherical_angles(
+            dist, elev, azim, degrees=degrees, device=device)
+
     R = look_at_rotation(C, at, up, device=device)
     T = -torch.bmm(R.transpose(1, 2), C[:, :, None])[:, :, 0]
     return R, T