IoU for 3D boxes

Summary:
I have implemented an exact solution for 3D IoU of oriented 3D boxes.

This file includes:
* box3d_overlap: which computes the exact IoU of box1 and box2
* box3d_overlap_sampling: which computes an approximate IoU of box1 and box2 by sampling points within the boxes

Note that both implementations currently do not support batching.

Our exact IoU implementation is based on the fact that the intersecting shape of the two 3D boxes will be formed by segments of the surface of the boxes. Our algorithm computes these segments by reasoning whether triangles of one box are within the second box and vice versa. We deal with intersecting triangles by clipping them.

Reviewed By: gkioxari

Differential Revision: D30667497

fbshipit-source-id: 2f747f410f90b7f854eeaf3036794bc3ac982917

pytorch3d/ops/sample_farthest_points.py

@@ -5,7 +5,7 @@
 # LICENSE file in the root directory of this source tree.
 
 from random import randint
-from typing import Optional, Tuple, Union, List
+from typing import List, Optional, Tuple, Union
 
 import torch
 from pytorch3d import _C

tests/test_sample_farthest_points.py

@@ -10,17 +10,18 @@ import numpy as np
 import torch
 from common_testing import (
     TestCaseMixin,
+    get_pytorch3d_dir,
     get_random_cuda_device,
     get_tests_dir,
-    get_pytorch3d_dir,
 )
 from pytorch3d.io import load_obj
 from pytorch3d.ops.sample_farthest_points import (
-    sample_farthest_points_naive,
     sample_farthest_points,
+    sample_farthest_points_naive,
 )
 from pytorch3d.ops.utils import masked_gather
 
+
 DATA_DIR = get_tests_dir() / "data"
 TUTORIAL_DATA_DIR = get_pytorch3d_dir() / "docs/tutorials/data"
 DEBUG = False