screen cameras lose -1

Summary:
All the renderers in PyTorch3D (pointclouds including pulsar, meshes, raysampling) use align_corners=False style. NDC space goes between the edges of the outer pixels. For a non square image with W>H, the vertical NDC space goes from -1 to 1 and the horizontal from -W/H to W/H.

However it was recently pointed out that functionality which deals with screen space inside the camera classes is inconsistent with this. It unintentionally uses align_corners=True. This fixes that.

This would change behaviour of the following:
- If you create a camera in screen coordinates, i.e. setting in_ndc=False, then anything you do with the camera which touches NDC space may be affected, including trying to use renderers. The transform_points_screen function will not be affected...
- If you call the function “transform_points_screen” on a camera defined in NDC space results will be different. I have illustrated in the diff how to get the old results from the new results but this probably isn’t the right long-term solution..

Reviewed By: gkioxari

Differential Revision: D32536305

fbshipit-source-id: 377325a9137282971dcb7ca11a6cba3fc700c9ce

docs/notes/cameras.md

@@ -16,10 +16,11 @@ This is the system that has its origin on the image plane and the `Z`-axis perpe
 This is the normalized coordinate system that confines in a volume the rendered part of the object/scene. Also known as view volume. For square images, under 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. For non-square images, the side of the volume in `XY` with the smallest length ranges from `[-1, 1]` while the larger side from `[-s, s]`, where `s` is the aspect ratio and `s > 1` (larger divided by smaller side).
 The transformation from view to NDC happens after applying the camera projection matrix (`P`).
 * **Screen coordinate system**
-This is another representation of the view volume with the `XY` coordinates defined in pixel space instead of a normalized space.
+This is another representation of the view volume with the `XY` coordinates defined in pixel space instead of a normalized space. (0,0) is the top left corner of the top left pixel
+and (W,H) is the bottom right corner of the bottom right pixel.
 
 An illustration of the 4 coordinate systems is shown below
-![cameras](https://user-images.githubusercontent.com/4369065/90317960-d9b8db80-dee1-11ea-8088-39c414b1e2fa.png)
+![cameras](https://user-images.githubusercontent.com/669761/145090051-67b506d7-6d73-4826-a677-5873b7cb92ba.png)
 
 ## Defining Cameras in PyTorch3D
 
@@ -83,8 +84,8 @@ cameras_ndc = PerspectiveCameras(focal_length=fcl_ndc, principal_point=prp_ndc)
 
 # Screen space camera
 image_size = ((128, 256),)    # (h, w)
-fcl_screen = (76.2,)          # fcl_ndc * (min(image_size) - 1) / 2
-prp_screen = ((114.8, 31.75), )  # (w - 1) / 2 - px_ndc * (min(image_size) - 1) / 2, (h - 1) / 2 - py_ndc * (min(image_size) - 1) / 2
+fcl_screen = (76.8,)          # fcl_ndc * min(image_size) / 2
+prp_screen = ((115.2, 48), )  # w / 2 - px_ndc * min(image_size) / 2, h / 2 - py_ndc * min(image_size) / 2
 cameras_screen = PerspectiveCameras(focal_length=fcl_screen, principal_point=prp_screen, in_ndc=False, image_size=image_size)
 ```
 
@@ -92,9 +93,9 @@ The relationship between screen and NDC specifications of a camera's `focal_leng
 The transformation of x and y coordinates between screen and NDC is exactly the same as for px and py.
 
 ```
-fx_ndc = fx_screen * 2.0 / (s - 1)
-fy_ndc = fy_screen * 2.0 / (s - 1)
+fx_ndc = fx_screen * 2.0 / s
+fy_ndc = fy_screen * 2.0 / s
 
-px_ndc = - (px_screen - (image_width - 1) / 2.0) * 2.0 / (s - 1)
-py_ndc = - (py_screen - (image_height - 1) / 2.0) * 2.0 / (s - 1)
+px_ndc = - (px_screen - image_width / 2.0) * 2.0 / s
+py_ndc = - (py_screen - image_height / 2.0) * 2.0 / s
 ```