def test_perspective(self):
far = 10.0
near = 1.0
cameras = FoVPerspectiveCameras(znear=near, zfar=far, fov=60.0)
P = cameras.get_projection_transform()
# vertices are at the far clipping plane so z gets mapped to 1.
vertices = torch.tensor([1, 2, far], dtype=torch.float32)
projected_verts = torch.tensor(
[np.sqrt(3) / far, 2 * np.sqrt(3) / far, 1.0], dtype=torch.float32)
vertices = vertices[None, None, :]
v1 = P.transform_points(vertices)
v2 = perspective_project_naive(vertices, fov=60.0)
self.assertClose(v1[..., :2], v2[..., :2])
self.assertClose(far * v1[..., 2], v2[..., 2])
self.assertClose(v1.squeeze(), projected_verts)
# vertices are at the near clipping plane so z gets mapped to 0.0.
vertices[..., 2] = near
projected_verts = torch.tensor(
[np.sqrt(3) / near, 2 * np.sqrt(3) / near, 0.0],
dtype=torch.float32)
v1 = P.transform_points(vertices)
v2 = perspective_project_naive(vertices, fov=60.0)
self.assertClose(v1[..., :2], v2[..., :2])
self.assertClose(v1.squeeze(), projected_verts)
def test_perspective_kwargs(self):
cameras = FoVPerspectiveCameras(znear=5.0, zfar=100.0, fov=0.0)
# Override defaults by passing in values to get_projection_transform
far = 10.0
P = cameras.get_projection_transform(znear=1.0, zfar=far, fov=60.0)
vertices = torch.tensor([1, 2, far], dtype=torch.float32)
projected_verts = torch.tensor(
[np.sqrt(3) / far, 2 * np.sqrt(3) / far, 1.0], dtype=torch.float32)
vertices = vertices[None, None, :]
v1 = P.transform_points(vertices)
self.assertClose(v1.squeeze(), projected_verts)
def test_perspective_mixed_inputs_grad(self):
far = torch.tensor([10.0])
near = 1.0
fov = torch.tensor(60.0, requires_grad=True)
cameras = FoVPerspectiveCameras(znear=near, zfar=far, fov=fov)
P = cameras.get_projection_transform()
vertices = torch.tensor([1, 2, 10], dtype=torch.float32)
vertices_batch = vertices[None, None, :]
v1 = P.transform_points(vertices_batch).squeeze()
v1.sum().backward()
self.assertTrue(hasattr(fov, "grad"))
fov_grad = fov.grad.clone()
half_fov_rad = (math.pi / 180.0) * fov.detach() / 2.0
grad_cotan = -(1.0 / (torch.sin(half_fov_rad)**2.0) * 1 / 2.0)
grad_fov = (math.pi / 180.0) * grad_cotan
grad_fov = (vertices[0] + vertices[1]) * grad_fov / 10.0
self.assertClose(fov_grad, grad_fov)
def test_perspective_mixed_inputs_broadcast(self):
far = torch.tensor([10.0, 20.0], dtype=torch.float32)
near = 1.0
fov = torch.tensor(60.0)
cameras = FoVPerspectiveCameras(znear=near, zfar=far, fov=fov)
P = cameras.get_projection_transform()
vertices = torch.tensor([1, 2, 10], dtype=torch.float32)
z1 = 1.0 # vertices at far clipping plane so z = 1.0
z2 = (20.0 / (20.0 - 1.0) * 10.0 + -20.0 / (20.0 - 1.0)) / 10.0
projected_verts = torch.tensor(
[
[np.sqrt(3) / 10.0, 2 * np.sqrt(3) / 10.0, z1],
[np.sqrt(3) / 10.0, 2 * np.sqrt(3) / 10.0, z2],
],
dtype=torch.float32,
)
vertices = vertices[None, None, :]
v1 = P.transform_points(vertices)
v2 = perspective_project_naive(vertices, fov=60.0)
self.assertClose(v1[..., :2], torch.cat([v2, v2])[..., :2])
self.assertClose(v1.squeeze(), projected_verts)