def test_perspective(self): far = 10.0 near = 1.0 cameras = OpenGLPerspectiveCameras(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 = OpenGLPerspectiveCameras(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 = OpenGLPerspectiveCameras(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 = OpenGLPerspectiveCameras(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)