FoVPerspectiveCameras camera projection transform matrix K may be wrong

[vickersmt]

The code is pytorch3d/blob/main/pytorch3d/renderer/cameras.py

 def compute_projection_matrix(
        self, znear, zfar, fov, aspect_ratio, degrees: bool
    ) -> torch.Tensor:
        """
        Compute the calibration matrix K of shape (N, 4, 4)
        Args:
            znear: near clipping plane of the view frustrum.
            zfar: far clipping plane of the view frustrum.
            fov: field of view angle of the camera.
            aspect_ratio: aspect ratio of the image pixels.
                1.0 indicates square pixels.
            degrees: bool, set to True if fov is specified in degrees.
        Returns:
            torch.FloatTensor of the calibration matrix with shape (N, 4, 4)
        """
        K = torch.zeros((self._N, 4, 4), device=self.device, dtype=torch.float32)
        ones = torch.ones((self._N), dtype=torch.float32, device=self.device)
        if degrees:
            fov = (np.pi / 180) * fov

        if not torch.is_tensor(fov):
            fov = torch.tensor(fov, device=self.device)
        tanHalfFov = torch.tan((fov / 2))
        max_y = tanHalfFov * znear
        min_y = -max_y
        max_x = max_y * aspect_ratio
        min_x = -max_x

        # NOTE: In OpenGL the projection matrix changes the handedness of the
        # coordinate frame. i.e the NDC space positive z direction is the
        # camera space negative z direction. This is because the sign of the z
        # in the projection matrix is set to -1.0.
        # In pytorch3d we maintain a right handed coordinate system throughout
        # so the so the z sign is 1.0.
        z_sign = 1.0

        # pyre-fixme[58]: `/` is not supported for operand types `float` and `Tensor`.
        K[:, 0, 0] = 2.0 * znear / (max_x - min_x)
        # pyre-fixme[58]: `/` is not supported for operand types `float` and `Tensor`.
        K[:, 1, 1] = 2.0 * znear / (max_y - min_y)
        K[:, 0, 2] = (max_x + min_x) / (max_x - min_x)
        K[:, 1, 2] = (max_y + min_y) / (max_y - min_y)
        K[:, 3, 2] = z_sign * ones

        # NOTE: This maps the z coordinate from [0, 1] where z = 0 if the point
        # is at the near clipping plane and z = 1 when the point is at the far
        # clipping plane.
        K[:, 2, 2] = z_sign * zfar / (zfar - znear)
        K[:, 2, 3] = -(zfar * znear) / (zfar - znear) #**I am confused about the K[:,2,3], I think it should be -2*(zfar * znear) / (zfar - znear)** 

I am confused about the K[:,2,3], I think it should be -2(zfar znear) / (zfar - znear) . Could anyone help me?

[xhlbetter]

I am confused about the K[:, 0, 2] and K[:, 1, 2]，I think it goes something like this: K[:, 0, 2] = -(max_x + min_x) / (max_x - min_x) K[:, 1, 2] = -(max_y + min_y) / (max_y - min_y)