How to draw a line through a camera defined by [location, orientation] from extrinsicsToCameraPose?

I want to visualize the FOV of a camera on a matlab plot. I have the location and orientation of the camera from the extrinsicsToCameraPose function in the CV toolbox. Now, I am trying to draw a line depicting the principal axis of the Camera. How would I go about drawing that line in 3D?

I have the following code, currently. But, I know that I am not using the orientation correctly to calculate the Y and Z points on the line.

if (isVisualize)
    cam = plotCamera('Location',location,'Orientation',orientation,'Size',25);
%     cam = plotCamera('Location',location,'Orientation',orientation);

      grid on
      axis equal
      axis manual

      xlim([-1600,0]);
      ylim([-600,200]);
      zlim([0,200]);

      hold on
      plot3(0,0,0,'g*');

      %According to 3D line equation 
      clX = linspace(-1400,200);
      clY = (((clX - location(1))/orientation(1)) * (orientation(2))) + location(2);
      clZ = (((clX - location(1))/orientation(1)) * (orientation(3))) + location(3);

      line(clX, clY, clZ)

      xlabel('X (mm)');
      ylabel('Y (mm)');
      zlabel('Z (mm)');
  end

I believe I am missing something trivial here. I would like the lines to start at the camera and end at the plane z=0.

Eventually, I also want to draw lines coming out of the corners of the Camera to visualize the Vertical FOV and Horizontal FOV. If there's an easier way to do this, I'd really appreciate it.

The following is the current output. The green * signifies the origin. The line is obviously pointing in the wrong direction.

The MATLAB figure is attached too.

EDIT 1:

The following are the location and orientation.

>> location

location =

     1.0e+03 *

     -1.3975   -0.3178    0.0850

>> orientation

orientation =

     -0.0103   -0.9999    0.0112
     -0.2542   -0.0083   -0.9671
      0.9671   -0.0128   -0.2541

The orientation and location are computed using the following function from the Computer Vision Toolbox.

camMatrix = cameraMatrix(cameraParams,rotationMatrix,translationVector);
[orientation,location] = extrinsicsToCameraPose(rotationMatrix,translationVector);

[Joshua]

Amit,

It looks like you equation for calculating the line's coordinates just has a small mistake in it. However, we need you to post what orientation and location are to figure that out. Thanks.

[Amit Agarwal]

I have updated the question to include the information you asked for. Does this help to figure out the small mistake?

I think maybe that I am drawing the line perpendicular to the camera. Maybe this relates to something to do with the default orientation of the camera pointing towards negative-z?

[Joshua]

Amit,

Yes thank you it is helpful to see. I am not super familiar with the line equation you are using, but a possible mistake could be your indexing of the orientation matrix. Using single numbers to index a two dimansional matrix orders the columns first from top to bottom, and then moves right across each column. So here are the values you are getting in you line equation.

orientation(1)=-0.0103
orientation(2)=-0.2542
orientation(3)=0.9671

Are these the locations you were intending to access? If you happen to have the equation in variable form that would be great.