zooming - Move camera to fit 3D scene

Question

I'm looking for an algorithm to fit a bounding box inside a viewport (in my case a DirectX scene). I know about algorithms for centering a bounding sphere in a orthographic camera but would need the same for a bounding box and a perspective camera. I can not just change the FOV because this app has FOV as a user editable variable, so it must move the camera.

I have most of the data:

• I have the up-vector for the camera
• I have the center point of the bounding box
• I have the look-at vector (direction and distance) from the camera point to the box center
• I have projected the points on a plane perpendicular to the camera and retrieved the coefficients describing how much the max/min X and Y coords are within or outside the viewing plane.

Problems I have:

• Center of the bounding box isn't necessarily in the center of the viewport (that is, it's bounding rectangle after projection).
• Since the field of view "skew" the projection (see http://en.wikipedia.org/wiki/File:Perspective-foreshortening.svg) I cannot simply use the coefficients as a scale factor to move the camera because it will overshoot/undershoot the desired camera position

How do I find the camera position so that it fills the viewport as pixel perfect as possible (exception being if the aspect ratio is far from 1.0, it only needs to fill one of the screen axis)?

I've tried some other things:

• Using a bounding sphere and Tangent to find a scale factor to move the camera. This doesn't work well, because, it doesn't take into account the perspective projection, and secondly spheres are bad bounding volumes for my use because I have a lot of flat and long geometries.
• Iterating calls to the function to get a smaller and smaller error in the camera position. This has worked somewhat, but I can sometimes run into weird edge cases where the camera position overshoots too much and the error factor increases. Also, when doing this I didn't recenter the model based on the position of the bounding rectangle. I couldn't find a solid, robust way to do that reliably.

Help please!

Answer 1

There are many possible camera positions + orientations where the bounding box would fit inside the view frustum. But any procedure would select one specific camera position and orientation.

If you would consider bounding spheres, one solution could be to

• first change orientation to look at bounding sphere center
• then move back sufficiently (negative look direction) for bounding sphere to fit inside frustum

With bounding boxes you could consider an earlier step of first positioning the camera at perpendicular to the center of the largest (or smallest, whatever you prefer) cube face.

I have no experience with DirectX, but moving and changing the looking direction of the camera to center a certain point should be easy. The hard part is to do the math of deciding how far to move to view the object.

Math

If you know the bounding size s of the object in world coordinates (we are not interested in pixels or camera coordinates, since those are dependent on your distance) from the orientation of the camera, you can compute the required distance d of the camera to the bounding shape if you know the x and y Field-Of-View angle a of the perspective projection.

     frustum      ------            
            ------    *****          -  
       -----          *   *          |
   -===     ) FOV a   *bounding box  | BB size s
camera -----          *   *          |
            ------    *****          -
                  ------
  
  |-------------------|
        distance d

So, the math is tan(a/2) = (s/2) / d => d = (s/2) / tan(a/2) Which will give you the distance the camera should be placed from the closest bounding surface.