Can't center a 3D object on screen

Question

Currently, I'm taking each corner of my object's bounding box and converting it to Normalized Device Coordinates (NDC) and I keep track of the maximum and minimum NDC. I then calculate the middle of the NDC, find it in the world and have my camera look at it.

<Determine max and minimum NDCs>

centerX = (maxX + minX) / 2;
centerY = (maxY + minY) / 2;

point.set(centerX, centerY, 0);
projector.unprojectVector(point, camera);
direction = point.sub(camera.position).normalize();
point = camera.position.clone().add(direction.multiplyScalar(distance));

camera.lookAt(point);
camera.updateMatrixWorld();

This is an approximate method correct? I have seen it suggested in a few places. I ask because every time I center my object the min and max NDCs should be equal when their are calculated again (before any other change is made) but they are not. I get close but not equal numbers (ignoring the negative sign) and as I step closer and closer the 'error' between the numbers grows bigger and bigger. IE the error for the first few centers are: 0.0022566539084770687, 0.00541687811360958, 0.011035676399427596, 0.025670088917273515, 0.06396864345885889, and so on.

Is there a step I'm missing that would cause this?

I'm using this code as part of a while loop to maximize and center the object on screen. (I'm programing it so that the user can enter a heading an elevation and the camera will be positioned so that it's viewing the object at that heading and elevation. After a few weeks I've determined that (for now) it's easier to do it this way.)

However, this seems to start falling apart the closer I move the camera to my object. For example, after a few iterations my max X NDC is 0.9989318709122867 and my min X NDC is -0.9552042384799428. When I look at the calculated point though, I look too far right and on my next iteration my max X NDC is 0.9420058636660581 and my min X NDC is 1.0128126740876888.

Answer 1

Your approach to this problem is incorrect. Rather than thinking about this in terms of screen coordinates, think about it terms of the scene.

You need to work out how much the camera needs to move so that a ray from it hits the centre of the object. Imagine you are standing in a field and opposite you are two people Alex and Burt, Burt is standing 2 meters to the right of Alex. You are currently looking directly at Alex but want to look at Burt without turning. If you know the distance and direction between them, 2 meters and to the right. You merely need to move that distance and direction, i.e. right and 2 meters.

In a mathematical context you need to do the following:

Get the centre of the object you are focusing on in 3d space, and then project a plane parallel to your camera, i.e. a tangent to the direction the camera is facing, which sits on that point.

Next from your camera raycast to the plane in the direction the camera is facing, the resultant difference between the centre point of the object and the point you hit the plane from the camera is the amount you need to move the camera. This should work irrespective of the direction or position of the camera and object.

Answer 2

You are playing the what came first problem. The chicken or the egg. Every time you change the camera attributes you are effectively changing where your object is projected in NDC space. So even though you think you are getting close, you will never get there.

Look at the problem from a different angle. Place your camera somewhere and try to make it as canonical as possible (ie give it a 1 aspect ratio) and place your object around the cameras z-axis. Is this not possible?