How to Fit Camera to Object

I am assuming you are using a perspective camera.

You can set the camera's position, field-of-view, or both.

The following calculation is exact for an object that is a cube, so think in terms of the object's bounding box, aligned to face the camera.

If the camera is centered and viewing the cube head-on, define

dist = distance from the camera to the _closest face_ of the cube

and

height = height of the cube.

If you set the camera field-of-view as follows

fov = 2 * Math.atan( height / ( 2 * dist ) ) * ( 180 / Math.PI ); // in degrees

then the cube height will match the visible height.

At this point, you can back the camera up a bit, or increase the field-of-view a bit.

If the field-of-view is fixed, then use the above equation to solve for the distance.

EDIT: If you want the cube width to match the visible width, let aspect be the aspect ratio of the canvas ( canvas width divided by canvas height ), and set the camera field-of-view like so

fov = 2 * Math.atan( ( width / aspect ) / ( 2 * dist ) ) * ( 180 / Math.PI ); // in degrees

three.js r.69

Based on WestLangleys answer here is how you calculate the distance with a fixed camera field-of-view:

dist = height / 2 / Math.tan(Math.PI * fov / 360);

To calculate how far away to place your camera to fit an object to the screen, you can use this formula (in Javascript):

// Convert camera fov degrees to radians
var fov = camera.fov * ( Math.PI / 180 ); 

// Calculate the camera distance
var distance = Math.abs( objectSize / Math.sin( fov / 2 ) );

Where objectSize is the height or width of the object. For cube/sphere objects you can use either the height or width. For a non-cube/non-sphere object, where length or width is greater, use var objectSize = Math.max( width, height ) to get the larger value.

Note that if your object position isn't at 0, 0, 0, you need to adjust your camera position to include the offset.

Here's a CodePen showing this in action. The relevant lines:

var fov = cameraFov * ( Math.PI / 180 );
var objectSize = 0.6 + ( 0.5 * Math.sin( Date.now() * 0.001 ) );

var cameraPosition = new THREE.Vector3(
    0,
    sphereMesh.position.y + Math.abs( objectSize / Math.sin( fov / 2 ) ),
    0
);

You can see that if you grab the window handle and resize it, the sphere still takes up 100% of the screen height. Additionally, the object is scaling up and down in a sine wave fashion (0.6 + ( 0.5 * Math.sin( Date.now() * 0.001 ) )), to show the camera position takes into account scale of the object.

From user151496's suggestion about using the aspect ratio, this seems to work, although I've only tested with a few different parameter sets.

var maxDim = Math.max(w, h);
var aspectRatio = w / h;        
var distance = maxDim/ 2 /  aspectRatio / Math.tan(Math.PI * fov / 360);

try this for OrbitControls

    let padding = 48;
    let w = Math.max(objectLength, objectWidth) + padding;
    let h = objectHeight + padding;

    let fovX = camera.fov * (aspectX / aspectY);
    let fovY = camera.fov;

    let distanceX = (w / 2) / Math.tan(Math.PI * fovX / 360) + (w / 2);
    let distanceY = (h / 2) / Math.tan(Math.PI * fovY / 360) + (w / 2);

    let distance = Math.max(distanceX, distanceY);

I had the same question but I expected the object(s) (represented by a Box3 as a whole) could rotate on my phone if the whole was wider than my screen so I could view it by zooming in as near as possible.

const objectSizes = bboxMap.getSize();
console.log('centerPoint', centerPoint, bboxMap, objectSizes, tileMap);

//setupIsometricOrthographicCamera(bboxMap);
//https://gamedev.stackexchange.com/questions/43588/how-to-rotate-camera-centered-around-the-cameras-position
//https://threejs.org/docs/#api/en/cameras/PerspectiveCamera
//https://stackoverflow.com/questions/14614252/how-to-fit-camera-to-object
//          Top
//      +--------+
// Left | Camera | Right
//      +--------+
//         Bottom
// canvas.height/2 / disance = tan(fov); canvas.width/2 / disance = tan(fovLR);
// => canvas.width / canvas.height = tan(fovLR)/tan(fov);
// => tan(fovLR) = tan(fov) * aspectRatio;
//If rotating the camera around z-axis in local space by 90 degrees.
//        Left
//        +---+
// Bottom |   | Top
//        |   |
//        +---+
//        Right
// => tan(fovLR) = tan(fov) / aspectRatio;
const padding = 0, fov = 50;
let aspectRatio = canvas.width / canvas.height;
let tanFOV = Math.tan(Math.PI * fov / 360);
let viewWidth = padding + objectSizes.x, viewHeight = padding + objectSizes.y;
//The distances are proportional to the view's with or height
let distanceH = viewWidth / 2 / (tanFOV * aspectRatio);
let distanceV = viewHeight / 2 / tanFOV;
const camera = this.camera = new THREE.PerspectiveCamera(fov, aspectRatio, 0.1, 10000); //VIEW_ANGLE, ASPECT, NEAR, FAR
if (aspectRatio > 1 != viewWidth > viewHeight) {
    console.log('screen is more narrow than the objects to be viewed');
    // viewWidth / canvas.width => viewHeight / canvas.width
    // viewHeight / canvas.height => viewWidth / canvas.height;
    distanceH *= viewHeight / viewWidth;
    distanceV *= viewWidth / viewHeight;
    camera.rotateZ(Math.PI / 2);
}
camera.position.z = Math.max(distanceH, distanceV) + bboxMap.max.z;
//camera.lookAt(tileMap.position);

I had tested two different aspect of Box3 on tow different orientations (landscape and portrait) using my phone, it worked well.

References

• Box3.getSize ( target : Vector3 ) : Vector3

  target — the result will be copied into this Vector3. Returns the width, height and depth of this box.

• Object3D.rotateZ ( rad : Float ) : this (PerspectiveCamera)

  rad - the angle to rotate in radians. Rotates the object around z axis in local space.

• Other answers