Scale a sprite to the same size of a 3D object

[Zylann]

I have an object with a sphereCollider in my scene, and a 2D sprite on my GUI.
I managed to position the sprite right over the object, but I want the sprite to have the same width as the sphere in the scene.
I tried projecting the center and a point on the surface of the sphere to get an on-gui distance,
and then using it as localScale value, but it doesn't works at all (it's ridiculously small).
How can I achieve that?

Here is the code I'm currently using :

1.         private Vector3 SceneToUIPos(Vector3 scenePos)
2.         {
3.                 return uiCamera.ViewportToWorldPoint(
4.                         Camera.mainCamera.WorldToViewportPoint(scenePos));
5.         }
6.        
7.         private float RadiusOnUI(Transform obj)
8.         {
9.                 // Assumes the object has a scale of (1,1,1) and a sphere collider
10.                
11.                 float r = obj.collider.bounds.extents.x;
12.                 Vector3 objPos = transform.position + obj.collider.bounds.center;
13.  
14.                 // Take center and edge positions to compute the on-UI-space radius
15.                 Vector3 a = SceneToUIPos(objPos);
16.                 objPos += r * Camera.mainCamera.transform.right;
17.                 Vector3 b = SceneToUIPos(objPos);
18.                 return Vector3.Distance(a, b);
19.         }
20.        
21.         ...
22.        
23.         float diameter = RadiusOnUI(catchObj);
24.         // HelperCircle is a UISprite with a 256x256 texture
25.         _helperCircle.transform.localScale = new Vector3(diameter, diameter, 1);

Note: I know there is a little bias due to the perspective projection (a sphere is not really a perfect circle when projected), but I only need an average accuracy.

[ArenMook]

Lots of math.

Calculate the bounds of your object, calculate the on screen rect of those bounds, then resize the widget to match.