计算相机位置以在固定相机旋转的情况下查看所有对象

Question

for my 3d board game I am trying to build a "see the whole board" feature which should move the camera to a point where it is able to see the whole board, but without changing the rotation of the camera.

For now, I tried to get the minimum and maximum points which include all objects of interest and use these two points to mock a sphere around them (visualized it by actually placing a sphere there programmatically), so I am ending up like this right now: Visualization of the sphere

My current problem is, that I am not able to build up a math formula to actually calculate the position of the camera to have the whole sphere in view (remember: rotation has to be unchanged).

This is my code so far for finding the smalles and biggest point and visualizing it by building the sphere:

        // Find smallest and biggest point of all objects
        var p1 = new Vector3(float.PositiveInfinity, float.PositiveInfinity, float.PositiveInfinity);
        var p2 = new Vector3(float.NegativeInfinity, float.NegativeInfinity, float.NegativeInfinity);
 
        foreach (var gameObject in gameObjects)
        {
            foreach (var vertice in gameObject.GetComponent<MeshFilter>().sharedMesh.vertices)
            {
                var p = vertice + gameObject.transform.position;
 
                p1.x = Math.Min(p1.x, p.x);
                p1.y = Math.Min(p1.y, p.y);
                p1.z = Math.Min(p1.z, p.z);
 
                p2.x = Math.Max(p2.x, p.x);
                p2.y = Math.Max(p2.y, p.y);
                p2.z = Math.Max(p2.z, p.z);
            }
        }
 
        // Center of all objects
        var average = (p1 + p2) / 2;
 
        // Visualize by creating a sphere
        var diameter = Vector3.Distance(p1, p2);
        var sphere = GameObject.CreatePrimitive(PrimitiveType.Sphere);
        sphere.transform.position = average;
        sphere.transform.localScale = new Vector3(diameter, diameter, diameter);

Can you help me with the formula to actually calculate the position of my camera?

Regards

Answer 1

The easiest thing to do would be to move the camera back, with or without code. just use the game view to check whether the sphere is in view. if you got that point then you could leave it there or use code to do this:

Vector3 camPos;
//define the camera position in the inspector!
private void Start()
{
    transform.position = camPos;
}

Answer 2

For each side of the view frustrum, find the parallel plane that is as close to the scene as possible. Each of these planes should just touch one of the objects in the scene.

Each pair of opposite planes will intersect along a line. Find these two lines. They will be perpendicular.

The camera should be located on whichever line is furthest away from the scene, situated so that the other line passes through the center of the field of view.

In the resulting view, one pair of opposite sides will just touch some objects in the scene, because the corresponding sides of the view frustrum will just touch those objects. In the other dimension, the objects will be centered.