Rotate camera around object and let it centered

Hi,

I have a scene where I have a game board (just like a chess board but with any possible Width x Height). My camera is child of a camera target empty object because I want to be able to move the camera completely independently the flipping angle I'm giving the camera around the local X axis (just like someone with a selfie stick looking up or down). The problem I have is when I'm no longer in top view (Flipping angle == 0 degree), the board is obviously no longer centered in the screen (because of the perspective). How can I manually find the middle point of the board (with the perspective taken into account) as well as finding the distance the camera should be from that middle point to see the complete board with some kind of padding ?

I know the formula to know how far the camera needs to be to view a specific frustum size (width and height), so to find the middle point or the board in perspective, it's probably just a matter of projecting the board to a plane parallel to the frustum, measure the corresponding trapezoid, divide in half, took the middle point and ray casting back to a plane with Vector3.up as the normal.

I know I could use Camera methods like WorldToScreenPoint to project the corners of my board on the frustum and then adjust accordingly but I would like to calculate it directly and have some functions I could use without moving the real camera (in order to move it smoothly with lerp functions). The 2 methods I'm trying to write are

Vector3 FindMiddleBoard(float cameraFlippingAnglesAroundX, int boardWidth, int boardHeight) float FindFrustumHeightNeededToDisplayEntireBoard(int boardWidth, int boardHeight)

It's probably easier than I think, but I'm lost in all those maths.

F.Y.I. the method I'm using to get the frustum size needed to display my board is:

float FindCameraDistanceNeeded(int boardWidth, int boardHeight, int padding, float cameraAspect, float cameraFieldOfView)

{

float result = 0.0f;

var widthFromFrustumHeight = (boardWidth + padding) / cameraAspect; var maxFrustumHeight = Mathf.Max(widthFromFrustumHeight, (boardHeight + padding));

result = (maxFrustumHeight 0.5f) / Mathf.Tan (cameraFieldOfView 0.5f * Mathf.Deg2Rad);

return (result);

}

Thanks