Calculating position of projected object in reflection

For a puzzle game I’m working on, I need to track the position of the reflection of an object on a plane. I have a window in which the reflection of the moon is visible, and I would like to find the world space coordinates of the moon’s projection on the reflective plane. My scene setup:

  • Window: an upright plane with a renderer that receives reflection probe information (Standard Shader)
  • Camera: perspective camera facing the window
  • Moon: a sphere behind the camera, facing the window
  • Reflection probe: realtime, refreshes every frame, at same position as camera

What I’ve been trying to do so far is to get the angle between the reflection vector and the camera. This gives me a rough indication of whether the moon is visible, but not a precise position which is what I need.

public Transform window;
public Transform moon;

// Used in Update
float moonWindowAngle()
{
	Vector3 reflectionVec = Vector3.Reflect(window.position - moon.position, window.forward);
	Vector3 cameraVec = Camera.main.transform.position - window.position;
	float angle = Vector3.Angle(reflectionVec, cameraVec);
	return angle;
}

I’m sure I need to somehow take into account the projection system (box/dome) and compare against a plane and not a single point, but I have no idea how to do this. Anything to set me on the right track greatly appreciated!

It requires a some vector math but nothing too intense:

public Transform window;
public Transform moon;
public Transform cam;

Vector3? moonInWindowPos() {
	// Vector perpendicular to window, facing outward (change if necessary)
	Vector3 planeNormal = -window.forward;

	// Project moon position into plane the window lies in
	Vector3 projectedPos = window.position + Vector3.ProjectOnPlane(moon.position, planeNormal);

	// Subtract moon position from projection, to get the point of the moon "inside" the reflection
	Vector3 insideReflectionPos = projectedPos - moon.position;

	// Create ray from camera to "inside" point (it goes through the reflection point)
	Ray ray = new Ray(cam.position, (insideReflectionPos - cam.position).normalized);

	// Do ray-plane intersection test to see where the ray hits the plane
	float rayDist;
	if (new Plane(planeNormal, window.position).Raycast(ray, out rayDist)) {
		// The point along the ray that intersects the plane is the reflection position
		return ray.GetPoint(rayDist);
	} else {
		// If the intersection test fails, the camera is behind the window or something, and the point is undefined
		return null;
	}
}

Note that you may also want to check if the point is actually visible to the camera.