Align Relative Portal Camera Position

Question

I've been having a bit of trouble with this small piece of code. To set my relative PortalCam position, I first take the distance and angle from the Portal and Player Cam. Then apply the distance and rotation to my OtherPortal to get the PortalCams position.

Desmos link to all the maths

float newX, newY, newZ;
float d;    // Distance between Portal and PlayerCam
float phi;  // Angle between Portal and PortalCam
            // Angle between Portals
float delta = Quaternion.Angle(portal.rotation, otherPortal.rotation);
d = Mathf.Sqrt( (playerCam.position.x - portal.position.x)^2 +
                (playerCam.position.z - portal.position.z)^2 );
if(playerCam.position.x >= portal.position.x)
    d = -d;
phi = Mathf.Atan( (playerCam.position.z - portal.position.z)
                / (playerCam.position.x - portal.position.x) );

newX = otherPortal.position.x - d*Mathf.Sin(phi - delta);
newY = playerCam.position.y + otherPortal.position.y - portal.position.y;
newZ = otherPortal.position.z + d*Mathf.Cos(phi - delta);
transform.position = new Vector3(newX, newY, newZ);

My problem is that, while this works perfectly when the portals are at 90degrees to each other. The code seems to fail when the portals are in-line.
Is there a mistake in my math? In my code? How can I best fix this bug?

Answer 1

Myself, I'd skip the manual math and use Unity's built-in transformation functions for this.

const Quaternion FLIP = Quaternion.Euler(0, 180, 0); // (0, 1, 0, 0)

void CrossPortals(Transform subject, Transform entrance, Transform exit) {
    // Map subject position into "entrance portal space" coordinates.
    Vector3 entrancePosition = entrance.InverseTransformPoint(subject.position);

    // Here I assume both portals face "outwards", 
    // so "into" the entrance portal needs to be rotated
    // to map to "out" of the exit portal.
    Vector3 exitPosition = FLIP * entrancePosition;
    
    subject.position = exit.TransformPoint(exitPosition);

    // Order matters here (read from the end, back toward the beginning).
    Quaternion relativeRotation =
            // 3. Apply exit portal's orientation.
            exit.rotation 
            // 2. Account for portals facing opposite directions.
            * FLIP
            // 1. Express orientation in entrance coordinates.
            * Quaternion.Inverse(entrance.rotation);

    subject.rotation = relativeRotation * subject.rotation;
}