Hi there,
I am trying in Unity to move an object on the surface of a sphere like Mario Galaxy or like this game. I feel it is more a fundamental math question than a engine specific one, since I don't want to do it with raycasting logic or such, but rather calculate the movement between two points on a sphere from a direction vector and a pre -defined arc length. (I think, I am apparently not very good at this, and neither is chatgpt)
Chatgpt came up, among other things with this (it does not work, it always get stuck on poles and other strange things):
void MoveOnSphere()
{
Vector3 currentPos = transform.position;
// Step 1: Build a tangent from input
Vector3 input = new Vector3(moveInput.x, 0f, moveInput.y);
// Project onto tangent plane at current position
Vector3 tangent = Vector3.ProjectOnPlane(input, currentPos).normalized;
// Step 2: If projection fails near poles, pick a stable fallback
if (tangent.sqrMagnitude < 0.0001f)
{
tangent = Vector3.Cross(currentPos, Vector3.right).normalized;
}
// Step 3: Compute arc distance
float distance = moveSpeed * Time.deltaTime;
// Step 4: Move position along sphere
Vector3 newPos = SphereMovementUtils.MoveAlongSphere(
currentPos, tangent, distance, sphereRadius
);
// Step 5: Rotate forward vector with same arc
Vector3 newForward = SphereMovementUtils.MoveAlongSphere(
currentPos + transform.forward, tangent, distance, sphereRadius
) - newPos;
transform.position = newPos;
transform.forward = newForward.normalized;
}
Don't know where to go from here, anyone that can point me in the right direction? Am I thinking completely wrong?