Sine movement in rotated object?

[morius]

Hello everyone. Basically, I want to do something like this:

I know it’s already been asked, specifically in this question:

sine movement at any angle

But the answer (which is “use an animation”) is not what I want to do. I want to do this using Mathematics.

I can easily move an object in a normal sine wave, and a quick “hack” for me to move it in a rotated sine wave was to put the object inside another parent object which was already rotated and then just move its localPosition.

However, I don’t want to do that.

Basically, I have the angle of rotation (and the aiming vector), I’m assuming there’s got to be a way to modify the normal formula for moving the position along a sine wave based on one of these two parameters?

If someone can help me out, I’d really appreciate it!

[Eno-Khaon]

Hmm… this shouldn’t be too bad, really. Have the projectiles take note of where they’re created and their intended direction, then your sine wave can come from the distance the projectile has traveled in that direction, or the time it’s existed.

For a quick idea:

// C#

// Assuming this is a 2D presentation, like the example gif file...
public Vector2 startPosition;
public Vector2 direction;
public float speed;

private float time; // and/or direction
private Vector2 crossDirection; // More important for a 3D approach, but still a good point of reference

void Start()
{
	time = 0.0f;
	direction = direction.normalized;
	crossDirection = new Vector2(direction.y, -direction.x); // A quick right angle for 2D
	startPosition = transform.position;
}

void Update()
{
	transform.position = startPosition + (direction * speed * time) + (crossDirection * Mathf.Sin(time));
	time += Time.deltaTime;
}

That should cover pretty much all the basic concepts. There are many ways to handle it, but the most uniform approaches need the most structure for consistent results.

Edit: Most importantly, I suppose, the key element is your defined direction and it’s crossing direction. Separate those elements out and you can have your distance traveled on a straight line while the perpendicular one defines your sine wave.