改变正弦函数的相位

Question

I need some help with mathematics in my Unity game. Here is the concept: Ball moves up and down using sine function (blue line). In any moment of time player may want to press space bar and change direction of ball according to red line. As example, I've chosen pi/4.

• The ball must save it's position on y axis
• it must invert it's vertical motion.

So the change should be smooth, I think, with no unnatural jumps.

Plot:

Here is my class:

public class GoForward : MonoBehaviour
{
    public float speed = 0.1f; // speed of forward motion
    public float amplitude = 5f; // strength of vertical motion
    public float frequency = 5f; // width of spikes of vertical motion

    // Update is called once per frame
    void Update ()
    {
        float phase = 0f; // phase displacement

        if (Input.GetKeyDown (KeyCode.Space))
        {
            // find phase displacement here
        }

        // apply new position to the ball
        float xpos = transform.position.x + speed * Time.deltaTime;
        float ypos = amplitude * Mathf.Sin (frequency * Time.time + phase);
        transform.position = new Vector3 (xpos, ypos, transform.position.z);
    }
}

Of course, I think solution is simpliest, but my mind can't concentrate. So I need your help, guys.

I need to find phase displacement in any moment of time, so that all my conditions must hold.

Thanks!

Solution found. Thank all of you a lot for help!

Answer 1

For a given time Time.time of the first half phase, the distance to the sine maximum is

dist = Pi/2 - frequency * Time.time

You need to offset the curve by twice the distance (up the hill, then down the same amount). So you need:

if (Input.GetKeyDown (KeyCode.Space))
{
    phase = Pi - 2 * frequency * Time.time - oldPhase;
}

This also works for the second half phase.