Projectile trajectory / flight path - unity3d

Question

I'm trying to make a projectile which has movement behaviour shown as red in the diagram.
What I know and have now is two vectors; Start and End.
The end goal is to have some randomness of the arc at iteration and projectile velocity change in a lerp-fashion. I've done linear movement generations before, but nothing like this.
If my question feels like asking you to do my work for me (My usual fear of asking questions as a novice coder) could I have some tips and hints on what methods/commands I should look into? The language is C# and Unity version is 5.6
EDIT # 1
After getting some head-direction I could achieve something closer to the end-goal function of this.
Blue linear line is just representation of distance and angle between A(initiation point) and B(target). The red arc is the trajectory I'm willing to make my projectile to move as.
Fortunately, I figured what I wanted my path to guide the projectile to follow was a cubic bezier and got the result in editor shown in the diagram above with A, B, modA, and modB. There are just a few more things I need to get working on actually mounting the projectile to follow this path and control its velocity and etc. Following are more questions which I couldn't get through today.
First, the general condition is A is fixed and B is not. In order to maintain the generally desired flight path, I figured I need another virtual line lineB(from modA to modB) to sync lineA's angle and distance so when B(the target) is moving around in all directions the arc is not too extremely skewed, but in my attempts today either I got the wrong angle from lineA or something modA just orbited around A and the numbers were weird like angle changing in straight line movement of B from A.
Second is to have some random-but-similar variety of the red arc after the first projectile fires and to the next. I'm guessing this would be somewhat easier when I get past the first one since it's just matter of controlling lineB.
Edit # 2
All the functions asked above are resolved: A path is generated from A to B with arc made with modA and modB as well as the randomness of modA and modB at each iteration as well as modA and modB adjusting according to B's position in real time.
Now All that's left is to actually make the projectile follow the path and control its velocity till reaching B. Below is the code generating the arc-path. How should I approach this?
public Transform[] controlPoints = new Transform[4];
public LineRenderer lineRenderer;
private int curveCount = 0;
private int SEGMENT_COUNT = 50;
private void DrawCurve()
{
for (int j = 0; j < curveCount; j++)
{
for (int i = 1; i <= SEGMENT_COUNT; i++)
{
float t = i / (float)SEGMENT_COUNT;
int nodeIndex = j * 3;
Vector3 pixel = CalculateCubicBezierPoint(
t,
controlPoints[nodeIndex].position,
controlPoints[nodeIndex + 1].position,
controlPoints[nodeIndex + 2].position,
controlPoints[nodeIndex + 3].position);
lineRenderer.positionCount = (((j * SEGMENT_COUNT) + i));
lineRenderer.SetPosition((j * SEGMENT_COUNT) + (i - 1), pixel);
}
}
}
private Vector3 CalculateCubicBezierPoint(float t, Vector3 start, Vector3 modA, Vector3 modB, Vector3 end)
{
float u = 1 - t;
float t2 = Mathf.Pow(t, 2);
float u2 = Mathf.Pow(u, 2);
float t3 = Mathf.Pow(t, 3);
float u3 = Mathf.Pow(u, 3);
Vector3 p = u3 * start;
p += 3 * u2 * t * modA;
p += 3 * u * t2 * modB;
p += t3 * end;
return p;
}

Answer 1

You should use AnimationCurve.
you can edit the "graphic curve" in the inspector (public variable AnimationCurve) then use this srcipt to move object along the path.
using UnityEngine;
using System.Collections;
public class AnimationPath : MonoBehaviour
{
public AnimationCurve XCurve;
public float TotalTravelTime = 5.0f;
public float TravelSpeed = 50.0f;
public float XRange = 10.0f;
// Use this for initialization
void Start ()
{
StartCoroutine("Travel");
}
IEnumerator Travel()
{
float ElapsedTime = 0.0f;
while(ElapsedTime < TotalTravelTime)
{
float XPos = XCurve.Evaluate(ElapsedTime/TotalTravelTime) * XRange;
transform.position = new Vector3(XPos, transform.position.y, transform.position.z + TravelSpeed * -Time.deltaTime);
yield return null;
ElapsedTime += Time.deltaTime;
}
}
}
I hope this can help you.