I got the intercept form working in code. It’s pretty interesting to see the curve working in real-time and how the root’s Y value doesn’t affect it.
Something I noticed while paying with the values is that setting a max height or modifying the value of ‘a’ directly have the same results, this can be used as optimization, since the following code:
public float CurveIntercept(float x, Vector3 root1, Vector3 root2, float highestPoint)
{
float midXPoint = (root1.x + root2.x) / 2;
float a = highestPoint / ((midXPoint - root1.x) * (midXPoint - root2.x));
return a * ((x - root1.x) * (x - root2.x));
}
Ends up with the exact same result as this one
public float CurveIntercept(float x, float a, Vector3 root1, Vector3 root2)
{
return a * ((x - root1.x) * (x - root2.x));
}
The main differences that I noticed are:
- ‘a’ can be harder to manipulate because of how small the number has to be.
- A max height is easier to understand.
- Setting ‘a’ requires far less calculations.
- It’s way harder to set perfect maximum height by directly modifying ‘a’.
- To make a curve that goes down, ‘a’ needs to be positive, while a max height needs to be negative.
I think it all comes down to optimization vs not having to teach math to your designer 