Smooth decelerate, interpolation?

Question

I have two points A and B. I want to perform a smooth deceleration from A stopping at B over time t. The only thing I managed to do so far was a lerp, which isn't right of course because it's unnatural. I also tried multiplying the velocity by some factor (0.9 or similar), but then I don't know how to choose the factor such that the end point B is reached (or as near to it as some epsilon value seems reasonable).

Does anyone have something relatively simple that I could use? I can read C++ and C# code.

Answer 1

Compute the ratio x in [0,1] of the current animation time and the animation duration t. Then use something like sqrtf(x) to decelerate. Compute the current position C = A + x * (B - A). You can make it decelerate more rapidly by using e.g. powf(x, f) with f = 1.0f / 3 or smaller.

Answer 2

I would use the "Arrive" behavior from Millington's book Artificial Intelligence for Games.

It's important to say that you need to constantly update positionB in order for it to work correctly.

float targetRadius = 0.1f;
float timeToTarget = 0.1f;
float maxSpeed = 10.0f;

Vector3 positionA;
Vector3 positionB;
Vector3 agentVelocity;

// calculation for slow radius given the initial
// distance between the two positions
Vector3 dist = positionB - positionA;
float slowRadius = dist.Length();

public Vector3 GetVelocity ()
{
    Vector3 velocity = new Vector3();
    Vector3 direction = positionB - positionA;
    float distance = direction.Lenght();
    float targetSpeed;
    if (distance < targetRadius)
        return velocity;
    if (distance > slowRadius)
        targetSpeed = maxSpeed;
    else
        targetSpeed = maxSpeed * distance / slowRadius;
    velocity = direction;
    velocity.Normalize();
    velocity *= targetSpeed;
    velocity -= agentVelocity;
    velocity /= timeToTarget;
    return velocity;
}