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Currently I am only using deceleration.

Here is how I do it

I need to cover Vector(x,y) unit distance to reach B from A.

I simply do -

rendering loop->

  1. position = A + Vector(x,y).scale(factor);
  2. Vector(x,y) = Vector(x,y) - Vector(x,y).scale(factor);

...factor = 10 for example So if I have to cover 100 units, I cover 10 then 9 then 8.1 and so on in every frame.

How do I simulate acceleration then deceleration here?

share|improve this question
Acceleration changes velocity in the same way velocity changes position. So, change your velocity over time to simulate acceleration. (BTW, "deceleration" isn't really a separate thing, it's just a short way of saying "acceleration in the direction opposite of travel") – Byte56 Jul 31 '13 at 16:39
Your have basically simulated drag coefficients, although you'd genereLly have a different "factor" for drag vs whatever your doing with position there, which some people struggle quite a bit with, so good job there. – Sean Middleditch Jul 31 '13 at 22:18

A simple way is to animate the object using a smoothstep curve:

lerpFactor = (curTime - startTime) / timeToReachTarget;
smoothstepFactor = lerpFactor * lerpFactor * (3.0 - 2.0 * lerpFactor);
position = lerp(startPos, targetPos, smoothstepFactor);

Here, I'm assuming a specified amount of time to reach the target (timeToReachTarget) and calculating how far the object should have moved by the current time (lerpFactor), then passing it through the smoothstep curve to make it accelerate and decelerate smoothly.

This isn't an especially physics-based approach, nor does it work well if the target point is moving, but it does create a smooth-looking motion.

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lerpFactor * lerpFactor * (3.0 - 2.0 * lerpFactor) is not the same that 3x^2 -2x^3, is there an error ? – tbruyelle Mar 24 '14 at 22:52
@kosokund They're the same; I just wrote it in a factored form that avoids redundant calculations. It's a common trick for polynomials. – Nathan Reed Mar 25 '14 at 1:20
ok thanks, I need to re-learn maths... – tbruyelle Mar 25 '14 at 12:27

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