Moving platform algorithm

Scripting
1

Hi!

I’m running through the 2D tutorial made by Unity3D team. The forumula they use to move the platform is this:

var weight = Mathf.Cos(Time.time * speed * 2 * Mathf.PI) * 0.5 + 0.5;
transform.position = targetA.transform.position * weight + targetB.transform.position * (1-weight);

I understand the first line that get the “weight” or the oscillation, but can anyone tell me where the second formula comes from? Some vector math theorem or what?

2

The second formula is simple linear interpolation (usually referred to as LERP).

(Also, I think Unity may already have a LERP function for vectors…)

3

Thanks, but while reading about LERP at wikipedia I couldn’t find anything that would lead me to that forumula used in the tutorial mentionend.

Any more hints? I would love how to understand how this formula was deduced.

Edit: I understand that the new vector (transform.position) can be “build” from adding a fraction of vector A (targetA) and vector B (targetB). But I’m looking for why this fraction is weight and 1-weight

4

The Wikipedia article is simply presenting LERP in a different context (that of a graph).

Try this instead. The formula given there is (I’m going to change the variable names for convenience):

p = A + t(B - A)

This formula basically ‘starts at A’, and then adds some amount of the difference between A and B to yield a point somewhere between A and B (assuming ‘t’ is in the range [0, 1]).

Now, let’s re-arrange this formula:

p = A + t(B - A)
p = A + tB - tA
p = tB + A - tA
p = tB + (1 - t)A

And we have the formula shown in your code example.

Another way to think of it is this. When ‘t’ is 0, you can see that we get ‘all’ of A and ‘none’ of B. Conversely, when ‘t’ is 1, we get ‘all’ of B and ‘none’ of A. Values of ‘t’ between 0 and 1 give us (in a linear progression) ‘some’ of A and ‘some’ of B. As ‘t’ increases, we get more B and less A (again, in a linear progression).

Does that make more sense?

5

Yes and thanks a million! :slight_smile:

Edit: And thanks for guiding me to that wiki, didn’t know about it before.