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Posted: **Wed Nov 03, 2021 11:49 pm**

Gunroar:Cannon() wrote: ↑Sat Oct 30, 2021 10:47 pm Though the sentence confuses me Does it find the origin of a line moving in a certain direction?

Let's say you want to find the point halfway between a and b.

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angl = direction(a.x, a.y, b.x, b.y)
dist = distance(a.x, a.y, b.x, b.y)
halfway.x, halfway.y = transposition(a.x, a.y, angl, dist/2)

transposition means "Move this point in this direction by this distance, and give me the new coordinates."

It tells you where you are going to be, if you start here and go this way that far.

Posted: **Thu Nov 04, 2021 9:23 am**

Xii wrote: ↑Wed Nov 03, 2021 11:49 pm
Gunroar:Cannon() wrote: ↑Sat Oct 30, 2021 10:47 pm Though the sentence confuses me Does it find the origin of a line moving in a certain direction?
Let's say you want to find the point halfway between a and b.

Over 9000 times faster:

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halfway.x, halfway.y = b.x-a.x, b.y-a.y

With normalization:

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local dx, dy = b.x-a.x,  b.y-a.y
local length = (dx*dx + dy*dy)^0.5
local nx, ny = dx/length, dy/length 
halfwayX, halfwayY = a.x + 0.5*length*nx, a.y + 0.5*length*ny

Posted: **Thu Nov 04, 2021 11:22 pm**

darkfrei wrote: ↑Thu Nov 04, 2021 9:23 am Over 9000 times faster:
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halfway.x, halfway.y = b.x-a.x, b.y-a.y

This gives you the difference (distance) on each axis. You cannot get a halfway without dividing by 2 somewhere. It'd be more like this:

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halfway.x, halfway.y = a.x + (b.x - a.x) / 2, a.y + (b.y - a.y) / 2

Anyway that's besides the point. There's always a better way to do any given thing. I was just illustrating how the function works.

Posted: **Sat Nov 06, 2021 6:27 am**

Oh, so that last one is the best option?

Posted: **Sat Nov 06, 2021 10:05 am**

The best option, for best clarity, is probably to lerp. Lerping is an operation that should be in every programmer's toolbox. Lerp is short for linear interpolation; you pass it the origin value and the destination value, and then a value between 0 (for which it returns the origin) and 1 (for which it returns the destination).

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function lerp(a, b, t)
  return a + (b - a) * t
end

Due to floating point rounding issues, however, it does not always return the destination when passing t = 1; in that case it's better to split it as follows:

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function lerp(a, b, t)
  return t < 0.5 and a + (b - a) * t or b + (a - b) * (1 - t)
end

Never use a formulation like a * (1 - t) + b * t because that's not monotonic, which causes serious issues in some circumstances; see https://math.stackexchange.com/question ... erpolation

Applied to the case at hand:

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halfway.x, halfway.y = lerp(a.x, b.x, 0.5), lerp(a.y, b.y, 0.5)

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