Getting direction from point a to point b

[BICstudios]

Hello,

I encountered a problem while making a space shooter game. I need the spaceship to point to the mouse. As always, I searched for the solution on the internet. I found some from this forum, but none are working for me. It's just I'm the one copying it wrong or it's outdated. I would like the solution to be this function.

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function getDir(x1, y1, x2, y2):
	-- Codes here

Hope you can help me, thanks for reading.

[veethree]

What you’re looking for is the angle between two points.

For that you need the atan2 function.

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angle = math.atan2(y2 - y1,  x2 - x1)

[Xii]

The three most commonly needed functions for me.

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-- returns the direction from point x1,y1 to x2,y2 (in radians)
function direction(x1, y1, x2, y2)
	return math.atan2(y2-y1, x2-x1)
end

-- returns the distance between points x1,y1 and x2,y2
function distance(x1, y1, x2, y2)
	return math.sqrt(((x2-x1)^2)+((y2-y1)^2))
end

-- returns the point located at x,y moved in direction by distance
function transposition(x, y, direction, distance)
	return distance*math.cos(direction)+x, distance*math.sin(direction)+y
end

[Gunroar:Cannon()]

What does transposition do?

[darkfrei]

Also you are need the normalization:

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-- player position:
local playerX, playerY = 100,200

-- mouse position:
local mouseX, mouseY = 315, 419

local dx = mouseX-playerX -- delta X
local dy = mouseY-playerY -- delta Y
local distance = (dx*dx+dy*dy)^0.5 -- the distance between player and mouse position
local nx, ny = dx/distance, dy/distance -- normal vector from player to mouse

--so, if your bullet has velocity
bulletV = 200
-- then the update is just
bulletX = bulletX + dt*bulletV*nx
bulletY = bulletY + dt*bulletV*ny
-- and it flies exactly between them with exactly this velocity

[pgimeno]

It's unfortunately too frequent to see people normalize by calculating the sine and cosine of the arctangent.

[GVovkiv]

It's unfortunately too frequent to see people normalize by calculating the sine and cosine of the arctangent.

*grumbling intensifies*

[Gunroar:Cannon()]

Because I searched it on Google and got AI related stuff.

Edit: Oh, I see.

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-- returns the point located at x,y moved in direction by distance

I browse in mobile so I'm sorry, it's easy for me to miss small details like this.

Though the sentence confuses me Does it find the origin of a line moving in a certain direction?

[darkfrei]

Does it find the origin of a line moving in a certain direction?

You can notice the abs(dx) and abs(dy) and if it's more than one step before, then it goes away from the target. Remove the particle or do what you need.

[pgimeno]

If the direction is a unit vector instead of an angle, as it should, transposition can be as simple as:

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function transposition(x, y, direction_x, direction_y, distance)
  return distance*direction_x+x, distance*direction_y+y
end

In fact, it's intuitive enough for not needing a function for it, you can just place the formulas inline where needed. IMO the function would be counter-productive clarity wise.

You would find direction by normalizing the difference between target and origin:

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function normalize(x, y)
  local length = distance(0, 0, x, y)
  if length == 0 then
    return 1, 0
  end
  length = 1 / length
  return x * length, y * length
end

function direction(x1, y1, x2, y2)
  return normalize(x2 - x1, y2 - y1)
end

That saves a sine and cosine every time you need the direction vector.

You only need atan2 because unfortunately, Löve doesn't accept a direction vector as input for the rotation argument in love.draw & co.