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randomluadirection

Random direction en 2D lua

I want to create a random direction for my sprite, in Lua 2D.

So, i've tried that :

Sprite.x = Sprite.x + vx
Sprite.y = Sprite.y + vy

Sprite.vx = math.random(-1,1)
Sprite.vy = math.random(-1,1)

So, i managed to create a random direction, but my problem is the speed of the sprite, is directly linked to the number of direction. For example if i want the speed to be 1, it can only have 4 direction. I made a sprite with a lot more, by setting the random speed between -3 and 3, but then it's faster than what i want.

What should i do?

I've seen a few posts talking about random direction, but the description wasn't about lua and i couldn't really understand it..

Thanks!

Solution

  • If I am understanding the problem correctly, you want to choose random directions for the velocity, but you don't want the speed to change. To do this you can choose random velocity components for the x- and y-directions, and then normalize this to a unit vector by dividing each component by the magnitude of the vector.

    Also, math.random(-1, 1) will only give value of -1, 0, or 1. If you want more variety in the directions, use math.random() to get floating point values in the range [0, 1). You can randomly choose to make the components negative to get a full spectrum of directions.

    Here is a little function that returns a pair of vx and vy velocity components:

    function rand_v_dir ()

   vx = math.random()
   vy = math.random()

   norm = math.sqrt(vx * vx + vy * vy)
   vx = vx / norm
   vy = vy / norm

   if math.random(0, 1) == 0 then
      vx = -vx
   end

   if math.random(0, 1) == 0 then
      vy = -vy
   end

   return vx, vy
end

    Here are ten random velocity vectors generated by the above function:

    > for i = 1, 10 do
vx, vy = rand_v_dir()
print("Velocity: ", vx, vy)
print("Speed: ", math.sqrt(vx * vx + vy * vy))
end

Velocity:   -0.70784982398251   0.70636295676368
Speed:  1.0
Velocity:   -0.28169296961382   -0.95950459658625
Speed:  1.0
Velocity:   0.71839382297246    -0.69563662577168
Speed:  1.0
Velocity:   0.29007205509751    0.9570048081653
Speed:  1.0
Velocity:   -0.40540707321421   0.91413626171807
Speed:  1.0
Velocity:   -0.7236198731718    0.69019872439091
Speed:  1.0
Velocity:   0.31888322750977    0.94779401096069
Speed:  1.0
Velocity:   -0.64427423170525   0.76479455696325
Speed:  1.0
Velocity:   -0.66481241135881   0.74701034644996
Speed:  1.0
Velocity:   -0.65843036923729   0.75264164704463
Speed:  1.0

    We can do better than this, though. This approach gives directions that are biased towards the corners, as pointed out by @JoelCornett and @nobody in the comments. One improvement would be to select a random angle between 0 and 2π, and to take the velocity vector to be a unit vector. Then the cosine of the angle will be the velocity component in the x-direction, and the sine of the angle will be the component in the y-direction (measuring the angle with respect to the positive x-axis).

    This approach also has the benefit of being simpler to code:

    function rand_polar_dir ()

   dir = 2 * math.pi * (math.random())

   vx = math.cos(dir)
   vy = math.sin(dir)

   return vx, vy
end

    Here are ten random velocity vectors generated with the second approach:

    > for i = 1, 10 do
vx, vy = rand_polar_dir()
print("Velocity: ", vx, vy)
print("Speed: ", math.sqrt(vx * vx + vy * vy))
end
Velocity:   0.093304068605003   -0.99563766038743
Speed:  1.0
Velocity:   -0.31453683190827   -0.9492452693446
Speed:  1.0
Velocity:   0.72403297094833    0.68976536371416
Speed:  1.0
Velocity:   -0.39261186353618   -0.91970425931962
Speed:  1.0
Velocity:   -0.74523744965918   0.66679917788303
Speed:  1.0
Velocity:   0.15192428057379    -0.98839213522374
Speed:  1.0
Velocity:   0.93666276755405    -0.35023257969239
Speed:  1.0
Velocity:   0.86478573695856    -0.50214104507902
Speed:  1.0
Velocity:   0.64665884247741    -0.7627793530542
Speed:  1.0
Velocity:   0.2877390096936 0.95770886092828
Speed:  1.0

    For both of the above approaches, the magnitude of the velocity vector is 1. If you want to double the speed, just multiply the random vector by 2.