Formula to make the ends of the arms of a spiral galaxy less dense

i wan't to make a spiral galaxy in Unity 3D using C# ( i use a derived logarithmic spiral ) but i wan't to set the end of the arms less dens than the middle.

I want that :

In my game i have this result actually :

Code (CSharp):

1. public int numArms = 5;
2. public float armOffsetMax = 0.5f;
3. public float rotationFactor = 5;
4. public float randomOffsetXY = 0.02f;
5. public float percentStarInCentre = 5;
6.  
7.  
8.  
9. for (int i = 0; i < PixelMath.instanceStarCount; i++)
10.         {
11.             if(type == GalaxyTypes.Spiral)
12.             {
13.                 float distance = Random.value;
14.                 distance = Mathf.Pow (distance, PixelMath.percentStarInCentre / 100) ;
15.  
16.  
17.                 // Choose an angle between 0 and 2 * PI.
18.                 float angle = Random.value * 2 * Mathf.PI;
19.                 float armOffset = Random.value * PixelMath.armsOffetSetMax;
20.  
21.                 armOffset = armOffset - PixelMath.armsOffetSetMax / 2;
22.                 armOffset = armOffset * (1 / distance);
23.  
24.                 float squaredArmOffset = Mathf.Pow (armOffset, 2);
25.  
26.                 if (armOffset < 0)
27.                     squaredArmOffset = squaredArmOffset * -1;
28.                 armOffset = squaredArmOffset;
29.  
30.                 float rotation = distance * PixelMath.rotationFactor;
31.  
32.                 // Compute the angle of the arms.
33.                 angle = (int) (angle / armSeparationDistance ) * armSeparationDistance + armOffset + rotation;
34.  
35.  
36.                 // Convert polar coordinates to 2D cartesian coordinates.
37.                 float starX =  Mathf.Sin (angle) * distance;
38.                 float starZ =  Mathf.Cos (angle) * distance;
39.                 float starY = 0;

 

up

 

just use falloff mask that modulate density with distance from the center

 

Right now you're adding one random star in every iteration of your loop. Create a probability function as prob = 1 - (distance / radius) or whatever falloff you want (square, log, etc). Generate a random number from 0 to 1. If number is more than probabilty then skip to next iteration.

 

Yep I would go with radius from the center.
Further you go, less particles you generate.

 

Hi, do you have any link or exemple of that ? I never heard about that and i found nothing possible to be that .

I just have the French College level, So....

 

folloff mask in similar concept to this

Is just like filter.
But you can do it programatically.

 

@Antypodish @neoshaman Thank you !
I found what i want after your help and someone other.

My Fallofff function is actually :

Code (CSharp):

1. distance = (Mathf.Pow(distance, 1f / 3f) - 1f) / (1-slopeMod);

Use that and you will get this :