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Fun With Gravity

, 28 Jul 2008 CPOL
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A gravity simulation particle system.

Introduction

This article is a fine example of what happens when programmers get bored. There's nothing exciting in the code, maybe a gentle introduction to GDI+. It was just a fun project to mess with, and it's addictive to play with. So I thought I might share it.

I was thinking about the fact that every particle in the universe is constantly gravitationally affected by every particle in the universe, and wanted to see what it would look like modeled in software. It's been a number of years since I cracked a Physics book, so I can't guaranty my accuracy with this project... But it sure is pretty.

The Code

Calculating Acceleration Due to Gravity

The method I chose for calculating the gravitational effect of each particle pn on particle p is this: I create a vector that extends from one particle to the other by subtracting ps location vector from pns location.

Vector unit = p2.Location - p.Location;

Then, calculate the magnitude of the resulting vector:

float magnitude = (float)Math.Sqrt(
      (unit.X * unit.X)
    + (unit.Y * unit.Y)
    + (unit.Z * unit.Z)
);

Then, you have what you need to calculate the acceleration.

float factor = (
    GravitationalConstant * (
        (p.Mass * p2.Mass) / (magnitude * magnitude * magnitude)
    )
) / p.Mass;

The resulting vector is what's needed to alter your particle's velocity due to the gravity of particle pn. I originally started with the actual gravitational constant G = 6.672e-11, but scaled it larger for simulation's sake, allowing smaller masses to be used.

The full calculation loop looks like this. Notice that for each particle, you calculate the gravitational effect on it by every other particle.

foreach (Particle p in particles) {
    ...
    if (particles.Count > 1) { 
        Vector a = new Vector();
        foreach (Particle p2 in particles) {
            if (object.ReferenceEquals(p, p2)) { continue; }
            Vector unit = p2.Location - p.Location;
            float magnitude = (float)Math.Sqrt(
                (unit.X * unit.X)
                + (unit.Y * unit.Y)
                + (unit.Z * unit.Z));
            float factor = (GravitationalConstant * (
                (p.Mass * p2.Mass) / (magnitude * magnitude * magnitude)
            )) / p.Mass;
            unit *= factor;
            a += unit;
        }
        p.Velocity += a;
    }
    ...
}

Conservation of Momentum with Inelastic Collisions

My collision detection is primitive. I'm only looking to see if a particle's bounding rectangle intersects with another. The Z axes was an afterthought, and in case the X and Y are intersecting, I look to see if the Z locations are with 5 of each other. I got lazy, what can I say. I wasn't that interested in the Z axes, but wanted to include it in the calculations.

In any event, when two particles collide, I combine their colors and masses. I increase their size slightly. And combine their momentum to find the resulting particle's velocity.

private Particle Merge(Particle i, Particle j, Graphics g) {
    ...
    Vector v = ((i.Velocity * i.Mass) + (j.Velocity * j.Mass));
    v /= i.Mass + j.Mass;
    ...
}

The Demo Application

Controls

There are menu options to Start, Stop, and Pause the simulation. Pause has a keyboard shortcut of F5, and Start has Ctrl+E (Execute from SQL Query Analyzer Smile | :) . You must start the simulation before you can add particles, and you can restart at any time to reset everything. Clicking anywhere in the picture box will create a particle at that location. The text boxes to the left under the check boxes determines the properties that the new particle will have. You can set the X, Y, and Z components of its initial velocity, its mass, and its size in pixels.

Buttons

The three buttons under the text boxes, labeled "B", "M" & "S", set the properties to predefined values for convenience. "B" creates a massive particle, "M" creates a medium, and "S" creates a small. The "Background" button allows you to change the picture box's background color.

Check Boxes

  • Trace: Toggles tracing. Tracing now shows a trail for each particle.
  • Collisions: Toggles collision detection.
  • Show Vel: Shows the velocity vector in red.
  • Vel Box: Shows the velocity vector's bounding box.
  • Show Acc: Shows the acceleration vector in the particle's color.
  • Acc Box: Shows the acceleration vector's bounding box.

The visual representation of the velocity and acceleration vectors is scaled up quite a bit so that they are visible at the scales I was working with. With more massive examples, the acceleration vector line can be pretty long. I may look at changing it to scale variably based on masses, but probably not.

Velocity Vector Velocity Box Acceleration Vector Acceleration Box Velocity & Acceleration

Particle ListView

Finally, the list view at the bottom of the window shows some attributes of the particles. The list view now shows all particles but only when paused. While paused, if you select particles in the list view and hit DELETE, it will remove the selected particles.

Conclusion

I don't think there's much to learn from this project, other than some simple GDI+ usage, and I suppose if you're not familiar with operator overloads, you could find some interesting things in the Vector class. It was just a fun project to play with, and it looks pretty cool. If I get bored enough some day, I may see about turning it into a screensaver.

History

07/24/2008

Based on the suggestions by protix & Zimriel I've updated calculations to more accurately represent orbits. I fixed the non-tracing flickering by drawing to an image and replacing the picturebox's image (poor man's double buffer). And tracing has been redone as well. Originally, I wanted to clear the image with a white color with a low alpha so that previous draws would fade. However, drawing an alpha color to the entire image takes far too long. In the end, I wound up having each particle keep track of a number of previous position, which get redrawn with decreasing alpha values. There may be a better solution, but this works for now.

License

This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)

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About the Author

BoneSoft
Software Developer (Senior) BoneSoft Software
United States United States
I've been in software development for more than a decade now. Originally with ASP 2.0 and VB6. I worked in Japan for a year doing Java. And have been with C# ever since.
 
In 2005 I founded BoneSoft Software where I sell a small number of developer tools.
Group type: Organisation (No members)



Comments and Discussions

 
GeneralMy vote of 5 PinmemberPhilip P Liebscher26-May-11 18:58 
GeneralMy vote of 5 Pinmemberalain_dionne29-Mar-11 5:30 
GeneralThumbs up! PinmemberBigdeak10-Jun-10 5:15 
General[Message Removed] Pinmemberimmetoz6-Oct-08 7:49 
JokeGood Article, But ... PinmemberMember 477036528-Jul-08 23:36 
GeneralRe: Good Article, But ... Pinmembercanozurdo29-Jul-08 2:23 
GeneralRe: Good Article, But ... Pinmember Xmen 22-Jan-09 16:25 
GeneralFun PinmemberTimmy Kokke28-Jul-08 20:14 
Generalgood Pinmemberdavid bagaturia20-Jul-08 20:06 
GeneralNice project Pinmemberfgjsdhgsdhg343242342323422-Aug-07 9:04 
GeneralRe: Nice project PinmemberBoneSoft22-Aug-07 12:10 
GeneralOrbits Pinmemberprotix26-Jul-07 1:32 
GeneralRe: Orbits PinmemberBoneSoft26-Jul-07 4:09 
AnswerRe: Orbits Pinmemberprotix26-Jul-07 21:45 
GeneralRe: Orbits Pinmemberprotix26-Jul-07 21:48 
GeneralRe: Orbits PinmemberZimriel14-Nov-07 19:21 
GeneralGreat Work!! PinmemberNeo_Shehpar24-Jul-07 11:35 
GeneralRe: Great Work!! PinmemberBoneSoft24-Jul-07 16:34 
GeneralPhysics from a physicist PinmemberKory.Postma24-Jul-07 1:20 
GeneralRe: Physics from a physicist PinmemberBoneSoft24-Jul-07 2:18 
GeneralRe: Physics from a physicist PinmemberBoneSoft24-Jul-07 6:02 
GeneralSuggestion PinmvpJosh Smith23-Jul-07 8:12 
Cool article. I think my productivity might suffer today! Smile | :)
 
I noticed that the particle rendering flickers a lot. I checked out the source code and saw that you're drawing straight to the screen. You might want to consider using a double-buffered approach if you want to greatly reduce the flickering.
 
I created a somewhat similar app a while back and posted an article about it. Here[^] is what I wrote about implementing double-buffering in WinForms.
 
Thanks again!
 
:josh:
My WPF Blog[^]
The greatest danger for most of us is not that our aim is too high and we miss it, but that it is too low and we reach it. - Michelangelo (1475-1564)

GeneralRe: Suggestion PinmemberBoneSoft23-Jul-07 16:50 
GeneralCool! PinmemberJay Gatsby22-Jul-07 21:42 
GeneralGravity Screen Saver PinmemberObiwan Jacobi22-Jul-07 19:59 
GeneralRe: Gravity Screen Saver PinmemberBoneSoft23-Jul-07 3:53 
GeneralRe: Gravity Screen Saver PinmemberChris Losinger3-Dec-07 10:31 
GeneralDang! Now I just have to know... Pinmembercharlieg22-Jul-07 13:04 
GeneralRe: Dang! Now I just have to know... PinmemberBoneSoft22-Jul-07 17:25 
GeneralVery nice PinmemberBradml22-Jul-07 2:49 
QuestionExtra Mass? PinmemberBerg4950822-Jul-07 1:19 
AnswerRe: Extra Mass? PinmemberObble25-Jul-07 10:16 
GeneralCool article PinmemberJoergen Sigvardsson22-Jul-07 0:07 
GeneralAwesome! PinmemberStephan Poirier21-Jul-07 20:11 

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