The aim of this demo is to try out OpenGL with a topic that I dig.

The Makefile is setup to build from a linux box (mine is Arch Linux) using clang, but you can easily change that line (clang++) for g++, and it will compile just as well. Also note that you must have library freeglut installed in your system. You can look at the Makefile to see where freeglut can be installed.

    cd opengl-demo-nbody
    make
    ./n-body-sim    # runs the demo (will start in fullscreen, `alt+F4 to exit`)

You can safely ignore the warnings (2 of them) produced.

Meh, I suck at calculus and stuff. In fact, I hope this project will motivate me in mastering it by giving me a purpose to learn.

I'm learning C++ with this project. However, freeglut (the library I use to manage the basic OpenGL stuff) makes it really hard to use OO programming, thus the procedural style.

If I keep working on this side-project long enough, I'll eventually port it to use SDL.

• Create a scene with 2-bodies.
• Give physic properties to the bodies.
  • Must include mass; (done)
  • Must include volume; (done)
  • Must include position/speed/acceleration; (done)
  • Must include collision detection (to avoid near-zero anomalities[1]). (remains to be implemented[2])
• Animate the bodies as a function of time. (done)
• EXTRA: Trace the future trajectory of the body
• EXTRA++: Make this trace time-colored (so if two trajectories cross at a similar color, I can predict a collision!)
• Increase to 3-bodies. (done)
• Increase to n-bodies. (done)
• Enter the properties of the Solar system and try to simulate it.
• Separate the computation of the n-bodies from the graphic rendering loop, to permit variable precision in the simulation step.

[1] When two bodies get too close, the influence they have over one another greatly increase, while the calculation step doesn't, leading to huge approximation errors. The most common effect is that the two bodies will be greatly accelerated at t_n, then be computed to a new much greater distance at t_n+1. Because the two bodies at t_n+1 are now so far from each other, the new force they exert on one another will not be sufficient enough to sufficiently slow back the two bodies. Although the two bodies will eventually come back closer, it will be at a great speed and the effect will only amplify with time.

[2] There are two ways I expect to do this. Either I will remove all velocity/acceleration in the direction of the collision between the two bodies (that is, the normal of the two touching surface). This would make the bodies start rolling around one another. Adding friction would simulate, I expect, bubble-like collisions. The other way would be to break the bodies in smaller bodies when they collide, and define some rule for the force they receive when they 'explode'. This would let me, I expect, simulate the formation of more complex systems based on particle-like behaviors. I expect it could form asteroid-like belts and some aggregate of particles would reform planet-like shapes. Both ways are interesting.