Runge Kutta fourth order explained. How it related to Nvidia PhysX

1. Application of
Integration Method
RUNGE KUTTA (RK4) method in game physics(NVIDIA
PhysX)

2. Presented by
Golam Rabby Jewel
ID:142-15-3819
Md. Irteza Rahman
ID:133-15-3057

3. Outline
Introduction
Short brief to RUNGE KUTTA (RK4)
Real life application RUNGE KUTTA method
Why it is better?
Conclusion
Reference

4. Introduction
Numerical method is for good solution
Make a program for offloading the work.
Numerical method is for testing.
How much it be wrong
Error analysis
Finding the types of error

5. RANJE KUTTA (RK4)
Runge kutta RK4 is 4th order differential integration method is a complex integration
It uses in physics.
It calculate the estimation in 4 steps

6. Real Life Application of RK4 Method
RK4 calculates xn+1 by the following calculation,
xn+1 = xn + 1/6(K1 + 2 * K2 + 2 * K3 +K4) * h
To calculate K1, K2, K3 and K4 the following calculations are needed, please note that
the time step in this equation is represented as ‘h’:
K1 = ODE (t + x)
K2 = ODE (t + 1/2* h, x + 1/2 * K1 * h)
K3 = ODE (t + 1/2 *h, x + 1/2 * K2 * h)
K4 = ODE (t + h, x + K3 * h)

7. Example
A rocket that is flying through the Earth’s atmosphere. First of all we have the ODE to
calculate the acceleration:
acceleration = (rocket force + force drag) / mass
We know that acceleration is the derivative of velocity (as mentioned earlier) so using
RK4 to calculate this should be relatively straight forward:

8. Example
K1 = ODE (time + velocity)
K2 = ODE (time + 1/2 * timeElapsed, x + 1/2 * K1 * timeElapsed)
K3 = ODE (time + 1/2 * timeElapsed, x + 1/2 * K2 * timeElapsed)
K4 = ODE (time + timeElapsed, x + K3 * timeElapsed)
And finally, to calculate the acceleration:
accelerationn+1 = accelerationn + 1/6 (K1 + 2 * K2 + 2 * K3 +K4) * timeElapsed
Sniper shot in Battlefield

9. Why it is Better
This is extremely accurate comparing it with it’s previous solution
 Less risky in real life application
Reduce bug in computer game

10. Conclusion
RK4 Takes longer and more complex in implementation. But as a reward it gives us
extreme accurate result. Runge Kutta doesn’t end at 4, it can go even further!
Fully depends on the Task and expectation.

11. Reference
https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods
https://www.quora.com/What-are-the-applications-of-numerical-methods
Bourg, D. M. (2002). Physics for Game Developers. California: O’Reilly

12. Thank you