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Range kutta numerical method techniques
This document discusses the application of the Runge-Kutta (RK4) numerical integration method in game physics simulations. RK4 is a 4th order method that calculates estimations in 4 steps to provide extremely accurate solutions with less risk compared to previous methods. It is commonly used to model rocket trajectories and sniper shots in games. While more complex to implement than other methods, RK4's increased accuracy rewards it with more realistic in-game physics simulations and fewer bugs.
Range kutta numerical method techniques
- 1. Application of Integration Method RUNGEKUTTA (RK4) method in game physics(NVIDIA PhysX)
- 2. Presented by Golam RabbyJewel ID:142-15-3819 Md. Irteza Rahman ID:133-15-3057
- 3. Outline Introduction Short brief toRUNGE KUTTA (RK4) Real life application RUNGE KUTTA method Why it is better? Conclusion Reference
- 4. Introduction Numerical method isfor 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) Rungekutta 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 Applicationof 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 thatis 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 isBetter 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 longerand 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
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