Building a Better Jump J. Kyle Pittman @ PirateHearts Co-founder, Minor Key Games

1. Building a Better JumpJ. Kyle Pittman@PirateHeartsCo-founder, Minor Key Games

2. Hi • I’m Kyle • Hi Kyle 2007-2013 2013-20XX

3. Motivation • Avoid hardcoding, guessing games • Design jump trajectory on paper • Derive constants to model jump in code

4. Motivation • Has this ever happened to you? • There’s GOT to be a better way!!

5. Assumptions • Model player as a simple projectile • Game state • Position, velocity integrated on a timestep • Acceleration from gravity • No air friction / drag

6. Gravity • Single external force • Constant accelerationover time

7. Integration • Integrate over timeto find velocity

8. Integration • Integrate over timeagain to find position

9. Projectile motion • Textbox Physics 101 projectile motion • Understand how we got there

10. Parabolas • Algebraic definition • Substituting

11. Properties of parabolas • Symmetric

12. Properties of parabolas • Geometric self-similarity

13. Properties of parabolas • Shaped by quadratic coefficient

14. Design on paper

15. Design on paper

16. Maths • Derive valuesfor gravity andinitial velocityin terms ofpeak height andduration to peak

17. Initial velocity Solve for v0:

18. Solve for g: Gravity Known values:

19. Solve for v0: Back to init. vel.

20. Review

21. Time  space • Design with x-axis as distance in space • Introduce lateral (foot) speed • Keep horizontal and vertical velocity components separate

22. Parameters

23. Time  space

24. Time  space

25. Maths • Rewrite gravity and initial velocity in terms of foot speed and lateral distanceto peak of jump

26. Maths

27. Review

28. Breaking it down • Real world: Projectiles always follow parabolic trajectories. • Game world: We can break the rules in interesting ways. • Break our path into a series of parabolic arcs of different shapes.

29. Breaks • Maintain continuityin position and velocity • Trivial in implementation • Choose a new gravityto shape our jump

30. Fast falling Position Velocity / Acceleration

31. Variable height jumping Position Velocity / Acceleration

32. Double jumping Position Velocity / Acceleration

33. Integration • Put our gravity and initial velocity constants to use in practice • Integrate from a past state to a future state over a time step

34. Integration

35. Euler • Pseudocodepos += vel * Δtvel += acc * Δt • Easy • Unstable • We can do better

36. Runge-Kutta (RK4) • The “top-shelf” integrator. • No pseudocode here. :V • Gaffer on Games: “Integration Basics” • Too complex for our needs.

37. Velocity Verlet • Pseudocodepos += vel*Δt + ½acc*Δt*Δtnew_acc = f(pos)vel += ½(acc+new_acc)*Δtacc = new_acc

38. Observations • Similarity to projectile motion formula • What if our acceleration were constant? • We could integrate with 100% accuracy

39. Assuming constant acceleration

40. Assuming constant acceleration • Pseudocodepos += vel*Δt + ½acc*Δt*Δtvel += acc*Δt • Trivially simple change from Euler • 100% accurate as long as our acceleration is constant

41. Near-constant acceleration • What if we don’t change a thing? • The error we accumulate when our acceleration does change (versus Velocity Verlet) will be: • Δacc * Δt * Δt • Acceptable?

42. The takeaway • Design jump trajectories as a series of parabolic arcs • Can author unique game feel • Trust result to feel grounded in physical truths

43. Questions? • In practice: You Have to Win the Game (free game PLAY IT PLAY MY THING) • The Twitters: @PirateHearts • http://minorkeygames.com • http://gunmetalarcadia.com