Lecture 9

1. Lecture 9 Announcements

2. Congrats! • You are done with all the assignments in this class! • From now on everything you work on is designed by you • Good work so far!

3. Final Coding • Time to start coding for your final project • Remember, you should be mostly finishing your engine this week • Don’t forget to set up a meeting with your mentor TA soon

4. Announcements Questions?

5. Lecture 9 Collision Detection III

6. Point of Collision • We want to find out where shapes hit • In our simulation, colliding shapes are intersecting • Generally the intersection is small • So we choose a point that approximately represents where the intersection is

7. Poly-Poly • When two polygons (AABs are polygons too!) collide, at least one vertex of one shape is inside the other • If there’s only one point, use that as the point of collision • If there’s more than one, average them!

8. Circle-Circle • Circle-Circle is easy: • It’s on the line connecting the centers, with ratio of the radii • Remember this is in world (absolute) coordinates

9. Circle-Poly • If vertices of the poly are within the circle, then average them • If not, then take the point along the MTV: • (Depends on MTV direction)

10. Collision Detection III Questions?

11. Lecture 9 Physics III

12. Physics III Rotation

13. Rotation • We currently have shapes that don’t rotate • First step is to be able to rotate shapes • Next step is to provide collision response for rotating entities

14. Terminology ω • Let’s define some things: • Angle, θ (CCW) • Angular velocity, ω • Angular acceleration, α • Moment of Inertia, • Analogous to mass (inertia) for rotation θ

15. Basics public class PhysicalEntity{ float angle, aVel, aAcc; void move(float time) { //integrate position aVel += aAcc*time; angle += aVel*time; aAcc = 0; rotate(aVel*time); } } • Your physical entities should have an angle, angular velocity, and angular acceleration • You should integrate these as before • But whenever you do this you have to physically rotate the shape

16. Rotating Shapes • What shapes do we need to rotate? • AAB doesn’t rotate, by definition • Circles are circles • You still need angular values for the circle though, what if the hitbox is a circle? • Therefore only polygons need to rotate • Rotate polygons by rotating their vertices

17. Centroid of Polygon • Every shape rotates around its centroid • The centroid of a polygon with vertices is: • Where • and are coordinates of vertices in CCW order

18. Rotating Polygons • To rotate a polygon, rotate each vertex by the angle • These vectors are the vertices relative to the centroid! • Remember to update edges as well θ

19. Inertia • We also need the moment of inertia of an object • You can define or calculate it • Circle: • Polygon:

20. Rotation Questions?

21. Physics III Rotational Physics

22. Impulse and Forces • How can we cause shapes to rotate in the world? • Currently we are applying impulse/forces the centroids of entities • Apply impulse/force to object, but not at centroid

23. Impulse and Forces • Now your impulses and forces have a magnitude and a point of application • is relative to the centroid • The magnitude is actually a vector • for impulse and for force from now on or

24. Angular Impulse and Forces • In relation with angular velocity and acceleration: or

25. Collision Response • We need to change the impulse we calculated in Physics II • It’s now a different value that is applied at some specific point • It’s applied to the point of collision!

26. Some Definitions • More definitions: • , are the vectors from the centroids of the shapes to the collision point • , are the perpendiculars to , • is the normalized MTV

27. Collision Response • Magnitude of the impulse • , are projections of velocities onto the • The impulse is in the direction of , determine the sign based on your MTV direction

28. Fixed Rotation • Just like with static shapes, there should also be shapes that don’t rotate • Just like with the previous impulse equation, have a special case for non-rotating objects • Replace with if the entity doesn’t rotate • Note that if both objects don’t rotate, the equation reduces to the old equation

29. Rotational Physics Questions?

30. Physics III Friction

31. Friction • We don’t want everything to be slippery • Friction slows things down • Give every physical entity a friction value greater than 0

32. Frictional Force • The frictional force is parallel to the surface of contact • i.e. perpendicular to MTV • The direction is determined by the direction of the relative velocity (1D): a b a b

33. Relative Velocity • Only velocity perpendicular to the MTV is relevant • Direction of the perpendicular () doesn’t matter • Consistency matters

34. How Much Force? • From physics, the friction force on object A due to object B is proportional to the force exerted on object A by object B • We don’t really have that force… • But we did apply impulse to the objects!

35. The Force • So we have • is the impulse applied in collision response • is a constant

36. Disclaimer ω • This friction works for the case when the relative velocity is linear • With rotation, things become much more difficult • If you want to combine these, good luck!

37. Friction Questions?

38. Lecture 9 Networking

39. Networking NETWORKING STRATEGIES

40. The Illusion • All players are playing in realtime on the same machine • But of course this isn’t possible • We need to emulate this as much as possible

41. Send the Entire World! • Players take turns modifying the game world and pass it back and forth • Works alright for turn-based games • …but usually it’s bad • RTS: there are a million units • FPS: there are a million players • Fighter: timing is crucial

42. Send Commands • Each player sends the other all actions that alter shared game world • “Deterministic P2P Lockstep” • Problem: everything must evaluate the same • Or else there are desyncs • Problem: have to wait for all the other players’ commands • So everyone is limited by laggiest player

43. Client-Server Model • One player is the authoritative server • Other player is a “dumb terminal” • Sends all input to server • Server updates the world and sends it back • Problem: client has to wait for server to respond to perform even basic actions

44. Client-side Prediction • Client responds to player input immediately • When the server sends back the authoritative game state, client state is overwritten

45. Rollback • But the server just sent a state that was 100ms in the past! • What if games have diverged since then? • For instance, both players think they’ve collected a single powerup • Client has to roll back the world and integrate commands since the last known good state

46. Masking the Timewarp • Problem: laggy players experience this jump often • Solution: if the server usually sends states from 100ms ago, run the client 100ms behind • Turns a jumpy experience into a smooth, only slightly slow one

47. Networking Strategies Questions?

48. Networking IMPLEMENTATION

49. TCP: Transmission Control Protocol • Abstracts over IP • All packets are guaranteed to be received and in the correct order • Good for sending important, permanent data (websites, databases, etc)

50. UDP: User Datagram Protocol • A very thin shell around IP • Much faster than TCP, but no guarantees about reception or order • Good for information where only the most recent state matters (streaming, etc)