Lecture 6

1. Lecture 6 Announcements

2. Next week will be great! • Three major things are happening next week: • Zyngaguest lecture • Your game pitches (more details later) • Christina Paxson

3. Feedback for M 1 • Some of you had stacking shapes • The stack probably exploded eventually • Don’t worry, stacking boxes is hard to do properly • This week’s lecture will help but not alleviate the problem

4. Feedback for M 1 • Sometimes shapes would settle overlapping other shapes • Two possible causes: • Not translating enough • Doing collision response before integration, hence drawing before translating

5. Announcements Questions?

6. Lecture 6 Physics II

7. M1 Collision Response • You obtained MTV in M1, how did you use it? • Move things out of collision • Apply some impulse along MTV • It probably worked most of the time, or only if you modeled specific behavior • Other times the response is weird

8. Controlling Impulse voidonCollide(Collision col) { Shape o1 = col.shape1; Shape o2 = col.shape2; Vec2fmtv = col.mtv; o1.move(mtv.smult(0.5f)); o2.move(mtv.smult(-0.5f)); //code to calculate impulse o1.applyImpulse(imp1); o2.applyImpulse(imp2); } • Want more realistic collisions • Two things to do: • Support a range of collision behavior • Determine the physically correct collision result • Also need to be able to code it

9. Restitution • Property of physical entities • Value between 0 and 1 • 0 is perfectly inelastic, 1 is perfectly elastic, etc. • The coefficient of restitution (COR) between two entities is the geometric mean of their restitutions:

10. Correct Collisions • How do we find the physically correct collision response? • i.e. given and , what are and ? • Use physical definition of the COR:

11. Translation to Code • Once we determine what the final velocities of the objects should, how do we apply this? • Impulse or velocity setting? • Setting velocity affects other collision response calculations

12. Translation to Code • We determined what the final velocities of the objects should, how do we apply this? • Impulse > velocity setting • Setting velocity affects other collision response calculations

13. Translation to Code • We determined what the final velocities of the objects should, how do we apply this? • Impulse > velocity setting • Setting velocity affects other collision response calculations

14. Translation to Code • We determined the final velocities of objects, what do we do with it? • Impulse > velocity setting • Setting velocity affects other collision response calculations • Recall the definition of the impulse: • We really want the difference of final and initial velocity

15. Final Velocities • Conservation of momentum: • The COR equationcan be rewritten as • So conservation of momentum becomes

16. Final Velocities • Solving for : • Similarly for (reverse and basically):

17. Velocity Difference • The velocity differences are:

18. Final Impulse • So the impulse you want to apply is: • You can see that they are equal and opposite, as we would expect

19. Static Shapes • If object is static, you can show that the equations in the last slide reduces to • Vice-versa if object is static • You should special case this

20. Note about Velocity • Note that all velocities in these equations are for the one-dimensional case • But your 2D engine is 2D! • Velocity only changes in the direction of the MTV • So the ’s and ’s in the equations are the projection of velocity onto the MTV

21. Putting it all together Physically correct collision response: • Calculate COR with the restitutions of the shapes • Project velocities onto MTV • Apply impulse formula to calculate impulses • Apply corresponding impulse to each shape

22. Physics II Questions?

23. Lecture 6 Raycasting

24. What is raycasting? • Determine the first object that a ray hits • A ray is like a ray of light, has a source and direction and goes on forever • It’s like a camera (or eye)

25. Raycasting Uses • When would we need to raycast? • Hitscan weapons • Line of sight for AI • Area of effect • Rendering

26. The Ray • A ray is a point (source) and a direction • Point on ray given by: • is the source point • is the direction • This must be normalized! • is a scalar value (length)

27. Basics • Raycasting boils down to finding the intersection of a ray and shapes • Kind of like collision detection all over again • You want the point of collision as well

28. Ray-Circle • If the point is outside • Project center onto ray • Check if the projection is positive and the point is within the circle • Point of intersection:

29. Ray-Circle • If the point is outside • Project center onto ray • Check if the projection is positive and the point is within the circle • Point of intersection?

30. Ray-Circle • If the point is outside • Project center onto ray • Check if the projection is positive and the point is within the circle • Point of intersection?

31. Ray-Circle • If the source point is inside the circle • Do the same thing as if outside, but: • Now is allowed to be negative

32. Ray-Polygon/AAB • A polygon/AAB is composed of edges • We can check for intersection of ray by checking for intersection of all edges • There is no shortcut for AABs this time

33. Ray-Edge • Edge is defined by two end points, and • We need some other vectors: • is direction of the segment (normalized) • is the perpendicular to the segment (normalized)

34. Ray-Edge • Firstly, determine if the segment straddles the ray • Use cross products • and must be of opposite sign • Therefore no intersection if

35. Ray-Edge • Secondly, determine if the two lines intersect • Point of intersection • Solve for • must be nonnegative!

36. Ray-Edge • Because lies on the segment • So plugging in:

37. Ray-Polygon • Intersect the ray with all the edges of the polygon • Ray intersects polygon if it intersects at least 1 edge • Keep track of the point that is closest to the source (the lowest value of )

38. Putting it all together Raycasting: • Intersect ray with every shape in the world • For circles, use the circle-ray algorithm in the slides • For polygons, intersect each edge and use the closest • Keep track of closest intersection point from the source as well as the corresponding shape

39. Raycasting Questions?

40. Lecture 6 Final Project Overview

41. Overview • Can be any 2D game and engine • You can work in groups if you want • Each person is responsible for 10 “points” worth of new engine features • More members in a group means more engine features • More details in the final project handout

42. Timeline • 4 main parts: • Week 1: Idea • Week 2: Form groups and get approved • Week 3: Design • Weeks 4-8: Code, playtest, polish, present

43. Week 1: Idea • A ½ to 1 page document • Describe basic gameplay idea • How is your game fun? • Describe engine feature(s) you plan on implementing • Give a 60-second “elevator pitch” of your game in class

44. Week 2: Groups • Form a group (or decide to work alone) • Finalize game and engine features • Each group must meet with a TA to present the following: • A more polished idea of the game • Breakdown of member responsibilities for engine

45. Week 3: Design • Research new engine features • Design the engine and game • Exact breakdown of member responsibilities • Choose someone’s engine to use or integrate engines • For groups of 3 or more • Explain how you will use version control

46. Weeks 4-8 • Week 4: • Engine should be mostly done • Game exists • Week 5: • Engine should be done • Game is playable • 5 playtests per member from people not in CS195n

47. Weeks 4-8 • Week 6: • Game should be mostly done • 5 more playtests per member from outsiders • Week 7: • Game should be done • 5 playtests per member • Powerpoint slideshow for postmortem presentation

48. Weeks 4-8 • Week 8: • Polish up your game, bug fixes, etc • Create an executable and put it in /contrib • Make a video demo of your game from gameplay footage • It is now December 19th • And then you’re done!

49. Final Project Overview Questions?

50. Lecture 6 Tips for M II