1. References: Wikipedia PHYSICS + VECTORS

2.  Why physics?  Good for every game developer to know.  Physics formulae are often vector-based  A good chance to try out math3d!  Often thinking "backwards" (from pictures to symbolic algorithms)  To show you how math3d is usable in pygame  Some cherry-picked topics we'll explore:  velocity + acceleration (w/ variable frame-rate)  Newton's laws of motion  Friction  Terminal velocity OVERVIEW

3.  Suppose you are moving at 50mph for 3 hours. How far are you from your original position?  A: 150 miles  50 * 3  Express this as a graph  We're really calculating the area of this rectangle. VELOCITY AND ACCELERATION Speed (mph) Time (hours) 50 3

4.  What about (abruptly) changing velocity? VELOCITY AND ACCELERATION, CONT. Speed (mph) Time (hours) 50 3 Q: How far have we travelled after these 5 hours? Q (rephrased): In other words, what is the area of the pink area? A: 0.5*(50x1) + (50x3) + 0.5*(50x1) = 200 miles

5.  Two options for handling it:  Option1: Cap frame rates  When moving / rotating express in units / update  Bad: Slow machines can't reach the frame-rate  Bad: *Very* painful to modify our fps-cap.  Option2: Let computer run as fast as possible  When moving / rotating express in units / second  The multiply by the time since the last frame  Good: Runs on any speed machine  Bad: Have an extra multiplication VARIABLE FRAME RATES (REVIEW)

6.  we can approximate the area of this curve using (small) discreet time intervals VELOCITY AND ACCELERATION, CONT. Speed (mph) Time (hours) 50 3 A dT value for one iteration of the game loop. import pygame # … clock = pygame.time.Clock() #... (inside the game loop) dT = clock.tick() / 1000.0

7. VELOCITY AND ACCELERATION, CONT.

8. VELOCITY AND ACCELERATION change in position due to velocity

9. ACCELERATION

10. ACCELERATION AND VECTORS, CONT.

11.  Gravity produces an acceleration on objects  Assuming we're on the earth, it points downwards GRAVITY

12.  In real life, there's a maximum speed objects can go  Theoretically the speed of light.  On earth, there's wind resistance.  In games, we often impose a terminal velocity  More numerically stable.  More consistent gameplay experience.  A little more like real life.  [Develop the formula] TERMINAL VELOCITY

13. NEWTON'S LAWS OF MOTION

14.  Gravity is a force  Proportional to the mass  But…when we apply the force  We divide by the mass (Newton's 2 nd )  So…the acceleration is the same regardless of mass  Unless there is air resistance (drag)  Proved by Gallileo around 1586.  In code: 1.Create a Force vector, F 2.Multiply F by mass. 3.Divide F by mass when applying the force 4.Apply acceleration to velocity as normal  (or just skip steps 2 & 3) GRAVITY AS A FORCE

15.  Friction causes an object to slow down  Air resistance  Contact with ground ……  Implemented as an accleration in the opposite direction of movement  Complication: "flipping direction"  Complication: magnitude (and connection to dt)  [Come up with formula on board] FRICTION