Basic Game Physics. IntroducBon (1 of 2) IMGD What is game physics? CompuBng mo)on of objects in virtual scene

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1 Basic Game Physics IMGD 4000 With material from: Introduc)on to Game Development, Second EdiBon, Steve Rabin (ed), Cengage Learning, (Chapter 4.3) and Ar)ficial Intelligence for Games, Ian Millington, Morgan Kaufmann, 2006 (Chapter 3) IntroducBon (1 of 2) What is game physics? CompuBng mo)on of objects in virtual scene Including player avatars, NPC s, inanimate objects CompuBng mechanical interac)ons of objects InteracBon usually involves contact (collision) SimulaBon must be real- Bme (versus high- precision simulabon for CAD/CAM, etc.) SimulaBon may be very realisbc, approximate, or intenbonally distorted (for effect) 2 1

2 IntroducBon (2 of 2) And why is it important? Can improve immersion Can support new gameplay elements Becoming increasingly prominent (expected) part of high- end games Like AI and graphics, facilitated by hardware developments (mulb- core, GPU) MaturaBon of physics engine market 3 Physics Engines Similar buy vs. build analysis as game engines Buy: Complete solubon from day one Proven, robust code base (hopefully) Feature sets are pre- defined Costs range from free to expensive Build: Choose exactly features you want Opportunity for more game- specificabon opbmizabons Greater opportunity to innovate Cost guaranteed to be expensive (unless features extremely minimal) 4 2

3 Physics Engines Open source Box2D, Bullet, Chipmunk, JigLib, ODE, OPAL, OpenTissue, PAL, Tokamak, Farseer, Physics2d, Glaze Closed source (limited free distribubon) Newton Game Dynamics, Simple Physics Engine, True Axis, PhysX Commercial Havok, nv Physics, Vortex RelaBon to Game Engines NaBve, e.g,. C4 Integrated, e.g., UE4 + PhysX Pluggable, e.g., C4 + PhysX, jme + ODE (via jme Physics) Basic Game Physics Concepts Why are we studying this? To use an engine effecbvely, you need to understand something about what it s doing You may need to implement small features or extensions yourself Cf., owning a car without understanding anything about how it works Examples KinemaBcs and dynamics ProjecBle mobon Collision detecbon and response 6 3

4 Outline IntroducBon (done) KinemaBcs (next) The Firing SoluBon Collision DetecBon Ragdoll Physics PhysX 7 KinemaBcs (1 of 3) Study of mobon of objects without taking into account mass or force Basic quanbbes: posibon, Bme... and their derivabves: velocity, accelerabon Basic equabons: 1) d = vt 2) v = u + at 3) d = ut + ½at 2 4) v 2 = u 2 + 2ad Where: t - (elapsed) )me d - distance (change in posi)on) v - (final) velocity (change in distance per unit )me) a - accelera)on (change in velocity per unit )me) u - (ini)al) velocity Note, equabon #3 is the integral of equabon #2 with respect to Bme (see next slide). EquaBon #4 can be useful. 8 4

5 KinemaBcs (2 of 3) Non- accelerated mobon Accelerated mobon d = ut Example: u = 20 m/s, t = 300 s d = 20 x 3000 = 6000 m d = ut + ½at 2 Example: u=0 m/s, a=4m/s 2, t=3s d = 0x x4x9 = 18m KinemaBcs (3 of 3) Predic)on Example: If you throw a ball straight up into the air with an inibal velocity of 10 m/ sec, how high will it go? v 2 = u 2 + 2ad u = 10 m/sec (inibal speed upward) a = - 10 m/sec 2 (approx gravity) v = 0 m/sec (at top of flight) 0 = (- 10)d d = 5 meters (Note, answer independent of mass of ball!) d v = 0 a = - 10 u =

6 Doing It In 3D MathemaBcally, onsider all quanbbes involving posibon to be vectors: d = vt v = u + at d = ut + at 2 /2 ComputaBonally, using appropriate 3- element vector datatype 11 Dynamics NoBce that preceding kinemabc descripbons say nothing about why an object accelerates (or why its accelerabon might change) To get a full modern physical simulabon you need to add two more basic concepts: force mass Discovered by Sir Isaac Newton Around 1700 J 12 6

7 Newton s Laws 1. A body will remain at rest or conbnue to move in a straight line at a constant speed unless acted upon by a force. 2. The accelerabon of a body is propor)onal to the resultant force acbng on the body and is in the same direcbon as the resultant force. 3. For every acbon, there is an equal and opposite reacbon. 13 MoBon Without Newton s Laws Pac- Man or early Mario style Follow path with instantaneous changes in speed and direcbon (velocity) Not physically possible Note - fine for some casual games (especially with appropriate animabons) 14 7

8 Newton s Second Law F = ma At each moment in Bme: F = force vector, in Newton s m = mass (intrinsic scalar property of maper), in kg a = accelerabon vector, in m/sec 2 Player cares about state of world (posibon of objects). EquaBon is fundamental driver of all physics simulabons. Force causes accelerabon (a = F/m) AcceleraBon causes change in velocity Velocity causes change in posibon 15 KinemaBcs equabons How Are Forces Applied? May involve contact Collision (rebound) FricBon (rolling, sliding) Without contact Rockets/Muscles/Propellers Gravity Wind (if not modeling air parbcles) Magic Dynamic (force) modeling also used for autonomous steering behaviors 16 8

9 CompuBng KinemaBcs in Real Time start = gettime() // start time p = 0 // initial position u = 10 // initial velocity a = -10 function update () { now = gettime() t = now start simulate(t) } // in game loop function simulate (t) { d = ut + at 2 /2 d = (u + (0.5 * a * t)) * t move object to p + d // move to loc. computed since start } Note! Number of calls and Bme values to simulate() depend on (changing) game loop )me (frame rate) Is this a problem? It can be! For rigid body simulabon with colliding forces and fricbon (e.g., many interesbng cases) leading to jerky behavior 17 d a = - 10 u, p Frame Rate Independence Complex numerical simulabons used in physics engines are sensibve to Bme steps (due to truncabon error and other numerical effects) But results need to be repeatable regardless of CPU/GPU performance for debugging for game play So, if frame rate drops (game loop can t keep up), then physics will change SoluBon: Control physics simulabon interval independently of frame rate 18 9

10 Frame Rate Independence delta simula)on )cks lag frame updates previous now start =... delta = 0.02 lag = 0 previous = 0 // physics simula)on interval (sec) // )me since last simulated // )me of previous call to update function update() { // in game loop now = gettime() t = (previous - start) lag // previous simulate() lag = lag + (now - previous) // current lag while ( lag > delta ) // repeat un)l caught up t = t + delta simulate(t) lag = lag - delta previous = now // simula)on caught up to current )me } 19 Outline IntroducBon (done) KinemaBcs (done) The Firing SoluBon (next) Collision DetecBon Ragdoll Physics PhysX 20 10

11 The Firing SoluBon (1 of 3) How to hit target Beam weapon or high- velocity bullet over short ranges can be viewed as traveling in straight line But projecble travels in parabolic arc Grenade, spear, catapult, etc. d = ut + at 2 /2 u = velocity vector a = [0, 0, - 9.8] m/sec 2 (but can use higher value, e.g., - 18) d Most typical game situabons, magnitude of u fixed. We only need to know relabve components (orientabon) à Challenge: Given a, d, solve for u 21 Remember QuadraBc EquaBons? Make nice curves Like firing at target! SoluBons are where equals 0. E.g., when firing with gun on ground: At gun muzzle At target But unlike in algebra class, not just solving quadrabc but finding angle with y = gun, y = target Angle changes speed in x- direcbon, but also Bme spent in air Aver hairy math [Millington 3.5.3], three relevant cases: Target is out of range (no solubon) Target is at exact maximum range (single solubon) Target is closer than maximum range (two possible solubons) Solve with quadrabc formula 22 11

12 The Firing SoluBon (2 of 3) long Bme trajectory u = muzzle velocity vector short Bme trajectory Usually choose short Bme trajectory Gives target less Bme to escape Unless shoobng over wall, etc. d [Millington 3.5.3] u = (2Δ - at 2 ) / (2 (muzzle_v) t) where muzzle_v = max muzzle speed Δ is difference vector from d to u a is gravity 23 The Firing SoluBon (3 of 3) function firingsolution (start, target, muzzle_v, gravity) { // Calculate vector back from target to start delta = target - start // Real- valued coefficents of quadra)c equa)on a = gravity * gravity b = - 4 * (gravity * delta + muzzle_v * muzzle_v) c = 4 * delta * delta // Check for no real solu)ons if ( 4 * a * c > b * b ) return null // Find short and long )mes to target disc = sqrt (b * b - 4 * a *c) t1 = sqrt ( ( - b + disc ) / (2 * a )) t2 = sqrt ( ( - b - disc ) / (2 * a )) Note, a, b and c are scalars so a normal square root. } // Pick shortest valid )me to target (Qt) if ( t1 < 0 ) && ( t2 < 0) return null // No valid )mes if ( t1 < 0 ) ttt = t2 else if ( t2 < 0 ) ttt = t1 else ttt = min ( t1, t2 ) // Return firing vector return ( 2 * delta - gravity * ttt * ttt ) / ( 2 * muzzle_v * ttt ) Note scalar product of two vectors using *: [a,b,c] * [d,e,f] = a*d + b*e + c*f 24 [Millington 3.5.3] 12

13 Outline IntroducBon (done) KinemaBcs (done) The Firing SoluBon (done) Collision DetecBon (next) Ragdoll Physics PhysX 25 Collision DetecBon Determining when objects collide is not as easy as it seems Geometry can be complex Objects can be moving quickly There can be many objects naive algorithms are O(n 2 ) Two basic approaches: Overlap tesbng Detects whether collision has already occurred IntersecBon tesbng Predicts whether collision will occur in future 26 13

14 Overlap TesBng Basics discussed and implemented in IMGD 3000! Most common technique used in games Exhibits more error than intersecbon tesbng Basic idea: at every simulabon step, test every pair of objects to see if overlap Easy for simple volumes (e.g., spheres), harder for polygonal models Results of test: collision normal vector (useful for reacbon) Bme that collision took place 27 Overlap TesBng: Finding Collision Time Calculated by doing binary search in Bme, moving object back and forth by 1/2 steps (bisecbons) A t 0 A A A t A A 0.25 t t t t 0.5 t 1 B Initial Overlap Test B Iteration 1 Forward 1/2 Iteration 2 Backward 1/4 In pracbce, five iterabons usually enough B B Iteration 3 Forward 1/8 B Iteration 4 Forward 1/16 B Iteration 5 Backward 1/

15 LimitaBons of Overlap TesBng Fails with objects that move too fast (no overlap during simulabon Bme slice) window t -1 t 0 t 1 t 2 bullet SoluBon approach: constrain game design so that fastest object moves smaller distance in one physics Bck (delta) than thinnest object may require reducing simulabon step size (adds computabon overhead) 29 IntersecBon TesBng Predict future collisions Extrude geometry in direcbon of movement e.g., swept sphere turns into capsule shape t 0 t 1 Then, see if extruded shape overlaps objects When collision found (predicted) Move simulabon to Bme of collision (have collision point) Resolve collision Works for bullet/window example (bullet becomes line segment) 30 15

16 Speeding Up Collision DetecBon Bounding Volumes Oriented Hierarchical ParBBoning Plane Sweep 31 Bounding Volumes Commonly used volumes sphere - distance between centers less than sum of radii boxes axis aligned (loose fit, easier math) oriented (Bghter fit, more expensive) 32 Axis-Aligned Bounding Box If bounding volumes don t overlap, then no more tesbng is required If overlap, more refined tesbng required Bounding volume alone may be good enough for some games Oriented Bounding Box 16

17 Complex Bounding Volumes MulBple volumes per object e.g., separate volumes for head, torso and limbs of avatar object Hierarchical volumes e.g., boxes inside of boxes [GoQschalk, Lin, Minocha, SIGGRAPH 96] 33 ParBBoning for Collision TesBng To address the n 2 problem... ParBBon space so only test objects in same cell In best case (uniform distribubon) reduces n 2 to linear Can happen for uniform size, density objects (e.g., cloth/fluids) In worst case (all objects in same cell) no improvement 34 17

18 Plane Sweep for Collision TesBng Observa)on: many moveable objects stay in one place most of the Bme Sort bounds along axes (expensive to do, so do just once!) Only adjacent sorted objects which overlap on all axes need to be checked further Since many objects don t move, can keep sort up to date very cheaply with bubblesort (nearly linear) y B 1 A 1 R 1 B 0 A 0 A R B C 1 R 0 C C 0 A 0 A 1 R 0 B 0 R 1 C 0 B 1 C 1 35 x Outline IntroducBon (done) KinemaBcs (done) The Firing SoluBon (done) Collision DetecBon (done) Ragdoll Physics (next) PhysX 36 18

19 What is Ragdoll Physics? Procedural animabon oven used as replacement for tradibonal (stabc) death animabon Generated by code, not hand Using physics constraints on body limbs & joints in real- Bme SBll from early animabon using ragdoll physics hpps://en.wikipedia.org/wiki/ragdoll_physics hpp:// physics- 2 Diablo 3 Ragdolls How to Smack a Demon Erin Capo (Game Developer s Conference, San Francisco, California, USA, 2013) Physics Programmer for Diablo 3 (Blizzard, 2012) 19

20 A ragdoll is a collecbon of collision shapes connected to bones 20

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22 Physics joints connect two bones Cone Joint (like shoulder) Revolute Joint (like elbow) Tech arbst connects bones with Physics joints Spherical Joint (for chandeliers) Weld Joint (locks two bodies, for advanced) 22

23 ParBal ragdolls add flavor to living characters Not just for death and destrucbon 23

24 More Physics We Are Not Covering Collision response ConservaBon of momentum ElasBc collisions Non- elasbc collisions coefficient of resbtubon Rigid body simulabon (vs. point masses) Joints as constraints to mobon Sov body simulabon [see excellent book by Millington, Game Physics Engine Development, MK, 2007] 47 Outline IntroducBon (done) KinemaBcs (done) The Firing SoluBon (done) Collision DetecBon (done) Ragdoll Physics (done) PhysX (next) 48 24

25 PhysX Overview Developed by NVIDIA for C++ applicabons Windows, Mac, Linux, PlaystaBon, Xbox, Android, Apple ios and Wii Simulate Fluids Sov bodies (cloth, hair) Rigid bodies (boxes, bones) Why Does NVIDIA Make Physics Sovware? NVIDIA is mainly known as a developer and manufacturer of graphics hardware (GPU s) So taking advantage of GPU for hardware accelerabon of their physics engine Algorithms can be tuned to their hardware Giving a compebbve advantage over other GPU manufacturers 50 25

26 Configure Video Card as Dedicated PhysX Processor Dedicated to PhysX What Algorithms Does PhysX Use? Hard to know exactly, because algorithm details are NVIDIA s intellectual property (IP) However from various forums and clues, it is clear PhysX uses: Both sweep and overlap collision detecbon AABB and OBBT and (both axis- aligned and oriented bounding bounding box trees) Constraints: hinges, springs, etc. and lots of other hairy stuff, see hpps://devtalk.nvidia.com/default/board/66/physx- and- physics- modeling/ 52 26

27 Rocket Sled CES 2010, Rocket Sled demonstrates both graphics and physics compubng capabilibes of new GF100 (Fermi) GPUs. Raging Rapids Ride Graphics ok, but with intensive and complex real- Ame fluid simulabon 27

28 Havok Cloth PhysX compebtor bought by Microsov Binary Free! Source code (e.g., to modify), costs How to Use PhsyX General documentabon NVIDIA PhysX SDK DocumentaBon hpp://docs.nvidia.com/gameworks/content/gameworkslibrary/physx/guide/index.html UE4 guide PhysX, IntegraBng PhysX Code into Your Project (by Rama) hpps://wiki.unrealengine.com/physx,_integrabng_physx_code_into_your_project 28