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Game Physics. Introduction to Game Physics. Traditional Game Physics Particle system Rigid body dynamics Flexible body dynamics Some State-of-art Topics Car physics Fluid dynamics Rag-doll physics Physics Rigid body kinematics Newton’s Laws Forces Momenta Energy.

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## Game Physics

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**Introduction to Game Physics**• Traditional Game Physics • Particle system • Rigid body dynamics • Flexible body dynamics • Some State-of-art Topics • Car physics • Fluid dynamics • Rag-doll physics • Physics • Rigid body kinematics • Newton’s Laws • Forces • Momenta • Energy**Basic Concepts from Physics (1/2)**• Newton’s Laws • 1st Law • “靜者恆靜，動者恆成等速度運動” • 2nd Law • F = ma = mdv/dt • 3rd Law • 作用力與反作用力 • Forces • Gravity / Spring forces / Friction / Viscosity • Torque • = r X F • Equilibrium**Basic Concepts from Physics (2/2)**• Momenta • Linear momentum • Angular momentum • Moment of inertia**Particle Dynamics**• Particles are objects with • Mass • Position • Velocity • Respond to forces • But no spatial extent (no size!) • Point mass • Based on Newton Laws • f = ma • x = f / m • v = f / m, x = v .. . .**Basic Particle System**x v f m x v f m x v f m x v f m x v f m x v f m typedef struct { float m; /* mass */ float *x; /* position */ float *v; /* velocity */ float *f; /* force accumulator */ } *Particle; typedef struct { Particle *p /* array of pointers to particles */ int n; /* number of particles */ float t; /* simulation clock */ } *ParticleSystem; states Particle n time …**/* gather states from the particles */**void ParticleGetState(ParticleSystem p, float *dst) { int i; for (i = 0; i < p->n; i++) { *(dst++) = p->p[I]->x[0]; *(dst++) = p->p[I]->x[1]; *(dst++) = p->p[I]->x[2]; *(dst++) = p->p[I]->v[0]; *(dst++) = p->p[I]->v[1]; *(dst++) = p->p[I]->v[2]; }}**/* scatter states into the particles */**void ParticleSetState(ParticleSystem p, float *src) { int i; for (i = 0; i < p->n; i++) { p->p[i]->x[0] = *(src++); p->p[i]->x[1] = *(src++); p->p[i]->x[2] = *(src++); p->p[i]->v[0] = *(src++); p->p[i]->v[1] = *(src++); p->p[i]->v[2] = *(src++); }}**/* calculate derivative, place in dst */**void ParticleDerivative(ParticleSystem p, float *dst) { int i; ClearForce(p); ComputeForce(p); for (i = 0; i < p->n; i++) { *(dst++) = p->p[i]->v[0]; *(dst++) = p->p[i]->v[1]; *(dst++) = p->p[i]->v[2]; *(dst++) = p->p[i]->f[0]/p->p[i]->m; *(dst++) = p->p[i]->f[1]/p->p[i]->m; *(dst++) = p->p[i]->f[2]/p->p[i]->m; }}**/* Euler Solver */**void EulerStep(ParticleSystem p, float DeltaT) { ParticleDeriv(p, temp1); ScaleVector(temp1, DeltaT); ParticleGetState(p, temp2); AddVector(temp1, temp2, temp2); ParticleSetState(p, temp2); p->t += DeltaT; }**Rigid Body Dynamics**• Mass of a Body • Mass center • Force • Linear momentum • P(t) = M v(t) • Velocity (v) • Torque • Angular momentum • L(t) = I w(t) • Local rotation (w) • Inertia Tensor • Reference • www-2.cs.cmu.edu/afs/cs/user/baraff/www/pbm**Flexible Body Dynamics (1/2)**• Particle-Spring Model • F = k x • Not a stress-strain model • Lack of Elasticity, Plasticity, & Viscous-Elasticity • Can be unstable**Flexible Body Dynamics (2/2)**• Finite Element Method • Solver for ODE/PDE • Boundary conditions • Energy equation • Stress-strain model • Very complicated computing process • Conservation of Energy**Advanced Topics in Game Physics**• Fracture Mechanics (破壞力學模擬) • Fluid Dynamics (流體力學) • Car Dynamics (車輛動力學) • Rag-doll Physics (人體物理模擬)**Introduction to Game FX**• Improve the Visual & Sound Game Effects • Includes • Combat FX • Environment FX • Character FX • Scene FX • Sound FX • FX Editor Needed • General 3D animation can not do it • Key-frame system is nor working • FX animation is always • Procedurally • Related to the previous frame • Small Work But Large Effect**Combat FX**• During the Combat • Weapon motion blur • Weapon effect • Skill effect • After the Combat • Damage effect • FX Editor**Motion Blur – Image Solution**• Computer Animation : • Image solution • Blending rendered image sequence • Render too many frames • Divide the frames • Average • Done!**Motion Blur – Geometry Solution**• In Games, Use Transparent Objects to Simulate the Motion Blur • “False” Motion Blur • Tracking the motion path of the object • Connecting them as a triangular mesh • Use time-dependent semi-transparency to simulate the “blur” • The path can be smoothed using Catmull-Rom spline • Local stability of the curve**FX Uses Texture Animation**• Almost All Game FXs Use this Trick • Geometry Object on which the Texture Animation Playing • Billboard • 3D Plate • Cylinder • Sphere • Revolving a cross section curve • Texture Sequence with Color-key • Semi-transparent Textures • Alpha blending • Source color added to background • Demo!!!!**Particle System for FXs in Combat**• The FXs • Fire / exposure / smoke / dust • Initial Value + Time dependency • Combined with Billboard FX • Billboard to play the texture animation • Particle system to calculate the motion path • Gravity is the major force used • Emitter pattern • Single emitter • Area emitter • Emitter on vertices • Demo !!!**Environment FX**• Weather • Use particle system • Rain • Snow • Wind • Fog • Traditional fog • From near to far • Hardware standard feature • Volume fog • Layered fog • Use vertex shader • Day & Night**Character FX**• Fatality • Case by case and need creative solutions • Rendering Effects on Skins • Environment mapping • Bump map • Normal map • Multiple texture map • Flexible body • Flexible body dynamics • Fur • Real-time fur rendering • …**Scene FX – Sky Box**• Use a very large box or dome-like model to surround the whole game scene • Use textures on the box or dome as the backdrop • Use multiple textures and texture coordinates animation to simulate the moving of the clouds**Scene FX – Len’s Flare**• Runtime calculate the position and orientation of the camera with the sun • Put textures to simulate the len’s flare**Scene FX – Light Scattering**• Atmospheric Light Scattering • Caused by dust, molecules, or water vapor • These can cause light to be: • Scattered into the line of sight (in-scattering) • Scattered out of the line of sight (out-scattering) • Absorbed altogether (absorption) • Skylight and sun light • Can be Implemented by Vertex Shader**Scene FX – Light Scattering Examples**Without scattering With scattering

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