Physically Based Animation and Modeling

Physically Based Animation and Modeling CSE 3541 Matt Boggus

Overview • Newton’s three laws of physics • Integrating acceleration to find position • Particle Systems • Common forces in physically based animation

Mass and Momentum • Associate a mass with an object. We assume that the mass is constant • Define a vector quantity called momentum (p), which is the product of mass and velocity

Newton’s First Law • A body in motion will remain in motion • A body at rest will remain at rest, unless acted upon by some force • Without a force acting on it, a moving object travels in a straight line

Newton’s Second Law • Newton’s Second Law says: • This relates the kinematic quantity of acceleration to the physical quantity of force (Kinematics – the branch of mechanics concerned with the motion of objects without reference to the forces that cause the motion)

Newton’s Third Law • Newton’s Third Law says that any force that body A applies to body B will be met by an equal and opposite force from B to A • Every action has an equal and opposite reaction • Do we really want this for games and animation?

Integration Given acceleration, compute velocity & position by integrating over time

a f v’ a Physics review, equations for: Zero acceleration Constant acceleration Constant acceleration No acceleration m v vave

Pseudocode for motion within an animation loop (Euler method) To update an object at point x with velocity v: a = (sum all forces acting on x) / m [ ∑vectors scalar: m ] v = v + a * dt [ vectors: v, a scalar: dt ] x = x + v * dt[ vectors: x, v scalar: dt ]

Pseudocode for motion within an animation loop (Euler 2) To update an object at point x with velocity v: a = (sum all forces acting on x) / m[ ∑vectors scalar: m ] endv = v + a * dt[vectors: endv, v, a scalar: dt] x = x + [vectors: x, endv, v scalars: 2, dt] v = endv[vectors: endv, v]

Comparison of methods See spreadsheet example

Particle Systems • A collection of a large number of point-like elements • Model “fuzzy” or “fluid” things • Fire, explosions, smoke, water, sparks, leaves, clouds, fog, snow, dust, galaxies, special effects • Model strands • Fur, hair, grass • Star Trek 2 – genesis sequence(1982) • The making of the scene • More examples

Particle Systems Lots of small particles - local rules of behavior Create ‘emergent’ element Common rules for particle motion: Do collide with the environment Do not collide with other particles Common rules for particle rendering: Do not cast shadows on other particles Might cast shadows on environment Do not reflect light - usually emit it

Particle Example Collides with environment but not other particles Particle’s midlife with modified color and shading Particle’s demise, based on constrained and randomized life span Particle’s birth: constrained and time with initial color and shading (also randomized) source

Particle system implementation • Update Steps • for each particle • if dead, reallocate and assign new attributes • animate particle, modify attributes • render particles Use constrained randomization to keep control of the simulation while adding interest to the visuals

Constrained randomization particleX = x particleY = y particleX = x + random(-1,1) particleY = y + random(-1,1)

Particle (partial example in C#) class Particle { Vector3 position; // Updates frame to frame Vector3 velocity; // Updates frame to frame Vector3 force; // Reset and recomputed each frame GameObjectgeom; // other variables for mass, lifetime, … public: void Update(float deltaTime); void ApplyForce(Vector3 &f) { force.Add(f); } void ResetForce() { force = Vector3.zero; } // other methods… };

Particle emitter (partial example in C#) using System.Collections.Generic; using System.Collections; class ParticleEmitter { ArrayListParticles = new ArrayList(); public: void Update(deltaTime); };

Particle Emitter Update() Update(float deltaTime) { foreach(Particle p in Particles) { // …add up all forces acting on p… } foreach(Particle p in Particles){ p.Update(deltaTime); p.ResetForce(); } }

Creating GameObjects for(inti = 0; i < numberOfAsteroids; i++){ GameObjectaSphere = GameObject.CreatePrimitive(PrimitiveType.Sphere); aSphere.transform.parent= transform; aSphere.name = "sphere" + i.ToString(); aSphere.transform.position= new Vector3(Random.Range(-10.0f, 10.0f), Random.Range(-10.0f, 10.0f), Random.Range(-10.0f, 10.0f)); aSphere.transform.localScale= new Vector3(Random.Range(0.0f, 1.0f), Random.Range(0.0f, 1.0f), Random.Range(0.0f, 1.0f)); }

Deleting GameObjects GameObjectmyParticle; // …create, animate, etc. … Destroy(myParticle); Note: this affects the associated GameObject; it does not delete the variable myParticle

Lab3 • Implement a particle system where each particle is a GameObject • Restrictions • No RigidBodies • No Colliders • Minimal credit if you use these for lab3

Forces – gravity

Static friction Kinetic friction Viscosity for small objects No turbulence For sphere Forces

Forces • Aerodynamic drag is complex and difficult to model accurately • A reasonable simplification it to describe the total aerodynamic drag force on an object using: • Where ρ is the density of the air (or water, mud, etc.), cd is the coefficient of drag for the object, a is the cross sectional area of the object, and e is a unit vector in the opposite direction of the velocity • In short – create a scaled vector in the opposite direction of velocity

Forces – spring-damper Hooke’s Law

Damping example Animation from http://www.acs.psu.edu/drussell/Demos/SHO/damp.html

Spring-mass-damper system f -f

Springs • At rest length l, the force f is zero • Points are located at r1 and r2 [scalar displacement] [direction of displacement]

Spring-mass system V3 E23 E31 V2 V1 E12 Example – Jello cube http://www.youtube.com/watch?v=b_8ci0ZW4vI

Spring mesh – properties for cloth Each vertex is a point mass Each edge is a spring-damper Diagonal springs for rigidity Angular springs connect every other mass point Global forces: gravity, wind Example http://www.youtube.com/watch?v=ib1vmRDs8Vw

Virtual springs – soft constraints

Physically Based Animation and Modeling