1. Physically Based Animation and Modeling
CSE 3541
Matt Boggus

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

3. 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

4. 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

5. 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)
Force = change in momentum over time = mass * acceleration

6. 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?

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

8. Physics review, equations for: Zero acceleration Constant acceleration
No acceleration
Constant acceleration f a m
Similarly, you’d need a different equation to handle cases where acceleration is linear, quadratic, or some other higher order. a v’ v
vave

9. 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 ]

10. 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 + 𝑒𝑛𝑑𝑣+𝑣 2 ∗dt [vectors: x, endv, v scalars: 2, dt] v = endv [vectors: endv, v]

11. See spreadsheet example
Comparison of methods
See spreadsheet example

12. Particle Systems Star Trek 2 – genesis sequence (1982) More examples
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

13. 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

14. Particle Example source
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
source
Particle’s birth: constrained and time with initial color and shading (also randomized)

15. 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

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

17. 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
GameObject geom;
// other variables for mass, lifetime, …
public:
void Update(float deltaTime);
void ApplyForce(Vector3 &f) { force.Add(f); }
void ResetForce() { force = Vector3.zero; }
// other methods… };

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

19. 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();

20. Creating GameObjects for(int i = 0; i < numberOfAsteroids; i++){
GameObject aSphere = 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)); }

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

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

23. Forces – gravity

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

25. 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

26. Forces – spring-damper
Hooke’s Law

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

28. Spring-mass-damper systemf -f

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

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

31. 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

32. Virtual springs – soft constraints