Physics Bases Animation

Question 1

2 common approaches to physics-based animation

Answer 1

Particle systems - fire, smoke, waves
Mass spring models - ideal for cloth animation

Question 2

What are particle systems

Answer 2

A way of modelling dynamics
Lots of points described by their current state and position
No interaction between particles
Modelling by Ordinary Differential Equations

Question 3

What are attributes of a particle

Answer 3

position, initial velocity, entry angle, lifespan, colour, etc

Question 4

Simplest case of point dynamics

Answer 4

Each particle is independent
Often have a lifetime or age
If there is enough randomness at the emitter, we can get nice effects (eg sand, water, fire)

Question 5

What are mass spring models

Answer 5

Used to model deformable objects like cloth
The surface is represented as a set of points
The forces between neighbouring points keeps the surface coherent
(Not independent like the particle system)

Question 6

Solving ODEs, Newtonian approach

Answer 6

Common second order ODE
F= ma
Can be rewritten:
F = m . d2x / dt2
(acceleration is the second derivative of position)

Can then solve using dv/dt = F / m

Question 7

Eulers method

Answer 7

h is small step size
t1 = t0 + h
X1 = X0 + h f(X0,t0)
X0 is position at time 0, and we are taking a step forward via h f(X0,t0) to X1

If we are at X(t) we want to know where the position will be after infinite number of small scale steps
f(X,t) is the external force (eg a wind)
multiplied by h gives the particle movement

Question 8

How can Eulers method be inaccurate

Answer 8

When moving along a tangent it becomes inaccurate
Eg when forming a circle, it always spirals outwards

Question 9

What is a Force

Answer 9

Changes the motion of a system
When there are no forces, motion continues uniformly in a straight line
Depends on position, time and velocity

For point masses, forces are vectors

Types of forces: gravity, spring

Question 10

What is Viscous Damping

Answer 10

Dampening force on a particle determines its velocity
It opposes the motion - eg Honey or wind resistance
It removes energy so the system can settle
A small amount of damping can stabilise a solver
Too much damping makes the emotion appear like glue or honey

Question 11

What are spatial fields

Answer 11

Externally specified forces or velocity fields
The force on particle i depends only on its position
These add energy
These spatial fields can also be procedural

Question 12

Modeling a hair

Answer 12

Each particle is linked to two other particles except the end points
We try to keep the forces that separate the two particles in the link constant
Forces are equal but just in different direction
- Essentially connected via a spring
Then we define a string force using hooke’s law

Question 13

Force of a spring

Answer 13

is always proportional to rest length L0

Question 14

Hooke’s law

Answer 14

K is the stiffness value
Fs = -kx
Fs = spring force
k = spring constant
x = spring stretch or compression

Question 15

Modeling a string

Answer 15

Springs link the particles
Drag them to make sure they preserve the length of the string - there are still oscillations that at some point stabilise at a rest state

Question 16

Modeling lots of hair

Answer 16

Deformation forces are proportional to the angle between segments to make it curly
External forces such as gravity or wind

Question 17

What are 3 types of forces

Answer 17

• Structural forces
  Tries to enforce invariant properties of the system like the distance between two particles to be constant
• Internal deformation forces
  For example a string deforms and tries to remain flat
• External forces
  Like gravity, wind, friction