physics of animation alej garcia dept. physics sjsu
TRANSCRIPT
Physics of Animation
Alej GarciaDept.
Physics SJSUwww.algarcia.org
Anatomy for Artists
Surgeons and artists learn anatomy, but for very different purposes.
Leonardo da VinciThomas Eakins
Life drawing is difficult but it’s not brain surgery
Physics for Animators
An engineer’s calculation of motion needs to be highly accurate, with precise measurements.Animators, on the other hand, usually don’t need such mathematical precision. It just has to look right.
It’s not rocket science.
Motion & Mechanics
The study of motion is a fundamental field of physics known as mechanics.
“In order to do the fantastic we must first understand the real.” Walt Disney
Motion & Mechanics
Physical laws apply equally to living characters, living beings are just a little more complex (but then so is an automobile engine)
Thomas Eakins
Physics in MayaAnimation software, such as Maya, have
sophisticated physics “engines” that use the laws of physics to compute motion.
Easier to use these tools knowing physics.
It’s all in the timing…
An essential element of animation is the timing between frames
“It’s not important what goes on each frame of film; it’s the spaces between the frames that are important. “ Norman McLaren
Timing: Frames, Keys, & Clocks
We’ll use three different ways of measuring time:
• Frames (intervals of 1/24th of a second)• Keys (given number of frames between poses)• Clocks (actual seconds as measured by a clock)
IMPORTANT: We’ll select the keys such that there are always the same number of frames between each key.
Uniform Motion
1 2 3 4 5
EqualDistances
NOTE: In all examples there are an equal number of frames between keys
Rolling ball is an example of uniform motion.Velocity of the ball is constant (with no friction).
Arbitrary
Uniform Motion in Perspective
Uniform Motion in Perspective
Uniform motion may not appear uniform due to distortion of scale when shown in perspective.
Distance
s are
equally-sp
aced, in
perspecti
ve.
VanishingPoint
Horizon Line
Accelerating Motion & Falling
1
2
3
4
1
3
5
7
1
4
9
16
Falling is an example of accelerating motion (in animation, “slowing out”).
Distance between keys increases in the ratios 1:3:5:7:9… starting from point of release (key #1).
Total distance from point of release (key #1) increases in the ratios 1:4:9:16:25:… or 12:22:32:42:52…
In “Straight Ahead” animation after drawing keys #1 and #2 the positions of the rest are given by these rules.
Distance FallenTime (seconds)
Frames Distance fallen (key #1 to #2)
1/24 1 1/3 inch
1/12 2 1 1/3 inches
1/8 3 3 inches
1/6 4 5 1/3 inches
¼ 6 1 foot
1/3 8 1 ¾ feet
½ 12 4 feet
2/3 16 7 feet
¾ 18 9 feet
1 24 16 feet
Distance fallen from key #1 (release point) to key #2 depends on the number of frames between keys.
Distance fallen from key #2 to #3 is three times further; from #3 to #4 is five times, from #4 to #5 is seven times, etc.
Note: These distance do not depend on the object’s weight.
Falling Bowling Ball
1 (Release)
2
3
3 frames per key(and dolly in)
4
6 frames per key
4
3
2
1 (Release)
Bowling ball is one foot in diameter.
Balls falls by one diameter in the first six frames.
Same times
5
5
(6 frames)
(12
fram
es)
Falls ¼ of diameter in the first three frames.
Demo: Catch a Buck
Put thumb and index fingers near Washington’s head. Can you react fast enough to catch the money? Half length of dollar bill is 3 inch so it takes about 1/8 of a second (0.125 seconds) to fall this distance.
Typical reaction time is 0.20 to 0.25 seconds.
Measuring Reaction Time
Release
Catch
Distance (inches) Time (sec.)1 0.072 0.103 0.124 0.145 0.166 0.177 0.198 0.2010 0.2312 0.2514 0.2716 0.2918 0.30
Rolling Downhill
13
7
1
2
3
4
Rolling downhill isalso accelerating motion
Very similar to falling except distances are smaller and depend on the slope of the incline.
Key #1 is point of release
5
Demo: Galileo’s Clicking Ramps
Roll balls down notched, inclined ramps and listen for the clicks.
Start
1 4 9 16 25 36 49 64
8 16 24 32 40 48 56 64
4=2x2 9=3x3 16=4x4 25=5x5 36=6x6 49=7x7 64=8x8
Sliding with Friction
Sliding this way
5 3 1
1 2 3 4
Sliding with friction is another example of accelerating motion but in this case the object “slows in.”
Draw last key (where object stops) first and draw keys leading up to it in the ratios 1:3:5:7:9:…
Blockstopshere
In-betweens of Accelerated Motion
1 3 5 762 4
3/4 5/4 7/4 9/4 11/41/4
531
5/4+7/4 = 12/4 = 3
Accelerating this way
To draw in-betweens of accelerating motion, divide first distance by 4, then keep the same ratios of 1:3:5:7.
Shooting on Twos (2 frames per key)
1 frame per key
Falling a la Chai
1
2
3
4
1
3
5
7
An approximation to real falling that’s easy to use for pose-to-pose animation
Recipe for “Falling a la Chai”:• Draw interval from first & last keys.• Divide interval in half. Mark a key.• Divide top part in half. Mark a key.• Divide top part in half.• Divide top part in half. Mark a key.
5
1
2
3
4
1
3
4
8
5
RealFalling
Fallinga la Chai
Key #4 is a bit too high but who’ll notice?
Falling a la Chai (Extended)
1
1
3
3 4
5 7 9 11
8 8 8
Accelerating this wayReal
Falling
Fallinga la Chai
The most noticeable acceleration occurs in the initial “slowing out.”
Though the separations increase as an object accelerates, you can approximate the motion as uniform for the second half of the fall.
Slowing out Uniform
Falling and Floating1
3
5
5
5
Accelerating Motion
Uniform Motion
Light objects, such as a beach ball, initially fall with accelerating motion.
Due to air resistance, the motion transitions to uniform motion after falling a certain distance.
For very light objects, such as a leaf, this transition is almost immediate.
5
Squirrels cannot die from a fall.
Hyper-acceleration
13
7
1
2
3
4
Constant accelerationRelease
5
1
2
3
4
Release
Hyper-acceleration
If the slope of an incline increases, the acceleration itself accelerates.
Tipping Over
A good example of hyper-acceleration is an object tipping over when off-balance.
Release
At 4º in ½ second
At 15º in
1 second
At 5
7º in
1½
seco
nd
No simple way to compute hyper-acceleration.
Brick tipped 2º off-balance then released.
Acceleration “Stretch”
Objects do not physically stretch as they fall (not even raindrops).
Objects visually stretch as they gain speed due to motion blur.
Motion blur does not depend on the object’s material, however, it will look more natural for rigid objects to stretch less than elastic objects.
High-speed camera
Human eye
Moving & Falling2 3 4
5
7
3
1Arbitrary 5
1
6
7
Ball rolling off of a table combines horizontal and vertical motion.
Falling starts with key #4, with vertical distances increasing as 1:3:5:7:…
Horizontal distances equally spaced as with uniform motion.
Arc is the combination of uniform horizontal motion and accelerating vertical motion.
Demo: Fall and Fire1
5
3
1 2
3
4 4
2
3
1FALL
FIRE
One ball is released and falls straight down.Other ball is fired horizontally.At all times the balls are at the same height.Hit the ground at the same time.
Parabolic Arc of Motion
2
3
4
5
7
3
15
1
6
7
Up and down motion is symmetric, as shown.Key #4 is highest point of the arc of motion.
ArbitraryApex
Bouncing
2
3
4
5
3
1 5
1
6
7
8
9
10
11
3
1Simple way to do bouncing is to copy upper part of the arc.
Bouncing ball losses energy so it doesn’t bounce up to its original height.
Copy
Bouncing with Squash & Stretch
Stretch is added where motion is the fastest.Squash is used to emphasize impact on bounce.
Parabolic Arc in Perspective
VP
HL
Ball starts and ends on the ground.
Maximum height (ball at midpoint)
Parabolic Arc in Perspective (cont.)
VP
HL
1
3
Add points to the curve by ‘tweening’ from the point of maximum height.
Spinning and Tumbling
2
3
4
5
7
3
1 5
1
6
7
A spinning object turns by the same (arbitrary) angle between keys.
Spinning occurs about the object’s center of mass.
Note: If axe is about 10” long then 4 frames between keys.
General tumbling motion (e.g., throw a chair) is very complicated!
Arbitrary
1 2
Brick Drop
5
3
1
3
4
5
6
A brick tipping off of a table combines all the elements described above:• Hyper acceleration as the brick tips over.• Constant acceleration in the vertical falling.• Uniform velocity in the horizontal motion.• Constant rotation as the brick falls.
What creates action?
Various types of physical motion are:
• Uniform motion (no acceleration)• Constant acceleration• Hyper-acceleration (non-constant)
But why do objects accelerate?Answer: Forces!
Newton’s First Law of Motion
An object moves with constant, uniform motion until acted on by a force.
FOR
CE
No force
First Law (Full Version)
An object at rest remains at rest &an object in motion remains
in uniform motion*,
unless a force acts on the object.
*Moving in a straight line with constant speed.
First Law is also known as principle of inertia.
Demo: Tablecloth Pull
Tablecloth
FlowerVase
Yank quickly
Due to the vase’s inertia it remains at rest since almost no force acts on the vase if one pulls quickly & straight.
Demo: Riding Light RailWhen a moving train stops, you continue moving forward.
When the stopped train starts moving again, you remain stationary and are thrown backwards.
In both cases, it’s due to your inertia.
Follow-through & Inertia
Follow-through is a good example of the principle of inertia.
An object won’t move until a force acts on it so long hair trails behind as head turns.
Hair then remains in motion even after the head stops turning.
Newton’s Second Law (Part 1)
The greater the force on acting on an object, the greater the acceleration of that object.
The greater the mass of an object, the less it accelerates when acted on by the same force.
Newton’s Second Law (Part 2)
Free Fall AccelerationNewton’s Second Law explains why heavy and
light objects fall with same acceleration.
Ratio of weight to mass always the same since weight depends on mass.
Demo: Drop the Sheet
A flat sheet of paper falls slowly because of air resistance.
What happens if we place it on top of a book, blocking the air from reaching it?
AirResistance
Weight
Book and sheet fall together
Settle, Squash & Force of Impact
The shorter the “settle” the greater the force of impact (since the deceleration is large if an object stops suddenly).
Similarly, less“squash”,
meansa greater forceof impact.
Demo: Bed of Nails
One may safely lay or sit on a bed of nails, as long as there are enough nails since the force per nail is small.
Weight of 150 pounds is distributed over 300 nails. Force per nail is ½ lb. Need 5 lb per nail to pierce skin.
The one thing you never want to do with a bed of nails is jump into bed! Big deceleration means big force. Ouch!
Demo: Vampire Stake
Safest when slowly moving stake placed on a soft, fleshy spot on the chest.
X XOuch!
Quick stop, BIG FORCE
Not safe if stake strikes hard skull
Slow settle, small force
Newton’s Third Law of Motion
For every action force there is an equal reaction force in the opposite direction.
Walking, Running & Jumping
What forces accelerate us into motion when we walk, run, or jump?
Forces when Walking or Jumping
For a person walking, running, or jumping, the three main forces on the person are:
• Gravity (Downward)• Support of the floor (Upward)• Frictional force of the floor (Horizontal)Only these forces can accelerate the person.Gravity is constant but the force exerted by
the floor can increase in reaction to the person exerting a force on the floor.
Back foot pushing back on the floor.
Reaction is the friction of the floor, which pushes your body forward.
If floor is frictionless then it is impossible to move forward.
ReactionAction
Walking Forward
Walk Cycle Timing
ReactionAction Reaction
Action
Right foot pushes back to accelerate forward
Right foot plants, pushing forward. Reaction of floor accelerates you rearward.
Jumping
Jumping is done by pushing downward on the ground (action) so the ground pushes upward on you (reaction).
How high you jump depends on the force and on the distance over which you apply that force. Can only push while in contact
with the ground so squatting helps by increasing distance.
Swinging Arms and Jumping
You swing your arms upward as you jump to increase the force pushing down on the ground.
Try jumping and swinging your arms upward after you leave the ground; you won’t jump as high.
Don’t be discouraged…
This may seem complicated (and it’s only Part I) but it’s no harder than learning anatomy.
Drawing of skeletal arms by Chuck Jones (from Chuck Amock)
Animation Books with Physics
The Most Important Law of Motion
The art director is always right.