physics of motion
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Physics of Animation
Alej Garcia
Dept. PhysicsSJSU
www.algarcia.org
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Anatomy for Artists
Surgeons and artists learn anatomy, but for verydifferent purposes.
Leonardo da VinciThomas Eakins
Life drawing is difficult but its not brain surgery
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Physics for Animators
An engineers calculation of motion needs to behighly accurate, with precise measurements.
Animators, on the
other hand, usuallydont need suchmathematicalprecision. It just hasto look right.
Its not rocket science.
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Motion & Mechanics
The study of motion is a fundamental field ofphysics known as mechanics.
In order to do the fantastic we must first understand the real.
Walt Disney
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Motion & Mechanics
Physical laws apply equally to living characters,living beings are just a little more complex (butthen so is an automobile engine)
Thomas Eakins
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Physics in Maya
Animation software, such as Maya, havesophisticated physics engines that usethe laws of physics to compute motion.
Easier to use these tools knowing physics.
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Its all in the timing
An essential element of animation is the timingbetween frames
Its not
important whatgoes on eachframe of film;its the spacesbetween the
frames that areimportant. Norman McLaren
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Timing: Frames, Keys, & Clocks
Well use three different ways of measuringtime:
Frames (intervals of 1/24th of a second) Keys (given number of frames between poses) Clocks (actual seconds as measured by a clock)
IMPORTANT: Well select the keys such thatthere are always the same number of framesbetween each key.
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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
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Uniform Motion in Perspective
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Uniform Motion in Perspective
Uniform motion may not appear uniform due todistortion of scale when shown in perspective.
Vanishing
Point
Horizon Line
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Accelerating Motion & Falling1
2
3
4
1
3
5
7
1
4
9
16
Falling is an example of acceleratingmotion (in animation, slowing out).
Distance between keys increases in
the ratios 1:3:5:7:9 starting frompoint of release (key #1).
Total distance from point of release
(key #1) increases in the ratios1:4:9:16:25: or 12:22:32:42:52
In Straight Ahead animation afterdrawing keys #1 and #2 the positionsof the rest are given by these rules.
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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
6 1 foot
1/3 8 1 feet
12 4 feet2/3 16 7 feet
18 9 feet
1 24 16 feet
Distance fallen fromkey #1 (release point)to key #2 depends onthe number of framesbetween keys.
Distance fallen fromkey #2 to #3 is threetimes further; from #3to #4 is five times,from #4 to #5 is seven
times, etc.
Note: These distancedo not depend on theobjects weight.
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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 onefoot in diameter.
Balls falls by onediameter in the firstsix frames.
Sametimes
5
5
Falls of diameter inthe first threeframes.
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Demo: Catch a Buck
Put thumb and index fingersnear Washingtons head. Can
you react fast enough tocatch the money?
Half length of dollar bill is 3inch so it takes about 1/8 of asecond (0.125 seconds) to fallthis distance.
Typical reaction time is 0.20 to0.25 seconds.
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Measuring Reaction Time
Release
Catch
Distance (inches) Time (sec.)1 0.072 0.103 0.12
4 0.145 0.166 0.177 0.198 0.2010 0.23
12 0.2514 0.2716 0.2918 0.30
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Rolling Downhill
13
7
1
2
3
4
Rolling downhill isalso accelerating motion
Very similar to falling except distances are smaller anddepend on the slope of the incline.
Key #1 is point of release
5
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Demo: Galileos Clicking Ramps
Roll balls down notched, inclined rampsand 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
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Sliding with Friction
Sliding this way
5 3 1
1 2 3 4
Sliding with friction is another example of acceleratingmotion but in this case the object slows in.
Draw last key (where object stops) first and draw keysleading up to it in the ratios 1:3:5:7:9:
Blockstops
here
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In-betweens of Accelerated Motion
1 3 5 7
62 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 firstdistance by 4, then keep the same ratios of 1:3:5:7.
Shooting on Twos (2 frames per key)
1 frame per key
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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 canapproximate the motion as uniform for the second half of the fall.
Slowing out Uniform
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Falling and Floating
1
3
5
5
5
AcceleratingMotion
UniformMotion
Light objects, such as abeach ball, initially fall withaccelerating motion.
Due to air resistance, themotion transitions to uniformmotion after falling a certaindistance.
For very light objects, suchas a leaf, this transition is
almost immediate.
5
Squirrels cannotdie from a fall.
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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.
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Tipping Over
A good exampleof hyper-acceleration isan objecttipping overwhen off-
balance.
No simple way to compute hyper-acceleration.
Brick tipped 2 off-balance then released.
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Acceleration Stretch
Objects do not physically stretch asthey fall (not even raindrops).
Objects visually stretchas they gain speed due tomotion blur.
Motion blur doesnot depend on theobjects material,however, it will lookmore natural forrigid objects tostretch less thanelastic objects.
High-speedcamera
Human eye
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Moving & Falling
2 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 verticaldistances increasing as 1:3:5:7:
Horizontal distances equally spaced as withuniform motion.
Arc is the combination of uniform horizontalmotion and accelerating vertical motion.
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Demo: Fall and Fire
1
5
3
1 2
3
4 4
2
3
1 FALL FIRE
One ball is releasedand falls straightdown.Other ball is fired
horizontally.At all times theballs are at thesame height.Hit the ground at
the same time.
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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 ofthe arc of motion.
ArbitraryApex
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Bouncing
2
3
4
5
3
1 5
1
6
7
8
9
10
11
3
1Simple way to do
bouncing is to copyupper part of the arc.
Bouncing ball losses energyso it doesnt bounce up to itsoriginal height.
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Bouncing with Squash & Stretch
Stretch is added where motion is the fastest.Squash is used to emphasize impact on bounce.
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Parabolic Arc in Perspective
VP
HL
Ball starts and endson the ground.
Maximum height(ball at midpoint)
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Spinning and Tumbling
2
3
4
5
7
3
15
1
6
7
A spinning object turns by
the same (arbitrary) anglebetween keys.
Spinning occurs about theobjects center of mass.
Note: If axe is about 10 long then 4 frames between keys.
General tumbling motion (e.g., throw achair) is very complicated!
Arbitrary
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12
Brick Drop
5
3
1
3
4
5
6
A brick tipping off of atable combines all theelements describedabove: Hyper acceleration asthe brick tips over. Constant accelerationin the vertical falling.
Uniform velocity in thehorizontal motion. Constant rotation asthe brick falls.
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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!
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Newtons First Law of Motion
An object moves with constant, uniformmotion until acted on by a force.
FORCE
No force
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First Law (Full Version)
An object at rest remains at rest &
an object in motion remains
in uniform motion*,unlessa force acts on the object.
*Moving in a straight line with constant speed.
First Law is also known asprinciple of inertia.
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Demo: Tablecloth Pull
Tablecloth
FlowerVase
Yank quickly
Due to the vases inertia it remains at rest since almostno force acts on the vase if one pulls quickly & straight.
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Demo: Riding Light Rail
When a movingtrain stops, youcontinue movingforward.
When the stoppedtrain starts movingagain, you remainstationary and arethrown backwards.
In both cases, itsdue to your inertia.
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Follow-through & Inertia
Follow-through is agood example of theprinciple of inertia.
An object wont moveuntil a force acts onit so long hair trailsbehind as head turns.
Hair then remains inmotion even afterthe head stops
turning.
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Newtons Second Law (Part 1)
The greater the force on acting on an object,the greater the acceleration of that object.
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The greater the mass of an object, the less itaccelerates when acted on by the same force.
Newtons Second Law (Part 2)
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Free Fall Acceleration
Newtons Second Law explains why heavy andlight objects fall with same acceleration.
Ratio of weightto mass alwaysthe same since
weightdepends onmass.
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Demo: Drop the Sheet
A flat sheet of paper falls slowly because of airresistance.
What happens if we place it on top of a book,blocking the air from reaching it?
AirResistance
Weight
Book and sheet falltogether
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Settle, Squash & Force of Impact
The shorter the settle the greater theforce of impact (since the decelerationis large if an object stops suddenly).
Similarly, less
squash, means
a greater force
of impact.
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Demo: Bed of Nails
One may safely lay or sit on abed of nails, as long as thereare enough nails since theforce per nail is small.
Weight of 150 pounds isdistributed over 300 nails.Force per nail is lb. Need 5lb per nail to pierce skin.
The one thing you never want to
do with a bed of nails is jumpinto bed! Big decelerationmeans big force. Ouch!
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Demo: Vampire Stake
Safest when slowly moving stake placed on asoft, fleshy spot on the chest.
X XOuch!
Quick stop, BIG FORCE
Not safe if stakestrikes hard skull
Slow settle, small force
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Newtons Third Law of Motion
For every action force there is an equalreaction force in the opposite direction.
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Walking, Running & Jumping
What forces accelerate us into motion when wewalk, run, or jump?
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Forces when Walking or Jumping
For a person walking, running, or jumping, thethree 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 personexerting a force on the floor.
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Back foot pushing backon the floor.
Reaction is the friction
of the floor, whichpushes your bodyforward.
If floor is frictionless
then it is impossible tomove forward.
ReactionAction
Walking Forward
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Walk Cycle Timing
ReactionAction Reaction
Action
Right foot pushesback to accelerateforward
Right foot plants,pushing forward.Reaction of flooraccelerates yourearward.
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Jumping
Jumping is done by pushingdownward on the ground(action) so the groundpushes upward on you
(reaction).How high you jump depends
on the force and on thedistance over which you
apply that force.
Can only push while in contactwith the ground so squatting
helps by increasing distance.
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Swinging Arms and Jumping
You swing your arms upward as you jump toincrease the force pushing down on the ground.
Try jumping and swinging your arms upward afteryou leave the ground; you wont jump as high.
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Dont be discouraged
This may seem complicated (and its only Part I)but its no harder than learning anatomy.
Drawing of skeletal arms by Chuck Jones (from Chuck Amock)
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Animation Books with Physics
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The Most Important Law of Motion
The art directoris always right.