Transcript Uniform Motion - Alejandro Garcia's Web Site

Physics of Animation
Alej Garcia
Dept. Physics
SJSU
www.algarcia.org
Anatomy for Artists
Surgeons and artists learn anatomy, but for very
different purposes.
Thomas Eakins
Leonardo da Vinci
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 Maya
Animation 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
Equal
Distances
4
5
Arbitrary
Rolling ball is an example of uniform motion.
Velocity of the ball is constant (with no friction).
NOTE: In all examples there are an equal number of frames between keys
Uniform Motion in Perspective
Uniform Motion in Perspective
Uniform motion may not appear uniform due to
distortion of scale when shown in perspective.
Horizon Line
Vanishing
Point
Accelerating Motion & Falling
1
1
4
1
2
3
3
9
5
7
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…
4
16
Falling is an example of accelerating
motion (in animation, “slowing out”).
In “Straight Ahead” animation after
drawing keys #1 and #2 the positions
of the rest are given by these rules.
Distance Fallen
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.
Time
(seconds)
Frames
Distance fallen
(key #1 to #2)
1/
24
1
1/
1/
12
2
1 1/3 inches
1/
8
3
3 inches
1/
6
4
5 1/3 inches
6
1 foot
8
1 ¾ feet
12
4 feet
16
7 feet
¾
18
9 feet
1
24
16 feet
¼
1/
3
½
2/
3
3
inch
Falling Bowling Ball
1 (Release)
1 (Release)
2
2
Same
times
3
Bowling ball is one
foot in diameter.
4
Balls falls by one
diameter in the first
six frames.
3
4
5
5
3 frames per key
(and dolly in)
6 frames per key
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
Distance (inches)
1
2
3
4
5
6
7
8
10
12
14
16
18
Time (sec.)
0.07
0.10
0.12
0.14
0.16
0.17
0.19
0.20
0.23
0.25
0.27
0.29
0.30
Release
Catch
Rolling Downhill
1
1
Key #1 is point of release
3
2
3
5
4
Rolling downhill is
also accelerating motion
Very similar to falling except distances are smaller and
depend on the slope of the incline.
7
Demo: Galileo’s Clicking Ramps
Roll balls down notched, inclined ramps
and listen for the clicks.
8
16
24
32
40
48
56
64
Start
1
4
4=2x2
9
16
9=3x3 16=4x4
25
25=5x5
36
49
36=6x6
49=7x7
64
64=8x8
Sliding with Friction
Block
stops
here
Sliding this way
3
5
1
2
1
3
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:…
4
In-betweens of Accelerated Motion
Shooting on Twos (2 frames per key)
1
3
5
Accelerating this way
1 2
1/4 3/4
3
4
5/4
1 frame per key
5
7/4
7
6
9/4
5/4+7/4 = 12/4 = 3
To draw in-betweens of accelerating motion, divide first
distance by 4, then keep the same ratios of 1:3:5:7.
11/4
Falling a la Chai
1
3
1
2
3
1
1
2
3
3
4
5
4
4
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.
8
7
5
5
Real
Falling
Falling
a la Chai
Key #4 is a bit too high but who’ll notice?
Falling a la Chai (Extended)
Real
Falling
Accelerating this way
1
3
1
3
Falling
a la Chai
5
4
Slowing out
7
8
9
11
8
8
Uniform
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.
Falling and Floating
1
3
5
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.
Squirrels cannot
die from a fall.
Hyper-acceleration
Release
1
1
Constant acceleration
3
2
5
3
1
Release
7
4
2
3
Hyper-acceleration
4
If the slope of an incline increases,
the acceleration itself accelerates.
Tipping Over
Brick tipped 2º offbalance then released.
A good example
of hyperacceleration is
an object
tipping over
when offbalance.
No simple way to compute hyper-acceleration.
Acceleration “Stretch”
Objects visually stretch
as they gain speed due to
motion blur.
Objects do not physically stretch as
they fall (not even raindrops).
High-speed
camera
Human eye
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.
Moving & Falling
1
2
3
4
Arbitrary
1
5
3
Ball rolling off of a table combines horizontal and
vertical motion.
6
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.
5
7
7
Demo: Fall and Fire
FALL
1
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.
1
2
1
FIRE
2
3
3
3
5
4
4
Parabolic Arc of Motion
4
1
3
Arbitrary
3
5
Apex
2
Up and down motion is
symmetric, as shown.
Key #4 is highest point of
the arc of motion.
5
1
7
6
7
Bouncing
4
1
3
Bouncing ball losses energy
so it doesn’t bounce up to its
original height.
5
3
2
6
9
Simple way to do
bouncing is to copy
upper part of the arc.
5
1
1
8
10
3
7
11
Bouncing with Squash & Stretch
Stretch is added where motion is the fastest.
Squash is used to emphasize impact on bounce.
Parabolic Arc in Perspective
Maximum height
(ball at midpoint)
VP
HL
Ball starts and ends
on the ground.
Parabolic Arc in Perspective (cont.)
1
VP
HL
3
Add points to the curve by
‘tweening’ from the point of
maximum height.
Spinning and Tumbling
Arbitrary
4
1
3
3
2
5
A spinning object turns by
the same (arbitrary) angle
between keys.
Spinning occurs about the
object’s center of mass.
5
General tumbling motion (e.g., throw a
chair) is very complicated!
1
7
6
Note: If axe is about 10” long then 4 frames between keys.
7
Brick Drop
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.
1
2
3
1
4
3
5
5
6
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.
No force
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
Flower
Vase
Tablecloth
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 Rail
When 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.
Newton’s Second Law (Part 2)
The greater the mass of an object, the less it
accelerates when acted on by the same force.
Free Fall Acceleration
Newton’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?
Air
Resistance
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”, means
a greater force
of 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.
Slow settle, small force
Quick stop, BIG FORCE
X X
Ouch!
Not safe if stake
strikes hard skull
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.
Walking Forward
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.
Action
Reaction
Walk Cycle Timing
Right foot pushes
back to accelerate
forward
Right foot plants,
pushing forward.
Reaction of floor
accelerates you
rearward.
Action
Action
Reaction
Reaction
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.