Upcoming DeadlinesFifth Homework (Video analysis of Path of Action):

Due Friday, September 25th (This Friday); 15 points (10 points if late)

Sixth Homework (Outline of First Term Paper)Due Wednesday, September 30th

Campus-wide Furlough Day Monday, October 19th(Art/Phys 123 will meet on Wed., Oct. 21st)

For full schedule, visit course website:ArtPhysics123.pbworks.com

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Homework Assignment #5Shoot reference of yourself doing a running jump. Use the Tracker software to mark your path of action while

in the air (tracking center of torso).Upload image showing track and graphs for one of your

jumps to your blog.Record a clip showing the tracked motion.Upload both original reference and the tracked Quicktime

clip to your blog.For details, see course website; for an example, see the

course blog.This assignment is due by 8am on Friday, September 18th

(This Friday). 15 points

Homework Assignment #6Write a one-page outline for your first

term paper.

The general topic for your first term paper is:The Laws of Physics in an Animation Universe

Modern science is based on the principles of experimental observation and theoretical analysis; in this assignment you will apply these principles in a critical analysis of animation and special effects.

Homework Assignment #6For the term paper, you will select an animation film (or a

live-action film featuring CGI animation special effects).

You will then formulate three distinct scientific hypothesis for the universe portrayed in that film (which may or may not obey the same physical laws as the real world).

For example, in your animation’s universe the laws gravity may be different (e.g., heavy objects may fall faster than light objects).

Homework Assignment #6Your hypotheses should be such that there is

relevant observational evidence in the film; you need to describe what that evidence is and how it supports your theories.

You will also formulate competing theories and present evidence that the universe portrayed in your film does not follow those alternate hypotheses.

Homework Assignment #6For this homework assignment you are to choose the film

that you'll analyze and write a one-page outline for the term paper.

Post this outline on your blog; an example has been

posted on the course blog.

This assignment is due by 8am on Wednesday, September 30th. (10 points; 5 points if late)

Note: The term paper will be due in mid-October.

Arcs in Animation

Disney’s Principles of AnimationIn their classic book, Disney Animation – The Illusion of Life, Frank Thomas and Olie Johnston list a set of basic principles for animation.1. Squash & Stretch2. Timing3. Anticipation4. Staging5. Follow Through

& Overlapping Action

6. Straight Ahead & Pose-to-Pose Action

7. Slow In and Slow Out8. Arcs9. Exaggeration10. Secondary

Action11. Appeal

Disney’s Principles of AnimationIn their classic book, Disney Animation – The Illusion of Life, Frank Thomas and Olie Johnston list a set of basic principles for animation.1. Squash & Stretch2. Timing3. Anticipation4. Staging5. Follow Through

& Overlapping Action

6. Straight Ahead & Pose-to-Pose Action

7. Slow In and Slow Out8. Arcs9. Exaggeration10. Secondary

Action11. Appeal

We have already discussed several of these principles of animation, specifically:

Disney’s Principles of AnimationIn their classic book, Disney Animation – The Illusion of Life, Frank Thomas and Olie Johnston list a set of basic principles for animation.1. Squash & Stretch2. Timing3. Anticipation4. Staging5. Follow Through

& Overlapping Action

6. Straight Ahead & Pose-to-Pose Action

7. Slow In and Slow Out8. Arcs9. Exaggeration10. Secondary

Action11. Appeal

Today we will discuss arcs and how they relate to animated motion.

Arcs of MotionMotion usually follows an arc, which may be simple, like a circle. or very complex and irregular.

Importance of Arcs

One of the major problems for the inbetweeners is that it is much more difficult to make a drawing on an arc.Drawings made as straight inbetweens completely kill the essence of the action.

Disney animation legends Frank Thomas and Olie Johnston write:

Circular ArcsCircular arcs are common since motion is often around a fixed pivot point, such as a joint.

Speed in Circular MotionRotational Speed: Revolutions per secondTangential Speed: Total distance per

secondSame Rotational Speed

Different Tangential Speeds

Throwing Arm TangentialSpeed

The longer the throwing arm, the greater the tangential speed so the farther it can throw. Sling lengthens

the arm at almost no cost in the weight.

Doubling the arm lengthquadruples the range!

Timing on Circular Arcs

In this golf swing the motion:• Slows out (accelerates) to hit the ball• Uniform after the hit• Slows in as the swing finishes follow-through

A circular arc is a simple path of action but the timing may be complex and textured.

Slow out

Unifo

rm

Slow in

Rolling & Slipping1 2 3 4 5 6 7

Rolling ball turns one revolution when it travels a distance equal to three times its diameter (actually 3.1416 diameter)

ROLLING

1 2 3 4 5

SLIPPING

Slipping and rolling are both uniform in spacing and rotation.

Wagon Wheel IllusionIn this illusion, the wheel seems to spin backwards.

Often seen in westerns

Nyquist EffectIn this illusion is due to persistence of vision.

The brain tracks the movement of the spokes by looking for the nearest location on each frame. This effect limits how fast a wheel can spin in an animation and still be seen as turning.

ActualRotation

Illusion

#1#2

Wheel on frames#1 and #2

Uniform Rotation in PerspectiveThe timing for uniform rotation has texture when seen in perspective.

Half orbit

Quarterorbit

Rotation from key #1 to #5 in background takes twice as long as from #6 to #8 in foreground.

Non-Uniform Circular MotionTwo common types of motion on circular arcs that have non-uniform timing and spacing are:

Exponential Spacing Pendulum Spacing

Example:Tipping over

Example:Stride inwalking

Tipping OverTipping over is a common example of motion on a circular arc. Two ways to tip over:

XX

Center tipped past point of contact

Center past an edge

Tipping RotationA brick rotates about a point as it tips;that point is the center of a circular arc.

XX

Friction tends to keep the brick from sliding until it loses contact with the table.

X

X

As the slope of the incline increases, the acceleration itself accelerates.

Exponential Spacing1

3

7

1

2

3

4

Constant acceleration (Odd Rule)Release

5

1

2

3

4

Release

Exponential Spacing

Slowing out from a tipping point is very slow initially, but then accelerates rapidly.

Rolling off a Tipping Point

1 2 3 4 56

7

8

Peak

Play

Anticipation & Exponential Spacing

Texture of the timing as the brick tips over creates anticipation, which you want at the start of a scene

Also notice motion blur near

top of brick, which has large

tangential speed.

Pendulum SpacingA pendulum’s path of action is also a circular arc but the spacing is very different from the exponential spacing of tipping over.

Spacing & Timing in SwingingA pendulum will slow in and out as it swings back and forth, the same as a ball rolling in a half-pipe.

Most of the texture in the timing is at the endpoints; the timing is even in the center.

Play

Motion GraphThe motion graph (angle vs. frame) confirms that the timing is mostly textured at the apexes.

Frame

Angl

e#1

#4

#7

Swinging in PerspectiveVisually the timing has even more texture when the swing occurs in perspective.

Who Framed Roger Rabbit? (1988)

The opening sequence in Who Framed Roger Rabbit? makes great use of the textured timing of arcs in perspective.

Animation byRichard Williams

Demo: Don’t FlinchPendulum swings back and forth yet it doesn’t hit your face.

Bowling Ball Pendulum

Play

This clip lets you experience what it’s like to do this demo.

SpiralsA spiral is just a circular arc with a radius that’s either increasing (spiral out) or decreasing (spiral in).

Concept art fromPirates of the Caribbean 3

Rotational Speed in SpiralsIf the radius decreases without pulling the object inward then the rotational speed increases (due to shrinking radius) but the tangential speed stays constant.

Spiral In

Spacings along the curve stay constant.

Demo: Interrupted Pendulum

Tangential speed does not increase due to the pendulum whipping around the interrupt bar.

Energy is not increased by the interrupt bar so ball swings back to the same spot.

Bar

An “interrupt” bar changes the radius of the arc for a pendulum.

Rotation in Spirals (cont.)If the radius decreases by pulling the object inward then the rotational speed increases due to shrinking radius and due to an increase in the tangential speed.

Spiral In

Spacings along the curve get

bigger and bigger.

Demo: Skater’s Spin

SlowRotation

FASTRotation

Exert a force to pull hand weights toward my body, causing a big increase in rotational and tangential speeds

Rotation in Spirals (cont.)If the tangential speed decreases (say by friction) but inward force constant then the rotational speed still increases.

Spiral In

Spacings along the curve get

shorteryet it

stillspinsfaster

and faster.Coin Vortex

How Does the Brick Fall?Does the brick rotate and then fall down the side of the table?

XX

No! The brick does not fall this way.

XX

4

3

2

1

Play

Forces on the Tipping Brick

XX

The table pushes on the brick upward and towards the right.

Gravity pulls downward

Center of the brick shifts down and towards the right.

If no table…

Pushing Off by the TableThe table pushes away on the brick, which causes the brick to move away from the table as it falls.

X

X

X

Once it loses contact with the table, only the force of gravity accelerates the brick.

Centrifugal Force

What we see

What theinsect feels

Insect inside a can rotating in a circle

When we move on an arc, it seems to us as if there is an outward force, pushing us away from the center of the circle.

Physicists call this apparent force the centrifugal force.

Class Demo: Bucket Overhead

I will put a bucket full of water over my head without getting wet. How?

CentrifugalForce

By rotating it fast enough.The water stays in the

bucked as if pressed into it by a centrifugal force.

You experience centrifugal force on taking a sharp turn

Wile E. Coyote & Loop-D-LoopPlay

In reality, it is impossible to travel upside-down, as Wile E. Coyote does in this scene. True or False?

“Beep Beep” (1952)

Demo: Loop-the-LoopIf the speed of the ball is large then not only does it stay on the track, the ball even pushes outward and against the rail.

Velocity

Release

GAP

Demo: Loop-the-LoopBall could even circle a loop with a gap, if the speed was just right so gravity was equal to the centrifugal force.

Velocity

Release

Simulated GravityCentrifugal force could be

used to simulate gravity in a space station.

With the right rate of rotation a person on the outer rim would feel as if they stood on the surface of Earth.

Scientifically accurate in the movie 2001: A Space Odyssey (1968)

Rotation

Simple Spinning1

5

7

3

1Arbitrary 2

3

4

In simple spinning, the angle rotates at a constant rate.

A brick tipped 45º as it loses contact with the table will fall spinning about 30º every two frames.

A falling brick may turn by simple spinning around its center.

Tumbling1

5

7

3

1Arbitrary 2

3

4

There is no simple way to describe tumbling. However, the brick’s center still follows the same path of action.

A falling brick may turn by a more complicated tumbling motion.

Tennis Racket TheoremWhen an object turns about its long or its short axis, it tends to spin.

When an object turns about its middle axis, it tends to tumble.

SPIN

SPIN

Irregular Objects

SPIN

SPIN

SPIN

SPIN

Spin or Tumble?

Rotation around two of these axes is spinning.The axis of rotation that tumbles is:A)Head-to-toe axisB)Side-to-side axisC)Front-to-back axis

A

B

C

Next LectureCreating Action

By Friday of this week:Complete the 5th homework

(Video analysis of Path of Action)

Please return the clickers!