Computer Animation
Animation
• Animate = “to give life to”
• Specify, directly or indirectly, how ‘thing’ moves
in time and space
Angel Games
Animation Applications
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Special Effects (Movies, TV)
Video Games
Virtual Reality
Simulation, Training, Military
Medical
Robotics, Animatronics
Visualization
Communication
Animation
• How do we describe and generate motion of
object in the scene?
Animation File Formats
Software
File Format
Director
.dir & .dcr
Animator Pro
.fli
Studio Max
.max
SuperCard and Director
.pics
Windows Audio Video Interleaved
.avi
Macintosh
.qt & .mov
Motion Video
.mpeg
CompuServe
.gif
Flash
.swf
Shockwave
.dcr
Web Page Animation File Formats
(1)
• GIF Files
–GIF89a’s ability to store a sequence
of images has been used to provide a
cheap and cheerful form of small
animation for Web page
advertisements.
Web Page Animation File Formats
•
(2)
GIF Shortcomings:
However, even when GIF animation is properly
implemented and enabled, it has many
shortcomings.
1) Sound can not be added.
2) Colour palette is restricted to 256.
3) Images are losslessly compressed.
QuickTime
• For animation of any duration, especially if it is
accompanied by sound, the best result will be
achieved using a video format, and QuickTime
has become the standard.
Heritage of Animation
• Persistence of vision: discovered about 1800s
– Zoetrope or “wheel of life”
– Flip-book
Heritage of Animation
• Camera to make lifeless things move
– Meleis 1890 using simple tricks
– Emil Cohl (1857-1938, French)
Disney: Animation as an art form
• Innovations
– Story board to review story
– Pencil sketch to review motion
– Multi-plane camera stand
– Color (not first to use color)
– Sound!
• Steamboat Willie (1928)
Two main categories
• Computer-assisted animation
– 2D & 2 1/2 D
– Inbetweening
– Inking, virtual camera, managing
data, etc
• Computer generated animation
– Low level techniques
• Precisely specifying motion
– High level techniques
• Describe general motion behavior
Low level techniques
• Shape interpolation (in-betweening)
• Have to know what you want
High level techniques
• Generate motion
with set of rules
or constraints
– Physically based
motion
http://www.cs.berkeley.edu/~job/Projects/SoundGen/video.html
Why animation works
• The eye cannot register images faster than
approximately 60 frames per second
(30 is just about adequate)
• If a gap in the projection occurs, the eye seems to
perform spatial interpolation over the gap
Animation and Frame Rates
• TV video builds 30 entire frames or pictures
every second.
• Movies are shot at a shutter rate of 24
frames per second, but using projections
tricks the flicker is increased to 48.
• On some projectors each frame is shown 3
times before the next frame, for a total of 72
flickers per second which helps eliminate
the flicker effect.
• Cel Animation – plays at 24 frames per
second.
Displaying animation sequences
• To achieve smooth animation, a sequence of
images (frames) have to be presented on a screen
with the speed of at least 30 per second
• Animations frames can be
– pre-computed in advance and pre-loaded in memory
– computed in real time (e.g. movement of the cursor)
Raster animation
• This is the most common animation technique
• Frames are copied very fast from off-screen
memory to the frame buffer
• Copying can be applied to
– complete frames
– only parts of the frame which contain some movement
Examples
Ship is redrawn in background colour
Step 1 (erase)
(x,y)
Step 2 (move)
(x,y)
(x+Dx,y+Dy)
x’ = x + Dx
y’ = y + Dy
Move ship
Step 3 (draw)
(x’,y’)
Double buffering
• Used to achieve smooth animation
• The next frame of animation is computed to
an off-screen buffer at the same time when
the current frame is transferred to the frame
buffer.
Create
Frame
Load to the
frame buffer
Create
Frame
Load to the
frame buffer
Create
Frame
Load to the
frame buffer
Time
2-D Animation
Two types:
Cel animation
Path animation
Cel Animation
• Made famous by Disney
• 24 frames per second therefore a minute
may require as many as 1,440 separate
frames.
• It is based on changes that occur from one
frame to the next.
• Cel stands for celluloid which is a clear sheet
with images drawn on them.
• The celluloid images are place on a
background that is usually stationary.
• The background remain fixed as the images
changes.
Cel Animation
• Those elements in a scene that might move are
drawn on sheets of transparent material known as
‘cel’, and laid over a background drawn separately.
Path Animation
• Moves an object along a predetermined path on
the screen
• The path can be a straight line or have a number of
curves.
• Starts with keyframes (the first and last frame of an
action).
• The series of frames in between the keyframes are
drawn in a process called tweening.
• Tweening requires calculating the number of
frames between keyframes and the path the action
takes, and then actually takes, and then sketches a
series of progressively different outlines.
3-D Animation
• 3-D Animation involves three steps: modeling,
animation, and rendering
Modeling – the process of creating objects and
scenes
Animation – the process of defining the object’s
motion
Rendering – the final step in creating 3-D
animation.
• Morphing is the process of blending two images
into a series of images
• Warping allows you to distort a single image
• Virtual reality (VR) creates an environment that
surrounds the user so that they become part of the
experience.
Hybrid Forms of Animation
• Mixing cel and 3-D
• Combining animation with live footage such as
Jurassic Park.
• Add time -> 4D
Steps of a simple computer animation
1. Creating animation sequences
– object definition
– path specification (for an object or a camera)
– key frames
– in-betweening
2. Displaying the sequences
– raster animation
– colour-table animation
Object definition
• In simple manual systems, the objects can be
simply the artist drawings
• In computer-generated animations, models are
used
• Examples of models:
– a "flying logo" in a TV advert
– a walking stick-man
– a dinosaur attacking its prey in Jurassic Park
Character Development
• 300 Drawings
Character Development
• 40 Sculptures
Character
Development
• Computer
Models
Storyboarding
• Explicitly define
– Scenes
– Camera shots
– Special effects
– Lighting
– Scale
• Used as guide by
animators
Layout and Look
• Build scenery
• Match colors
Path specification
• Impression of movement can be created for two
basic situations, or for their combination:
– static object, moving camera
– static camera, moving object
• The path defines the sequence of locations (for
either the camera or the object) for the
consecutive time frames
Static object, moving camera
Time
F1
F5
F2
F4
F3
Static camera, moving object
F1
F2
F3
F4
It is important to remember that when the
object moves along the path, not only its
position changes, but also its orientation
Y
Y
Z
Z
X
X
Keyframing
ACM © 1987 “Principles of traditional animation applied
to 3D computer animation”
s(t )
Describe motion of objects as a function of time
from a set of key object positions. In short,
compute the inbetween frames.
Key frames
• Compute first a small number of key frames
• Interpolate the remaining frames in-between
these key frames (in-betweening)
• Key frames can be computed
– at equal time intervals
– according to some other rules
– for example when the direction of the path changes
rapidly
In-betweening
• The simplest method of in-betweening is linear
interpolation
• Interpolation is normally applied to the projected
object points
1’
1
3’
3
added point
2’
2
Key frame k
Halfway frame
Key frame k+1
In-betweening - example
• Given coordinates of a 2D point
– key frame n: (xn,yn)
– key frame n+1: (xn+1,yn+1)
– time interval between the two key frames: 1/10 second
• To get smooth animation, needs at least 30 frames per
second
• Solution: insert at least further 2 frames between the
given two key frames
Keyframes and In-Betweening
Before
In-betweens
After
Calculating in-between frames using linear interpolation
x = (xn+1 - xn) / 3
 y = (yn+1 - yn) / 3
for ( i=1; i<3; i++ )
{
xi = xn + i * x
yi = yn + i * y
}
Example: Interpolating Positions
• Given positions:
• find curve
(x i , y i ,t i ), i  0,
 x (t )
C (t )  

y
(
t
)


(x 2 , y 2 , t 2 )
C (t )
such that
,n
x i 
C (t i )   
y i 
( xu0 , y 0 , t 0 )
(x 1 , y 1 , t 1 )
0
Linear Interpolation
(x 2 , y 2 , t 2 )
(x 0 , y 0 ,t 0 )
(x 1 , y 1 , t 1 )
• Simple problem: linear interpolation between
first two points assuming t 0 =0 and t 1=1 :
• The x-coordinate for the complete curve in the
figure: x (t )  x 0 1  t   x 1t
Linear Interpolation
• Two Problems with Linear
Interpolation
– Unnatural movement
• Nothing really moves like this – motion
begins and ends instantaneously, with
objects attaining their full velocity as soon
as they start to move, and maintaining it
until they stop.
• Solution: using hand-made animation
Polynomial Interpolation
(x 2 , y 2 , t 2 )
(x 0 , y 0 ,t 0 )
(x 1 , y 1 , t 1 )
parabola
• An n-degree polynomial can interpolate any n+1 points. The
Lagrange formula gives the n+1 coefficients of an n-degree
polynomial that interpolates n+1 points. The resulting
interpolating polynomials are called Lagrange polynomials.
Easing In
• The object accelerate from a standstill to its final
velocity.
(Hodkins, http://www.cc.gatech.edu/classes/cs8113a_98_spring/principles.pdf)
(Hodkins, http://www.cc.gatech.edu/classes/cs8113a_98_spring/principles.pdf)
Rigid body animation
• Rigid body animation uses standard 3D
transformations
• At least 30 frames per second to achieve smooth
animation
• Computing each frame would take too long
(Hodkins, http://www.cc.gatech.edu/classes/cs8113a_98_spring/principles.pdf)
Robotic Arm Example
•
•
•
•
Fingers first
Then wrist
Then elbow
Finally,
shoulder
Robotic Arm Example
y
R2
T2
R1
T1
T3
R3
T4
P
x
Find the new location of P (P’) after some
translations T1, T2, T3, T4 and rotations R1, R2, and
R3.
Express in terms of a matrix product, i.e.
P’ = R1R2R3P
Robotic Arm Example
y
P’
P
T4
P’ = T4P
x
Robotic Arm Example
y
P’’ = R3P’ = R3T4P
P’
R3
P’’
x
Robotic Arm Example
y
P’’’
P’’’ = T3P’’ = T3R3T4P
T3
P’’
x
Robotic Arm Example
y
P’’’
P4 = R2P’’’ = R2T3R3T4P
R2
P4
x
Robotic Arm Example
y
P5
T2
P4
P5 = T2P4 = T2R2T3R3T4P
x
Robotic Arm Example
y
P5
R1
P6
P6 = R1P5 = R1T2R2T3R3T4P
x
Robotic Arm Example
y
P7
T1
P6
P7 = T1P6 = T1R1T2R2T3R3T4P
x
Robotic Arm Example
y
R2
T2
R1
T1
T3
R3
T4
P7
T1
P6
P7 = T1P6 = T1R1T2R2T3R3T4P
x
Robotic Arm Example
y
R2
T2
R1
T1
T3
T4
P7
R3
x
P7 = T1P6 = T1R1T2R2T3R3T4P
3D Transforms
Pretty much exactly the same as
2D transforms
y
y
x
z
T
T
x
Physically Based Animation
• Assign physical properties to objects
(masses, forces, inertial properties)
• Simulate physics by solving equations
• Realistic but difficult to control
v0
m
g
Topics in Animation
• Scripted Animation
– Keyframe interpolation, articulated models,
inverse kinematics, deformations, …
• Procedural Animation
– Particle Systems, Flocks, Crowds, Cloth, Fire,
Smoke, Water, …
• Motion capture
– Filtering, editing, retargeting, stitching,…
76
Procedural animation
• describes the motion algorithmically
• express animation as a function of small number of
parameters
• Example: a clock with second, minute and hour hands
– hands should rotate together
– express the clock motions in terms of a “seconds” variable
– the clock is animated by varying the seconds parameter
Procedural animation
78
Scripted Animation
79
Motion capture
80
Motion Capture
• Usually uses optical markers and multiple
high-speed cameras
• Triangulate to get marker 3D position
• Faces or joints
• You must observe someone do something
(Hodkins, http://www.cc.gatech.edu/classes/cs8113a_98_spring/)
Quiz
• I sat in the car, and realized the side mirror is
0.4m on my right and 0.3m in my front
• I started my car and drove 5m forward, turned
30 degrees to right, moved 5m forward again,
and turned 45 degrees to the right, and
stopped
• What is the position of the side mirror now,
relative to where I was sitting in the
beginning?