Download 7M836 Animation & Rendering

7M836 Animation & Rendering
Animation
Jakob Beetz
Joran Jessurun
[email protected]
[email protected]
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Next Week
Subject: Virtual Reality
When: June 2nd
Where: Design Systems Lab. (Vertigo 9.16)
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Animation
• History of cartoon and computer animation
• Extensive description of techniques and algorithms
Rick Parent
Computer Animation, Algorithms and Techniques
www.cis.ohio-state.edu/~parent/book/outline.html
• How to make an animation
• Examples
www.pixar.com
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Animation
• Animation
– “To give live to”
– Make objects change over time
according to scripted actions
– By showing a sequence of fast
changing images
• Series images (frames)
– Film 24 fps
– Video 30 fps => 1 hour animation 108000 frames
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What can be animated?
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Position and orientation of objects
Geometry (shape) and scaling of objects
Illumination
Reflection
Camera
• In fact, everything!
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Animation process - traditional
• Storyboard
– The story
– Sequence of images with descriptions
• Key frames
– Draw a number of important images (key frames)
– Motion-based description
• Inbetweens
– Draw the rest of the frames
• Painting
– Redraw frames onto cels
– Color them in
• Put animation onto film
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Computer animation
• Computer animation pipeline
– 3D modeling
– Motion specification
Key framing
– Motion simulation
– Rendering
– Post-processing
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Keyframe animation
• Each “keyframe” specified by a number of key-parameters
(state)
• Inbetweening: Interpolate these parameters
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Keyframe animation
• For each key parameter, specify value at “important”
frames
• Computer creates path for each parameter by interpolating
this key parameter for inbetween frames
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Interpolation
• Linear interpolation
– Usually discontinuities
– Not a smooth movement
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Interpolation
• Spline interpolation
– Smooth transitions
– Beware of unwanted side effects
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Interpolation – speed control
• Include velocity of interpolation
– It is often more realistic to start a movement slowly,
then speed up, and end it again slowly
– Use speed curve
• Speed curve relates time with position on
interpolation spline
• Position on interpolation spline determines
interpolated key parameter value
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Interpolation – speed control
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Keyframing summarized
• Specification of key frames/parameters
– Determine key parameters and their values at certain
important points in time
– Specify type of interpolation
• Specify speed curve for interpolation
• Computer generates inbetween frames
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Animation of articulated structures
• Articulated structure:
– Object consists of a number of (sub-)objects (links)
connected by joints
– Each joint is specified by at least one (key-)parameter
– Movement of object described by changing parameter
values
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Examples of joints
• Constraints on joints
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Articulated structure
• Skeleton consists of 14
joints
• Each joint has 2 or 3
degrees of freedom
• Some parameters
constrained
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Kinematics
• Kinematics is the study of movement of (hierarchical)
objects
– Position, orientation, velocity, acceleration
– Without taking into account dynamic properties (forces)
(dynamics)
• Forward kinematics
• Inverse kinematics
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Forward kinematics
• Animator sets parameter values for joints
• Computer computes positions/orientations for links links:
X  f (1 , 2 )
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Forward kinematics
• Animation by specification / interpolation of joint
parameters
1
2
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Forward kinematics
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Forward kinematics
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Forward kinematics
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Kinematics
• What to do when animation knows the desired endposition of the (sub-)object?
– E.g. to grab something?
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Inverse kinematics
• Animator specifies position (and orientation) within scene
at wich link (end-effector) has to be positioned
• Computer computes joint parameter values to get link at
desired position:
1 , 2  f 1 ( X)
• After that. computer computes positions of all links by
applying these joint parameter values for all joints
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Inverse kinematics
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Inverse kinematics
• Animation by specification / interpolation of end-effector
position
x
y
• Or animation by interpolation of joint parameter values at
start and end frame
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Inverse kinematics
• Problems
– Often more than one solution
• Extra requirements to solution
– Result not always desired path (e.g. collisions)
– What to do when end-effector position specified outside
operation area of object?
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Inverse kinematics
• Inverse kinematics is also used to compute dependency of
joint parameter values
– E.g. for object with closed loops
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Kinematics summarized
• Forward kinematics
– Animator controls through joint parameters
– Direct control over object state
– Often many parameters to control
• Inverse kinematics
– Animator controls through position/orientation endeffector
– Simpler specification of movements
• Less parameters
• Better feeling for positions in scene
– Complex computations
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Rigid Body Simulation
Mechanical systems that have:
Rigid bodies
Springs
Contact and
collisions
Joints
Friction
Examples:
Vehicle
Bridge
Rope
Human
Robot arm
Tower of cards
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Rigid Body Simulation
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Physical process
Model
Simulation algorithm
Computer program
Object properties (e.g.
position, orientation,
linear and angular
momentum, mass)
Calculate change in
objects’ positions,
velocities, momenta
Calculate forces
(e.g. wind, gravity,
viscosity)
Calculate
accelerations from
objects’ masses
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Simulating position
x(t  t )  x(t )  v(t )  t
v(t  t )  v(t )  a(t )  t
F  m a
t  0.5
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Position
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Velocity
0
-2 0
-4
-6
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0
x(0)   
0
 5
v(0)   
 5
 0
a(t )   
  1
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Simulating rotational movement
• Angular velocity
• Torque
• Inertia Tensor is the angular
equivalent of mass
• Inertia Tensor is dependent on the
orientation of the body
P(t )  mv(t )
L(t )  I (t ) (t )
 (t )
v (t )
x(t )
 i (t )  (ri (t )  x(t ))  Fi (t )
ri (t )
x(t )
Fi (t )
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Springs
• Spring Force
spring
Fi ,spring


F
 k  (dist i , j (t )  leni , j )  vi , j
j
i, j
• Dampers
Fi damper  k d  vi (t )
mass point
spring
damper
mass point
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Collision
• Detecting the occurrence of collision
• Computing the response to those collisions
Point p at t(i-1)
F  k  d
d
Point p at t(i)
Penalty force
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Friction
• Static friction
Fs   s  FN
• Kinetic friction
Fk   k  FN
Parallel component
Applied force
Perpendicular component
(Normal force)
Normal
Ff
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Constraints
• Hard constraints
• Soft constraints
• Joints are constraints
• Point-spline constraint
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Flexible objects
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Spring-Mass-Damper model
Each vertex is a point mass
Between vertices a spring
Add interior springs to create
stability
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3D Max Reactor examples
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Demo1 – pencils fall out of cup
Demo2 – shoot cannon ball against wall that fractures
Demo3 – create box on a rope and let it swing
Demo4 – create a piece of cloth, let the wind blow and
drop something on it
• Demo5 – vehicle down a ramp and a simple roller coaster
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