1 7M836 Animation & Rendering Animation Jakob Beetz [email protected] Joran Jessurun...
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Transcript of 1 7M836 Animation & Rendering Animation Jakob Beetz [email protected] Joran Jessurun...
1
7M836 Animation & Rendering
Animation
Jakob Beetz
Joran Jessurun
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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 ParentComputer 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 timeaccording to scripted actions
– By showing a sequence of fastchanging images
• Series images (frames)
– Film 24 fps
– Video 30 fps => 1 hour animation 108000 frames
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What can be animated?
• 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
– Motion simulation
– Rendering
– Post-processing
Key framing
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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:
),(fX 21
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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 end-position 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:
• After that. computer computes positions of all links by applying these joint parameter values for all joints
)X(f, 1
21
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Inverse kinematics
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Inverse kinematics
• Animation by specification / interpolation of end-effector position
• Or animation by interpolation of joint parameter values at start and end frame
x
y
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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 end-effector
– Simpler specification of movements
• Less parameters
• Better feeling for positions in scene
– Complex computations
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Rigid Body Simulation
Rigid bodies Joints Contact and collisions Friction
Springs
Mechanical systems that have:
Examples:
Bridge Rope Robot arm
VehicleHuman
Tower of cards
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Rigid Body Simulation
• Physical process
• Model
• Simulation algorithm
• Computer program
Object properties (e.g. position, orientation, linear and angular momentum, mass)
Calculate forces (e.g. wind, gravity,
viscosity)
Calculate accelerations from objects’ masses
Calculate change in objects’ positions,
velocities, momenta
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Simulating position
ttvtxttx )()()(
ttatvttv )()()(
amF
-8
-6
-4
-2
0
2
4
6
8
10
12
14
0 10 20 30 40 50 60
Position
Velocity
5.0t
5
5)0(v
0
0)0(x
1
0)(ta
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Simulating rotational movement
)(tx
)(tv
)(t
)(tFi
)())()(()( tFtxtrt iii
)(tx
)(tri
• Angular velocity
• Torque
• Inertia Tensor is the angular equivalent of mass
• Inertia Tensor is dependent on the orientation of the body
)()()(
)()(
ttItL
tmvtP
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Springs
• Spring Force
• Dampers
)(tvkF iddamper
i
jijijispringji
springji vlentdistkFF ,,,,, ))((
mass point mass point
damperspring
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Collision
• Detecting the occurrence of collision
• Computing the response to those collisions
dkF Point p at t(i-1)
d
Point p at t(i) Penalty force
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Friction
• Static friction
• Kinetic friction
Nss FF Parallel component
Perpendicular component(Normal force)
Applied force
Normal
Ff
Nkk FF
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Constraints
• Hard constraints
• Soft constraints
• Joints are constraints
• Point-spline constraint
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Flexible objects
• 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
• 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