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7M836 Animation & Rendering

Animation

Jakob Beetz

J.Beetz@tue.nl

Joran Jessurun

A.J.Jessurun@tue.nl

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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

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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