Final exam date Final exam date has been announced: Articulated - - PDF document

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Articulated Figures I

Introduction Forward Kinematics Spacetime Constraints

Final exam date

 Final exam date has been announced:

 Tuesday, February 27, 2007  2:45 - 4:45pm  70-1435

Projects

 Presentations:

 Dates:

 Week 9: Wed, Feb 14  Week 10: Mon, Feb 19  Finals Week: Tues, Feb 27 (2:45-4:45)

 15 minutes / presentation  Schedule now on Web  Please send me choice of time/day

Project

 Mid-quarter report

 Due Friday, January 26th  Update on progress  Dropbox in mycourses.

Assignments



Assignment 1 -- Framework



Most have been graded



Assignment 2 -- Keyframing



Most have been graded.



Assignment 3 -- Billiards



Due Jan 26th (Friday)



Assignment 4 -- Group Motion



To be given today (both options)



Due Feb 7th.



NOTE: Dropbox close dates have been fixed.

Logistics

 Course Withdrawal deadline

 Friday, January 26th

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Plan for today

 Next 2 weeks: Articulated Figures

 Today: Forward Kinematics  Monday: Inverse Kinematics  Wednesday: Motion Capture  Monday: Advanced algorithms

 Then

 Wednesday: Character animation

Motivation Films

 Film featuring articulated figures.

Motivational Film

 Eurythmy (1989)

 Susan Amkraut and Michael Girard (Ohio

State)

 Based on the OSU work on the use of

inverse kinematics and dynamics for animation.

 Interview w/Amkraut and Girard on Web

Motivational Film

 Grinning Evil Death (1990)

 Mike McKenna (MIT Media Lab)

Plan For Today

 Topics

 Intro to Articulated Figures  Forward Kinematics  Spacetime Constraints

Building an animated character

 Rigging

 The process of preparing a character

model for animation, including setting up an underlying skeleton, complete with constraints, controllers and kinematic systems, and linking it to the mesh of the character model.

3 Building an animated character

 Skeleton

 An underlying network of bones used to define

and control the motion of a model during character animation. Moving a bone causes the mesh of the model to move and deform.

 Skinning

 The process of binding the surface of a model to

the underlying skeleton during character rigging.

Articulated Figures

 What is an articulated figure?

 A set of rigid objects connected by joints  Individual joints are linked together in a

parent-child hierarchy

 Each object has a joint at one end where

any child bones may be attached.

 The skeleton

Articulated Figures Articulated Figures

 main figure is described in terms of a

global frame of reference

 each individual joint is assigned its own

separate local co-ordinate frame of reference

 This coordinate system is with respect to

it’s parent.

 Can concatenate transformation matrices

Articulated Figures Articulated Figures

 TBW = transformation of B wrt world  TAW = transformation of A wrt world  TBA= transformation of B wrt A

AW BA BW

T T T

• =

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Articulated Figures Articulated Figures

 Given in graph form

Articulated Figures

 Now let’s consider rotations

Articulated Figures

 Multiple joints

Articulated Figures

 Most rendering systems / API maintain

a transformation matrix stack

 Push when going into the hierarchy  Pop when leaving the hierarchy

Articulated Figures

 Stack of transformation matrices

Arm wrt body Body wrt world Hand wrt arm Finger wrt hand

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Articulated Figures

robot base Upper body arm thumb

Articulated Figures

 We know how to transform of each

component with respect to another component.

 Use the matrix stack in order to calculate

the local coordinates of each component.

Articulated Figures

Define your camera orientation Push Matrix Concatenate transformation for robot as a whole PushMatrix Concatenate transformations for robot base wrt the center of the robot Draw robot base Pop Matrix Push matrix Concatenate transformations for robot body wrt the center of the robot Draw robot body …

Articulated Figures

Push Matrix Concatenate Transformations of Arm wrt body Draw arm Push Matrix Concatenate Transformation of Thumb wrt Arm Draw thumb Pop Matrix // Thumb Pop Matrix // Arm Pop Matrix // body Pop Matrix // robot

Articulated Figures

 applets  Questions?

Joint Constraints

 Note that translation should not be allowed.  Any joint is only permitted to rotate about the

three local axes of its parent joint.

 However, you may wish to limit the extent of

rotation

 Disallow rotation about one of the axes  Provide rotational constraints to a given axis.

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Degrees of freedom

 Degrees of freedom

 Number of parameters

whose values must be defined in order to fully position the articulated figure



44 DOF: 38 (joint angles) + 6 (position and orientation)

Degrees of freedom

 Motion data can be defined as

 f(t) – function of time  One function for each degree of freedom

 How many functions is that?

 For a CG character

 Typically 40-50 DOF

 For a real human

 > 250 DOF

 Purpose of animation

 Provide values to each of the DOF for each time

step.

Animation Control

 Purpose of animation

 Provide values to each of the DOF for each time step.

 So how does one do this?

 Keyframing – curve editors  Kinematics – based on position / velocity  Procedural  Dynamics – use physics  Use heuristics  Use AI  Motion capture  Using sampled data.

 Questions?

Animator control

End Effectors

 End effectors

 Term, borrowed from robotics, that

describes the end of a jointed link

 Also can be described as the bottom node

in a hierarchy

End Effectors

robot base Upper body arm thumb

Motion spaces

 Joint space

 Multidimensional space of joint angles  Dimensionality = degrees of freedom

 End effector space

 Multidimensional space of end effectors  Dimensionality = number of end effectors  Essentially described in world coords

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Forward vs Inverse Kinematics

 Forward Kinematics

 Define values for joint angles  Determines positions of end effectors  X = f (θ)

 Inverse Kinematics

 Define positions of end effectors  Determine joint angles to make it so  θ = f-1 (X)

Forward vs Inverse Kinematics

Joint space θ Space X X = f (θ) θ = f-1 (X) Forward Kinematics Inverse Kinematics

Inverse Kinematics

 Goal directed motion

 Reach over and grab that thing!  Note: roach motion (Grinning Evil Death) was goal directed

 Easier to specify  Harder to compute  More on Inverse Kinematics next time.  Questions?  Break

Standard Human Hierarchies

 H-Anim

 Goals

 specify a way of defining interchangeable

humanoids and animations in standard VRML 2.0 without extensions.

 Animations include limb movements, facial

expressions and lip synchronisation with sound.

 Our goal is to allow people to author

humanoids and animations independently.

Standard Human Hierarchies

 H-Anim

 Standard link/joint hierarchy with limits and

constraints

 Based on anatomical references

H-Anim

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H-anim Examples

 Nancy  Baxter  Dilbert

MPEG-4

 The MPEG-4 standard, initiated in 1995, aims

at proposing tools for efficient coding of multimedia scenes.

 efficient coding of diverse kind of data :

 Video Objects  StillTexture Objects  Face Objects  Body Objects  Mesh Objects

MPEG-4 and VRML

 Work of MPEG-4 systems group was

inspired and based on VRML.

 MPEG-4 = VRML + extensions.

Body Animation in MPEG-4 Body Animation in MPEG-4

 BAP (Body Animation Parameter) contains

296 parameters describing the topology of the skeleton.

 Interoperates with the work of the H-Anim group

 The BDP set defines the set of parameters to

transform the default body to a customized body optionally with its body surface, body dimensions, and texture.

Take Home Message

 There are standards for human body

hierarchies

 Any others?

 In the game word perhaps?

 Questions?

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Dynamics

 To get realistic motion, go to the source

Dynamics

 Determine values for DOF by simulation

• f physical forces.

 Problem with dynamics

 Little animator control  Animator provides initial conditions  Simulation does the rest  Can we give back some control to the

animator?

Spacetime Constraints

 Method developed by Witkin and Kass

(1988)

 Goals:

 Benefits of realistic physically based motion  Provide animator with a bit more control  Experimented with Luxo

Spacetime Constraints

 Animator specifies:

 The character’s physical structure

 I.e. Articulated figure

 What the character has to do

 Jump from here to there

 What physical resources are available

 Character’s muscles, floor to push off of

 How motion should be performed

 “Don’t waste energy”

Spacetime Constraints

 The problem turns into a constrained

• ptimization problem

 Find values Sj that minimize R subject to Ci

(Sj) = 0

 Si = DOF and forces for all time steps  Ci = constraints  R = minimization criteria

 Given these, there are well known

numerical techniques to solve

Spacetime Constraints

 Luxo

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Spacetime Constraints

 For luxo:

 Unkowns

 joint angles

 Constraints

 Laws of physics (forces: gravity and from joint

muslces)

 Initial/final positions (from here to there)  Hard gravitational constraints (don’t go through

floor)

Spacetime Constraints

 For luxo

 Minimization criteria

 Power consumed by the joint muscles

Spacetime Constraints

 Space time constraints

 Results – Luxo  Another example – Spacetime Chopsticks

Spacetime Constraints

 Challenges

 Specifying constraints  Choosing minimization criteria

 Problems

 Solves for parameters over entire time

interval.

 Can be computationally expensive

Spacetime Constraints

 Opened the door for creating physically

based, yet animator controlled, animation

 Other approaches (which we will consider in a

couple of weeks)

 Genetic motion – solves minimization problem using

genetic algorithms

 General procedural motion – applying procedural shading

paradigm to motion.

 Questions?

Next Time

 Details of Inverse Kinematics  Questions?