Physics Based Modeling III
Animation
Lecture 3
Kwang Hee Ko
Gwangju Institute of Science and
Technology
Introduction

What is “Animation”???
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To animate is, literally, to bring to life.
It covers all changes that have a visual effect.
Examples
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Motion dynamics: time varying position
Update dynamics: shape, color, texture,
transparency of an object.
Changes in lighting, camera position, orientation, etc.
Application Areas
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Entertainment industry, education, scientific
visualization, simulation.
Three-Dimensional Animation

Creating images for an animation using a
virtual 3D world involves three steps:
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Modeling
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Setting up the elements in a scene and describing
each of those elements
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Animating
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Rendering
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Converting the description of the objects and their
motion into images
Modeling Requirements
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To animate motion, the user needs


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a static description
information about how that object moves.
To add such additional information, we
use
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Articulated model
Particle system
Deformable objects
Hybrid models
Modeling Requirements

Articulated Model

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A collection of objects connected
together by joints in a hierarchical, treelike structure.
The location of an object is determined
by the location of the objects above it in
the hierarchy.
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
The object at the top of the hierarchy
affect the position and orientation of the
entire model.
Ex. The motion of the elbow joint in a
human model

Affect the position of the lower arm and
the hand and fingers.
Modeling Requirements

Particle System


Collection of points.
The motion of the particles through space is
determined by a set of rules.


Laws of physics.
Suitable for representing water spray, smoke
and flocks of birds
Modeling Requirements

Deformable Objects

Suitable for objects that do not have welldefined articulated joints but have too much
structure to be easily represented with a
particle system.

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Spring-mass lattices, volumetric models, surface
representations, etc.
Water, hair, clothing, etc.
Modeling Requirements

Hybrid Models

Complex systems that require
two or more types of models

Each part of the system to is
modeled by the most appropriate
technique.
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Diver: articulated model.
Pool: deformable model.
Spray: particle system.
Rendering Requirements

Motion Blur

One of the rendering techniques that is required for
animation.
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Anti-aliasing technique for time

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Without motion blur, rapid motion of an object in a
series of frames creates unpleasant strobing effects.
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As opposed to temporal anti-aliasing
Wheels which appear to move in the wrong direction
A fast moving object can be rendered in several of the
positions it had during the period of time represented
by each frame.

Create a blurred representation of the object.
Motion Generation
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The task of specifying the motion of an animated
object to the computer is surprisingly difficult.
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Even animating a simple object like a bouncing ball
can present problems.
Humans are very skilled at observing motion and
quickly detect motion that is unnatural or implausible.
To specify motion
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Keyframing
Procedural methods
Motion capture
Motion Generation
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Key-frame animation
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Creation of key frames
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Inbetweening
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The frames in which the entities being animated are at
extreme or characteristic positions, from which their
intermediate positions can be inferred.
The animator should understand in intimate detail how the
animated object should behave.
The intermediate frames are then filled in.
The entire process of producing an animation is
supposed to be sequential.

But often it could be iterative.
Motion Generation

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The most basic computer animation tools
assist the process of hand animation by
automatically interpolating between the key
frames of images or models.
Problems
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A human inbetweener can perceive the
circumstances of the object being interpolated.

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Is it a falling ball or a rolling ball?
A computer-based system is typically given
only the starting and ending positions.
Interpolation
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Easiest Interpolation: Linear interpolation
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Given the values vs and ve in the starting and
ending frames, the value vt at intermediate
frames is vt = (1-t)vs + tve.
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Can generate unrealistic results.
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Continuous motion
No continuous derivatives
 Abrupt changes in velocity
Interpolation
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Spline Interpolation
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To smooth out interpolation between key
frames.
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Introduce a function f(t).
A value can be interpolated by setting vt = (1-f(t))vs
+ f(t)ve.
A figure drawn as polyline can be interpolated
between keyframes by interpolating each vertex of
the polyline from its starting to ending position.
Interpolation

Defining interpolated shapes
Interpolation

Interpolation of Position and Rotation
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Position
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The position of the center of the body is
specified at certain key frames.
The intermediate positions are interpolated
by some spline path.
The rate at which the spline path is traversed
may be specified as well.
Interpolation

Interpolation of Position and Rotation
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Rotation: Much more difficult than
position
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Euler angle approach
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Rotating Euler angles is not intuitive, leading
to unnatural interpolations of rotations.
Unit quaternion approach
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Intuitive and better interpolation.
BUT!!!
Interpolation
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Unit quaternion approach
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Disadvantages
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Each orientation of an object can actually be
represented by two quaternions.
Orientations and rotations are not exactly the
same thing.

A rotation by 360 is very different from a
rotation by 0 in an animation. But the same
quaterion represents both.
Interpolation
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Unit quaternion approach
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Disadvantages
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Quaternions provide an isotropic method for
rotation.
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The interpolation is independent of everything except
the relation between the initial and final rotations.
Humans strongly prefer cameras to be held upright and
are profoundly disturbed by tilted camera.
Quaternions have no such preferences. Quaternions
should not be used for camera interpolation.
Motion Generation
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Procedural Methods
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A computer procedurally follows the steps in an
algorithm to generate the motion.
Advantages over keyframing techniques
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They make it easy to generate a family of similar motions.
They can be used for systems that would be too complex
to animate by hand such as particle systems or flexible
surfaces.
Physics-based simulation belongs to a class of
procedural methods.

It makes use of the laws of physics to generate motion.
Motion Generation
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Simulated motion is inherently realistic.
Unfortunately, building a new simulation is
a difficult process requiring an in-depth
understanding of the relevant physical
laws.
Simulations can be divided into two
categories
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Passive
Active
Motion Generation
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Passive Simulation
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Passive systems have no internal energy
source and move only when an external force
acts on them.
They are well suited to physically based
simulation.

Pools of water, clothing, hair, leaves, etc.
Motion Generation
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Active Simulation
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Active systems do have an internal source of energy
and can move of their own volition.
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These systems are more difficult to model because
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People, animals, robots, etc.
Implement the physical laws
Specify the behavior of the simulated muscles or motors.
An additional algorithm, a control system, must be
designed to allow the model to walk, run, or perform
other actions.
Motion Generation
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Control System
 A control system for standing
must contain
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Laws that specify how the hips
and knees should move to keep
the figure balanced when one
arm is extended out to the side.
Example
 The runner is an active
simulation.
 A control system generates the
running motion.
 The runner’s clothes are a
passive cloth simulation.
Motion Generation

Control System

Movement of arms
when the upper body
moves (bending the
back).
Motion Generation
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Procedural methods can also be used to
generate motion for groups of objects
that move together.

Flocks of birds, schools of fish, herds of
animals, etc.
Motion Generation
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Motion Capture
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Use special sensors, trackers, to record
the motion of a human performer.
The recorded data is then used to
generate the motion for an animation.
Problems.
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Accurate measurement of the motion of
the human body is tricky.
Due to different dimensions between the
recorded motion and the graphical
objects, noticeable flaws can be
observed.
But this technique is widely used.
Deformable Models in Computer
Graphics: Survey
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Non-Physical Models
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Purely geometric techniques
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They are generally computationally efficient.
They rely on the skill of the designer rather than on
physical principles.
Splines and Patches
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Bezier curves/surfaces, B-spline, NURBS, etc.
Support interactive modification of shape.
Subtle control of object shape is possible.
But precise specification or modification of curves or
surfaces can be laborious.
Deformable Models in Computer
Graphics: Survey

Non-Physical Models
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Free-Form Deformation (FFD)
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It is a general method for deforming objects that provides
a higher and more powerful level of control than adjusting
individual control points.
FFD changes the shape of an object by deforming the
space in which the object lies though mapping.
Ex.Twist about the z-axis
More complex deformations can be constructed by
composing mappings.
Deformable Models in Computer
Graphics: Survey
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Mass-Spring Models
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Non-physical methods for modeling
deformation are limited by the expertise and
patience of the user.
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Deformations must be explicitly specified and the
system has no knowledge about the nature of the
object being manipulated.
Modeling an object as complex as the human face is
a daunting task.
Therefore, physics is considered in the
modeling.
Deformable Models in Computer
Graphics: Survey

Mass-Spring Models
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They are physically based technique that has
been used widely and effectively for modeling
deformable objects.
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An object is modeled as a collection of point masses
connected by springs in a lattice structure.
The spring forces are linear/nonlinear.
Deformable Models in Computer
Graphics: Survey

Mass-Spring Models
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The equation of motion for the entire system are
assembled from the motions of all of the mass
points in the lattice.

The system is evolved forward through time by reexpressing the equations as a system of first-order
differential equations
Deformable Models in Computer
Graphics: Survey

Mass-Spring Models
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They have been used widely in facial animation.
Tension nets: static versions of mass-spring
systems. Kx = f.
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The face is modeled as a two-dimensional mesh of
points warped around an ovoid and connected by
linear springs.
Muscle actions are represented by the application of
a force to a particular region of nodes.
Deformable Models in Computer
Graphics: Survey

Mass-Spring Models

Dynamic mass-spring systems to facial
modeling
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A three-layer mesh of mass points based on three
anatomically distinct layers of facial tissue:
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The dermis
A layer of subcutaneous fatty tissue
The muscle layer
Deformable Models in Computer
Graphics: Survey

Mass-Spring Models
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Dynamic mass-spring systems to facial modeling
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Facial models are created
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Different spring constants were used to model the
different layers based on tissues properties.
Manually
Using a radial laser-scanned image data
Computer Tomography (CT)
Prediction of the post-operative appearance of patients
whose underlying bone structure has been changed
during cranio-facial surgery.

Spring stiffness for the system is derived from tissue
densities obtained by CT image data.
Deformable Models in Computer
Graphics: Survey

Mass-Spring Models
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Mass-spring models combined with free-form
deformations are used to animate muscles in
human character animation.
A mass-spring model for deformable bodies is
used to model a transition change from solid to
liquid.
Mass-spring systems can be used to generate
“artificial fish”.
Deformable Models in Computer
Graphics: Survey

Mass-Spring Models
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Advantages
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Simple, well understood dynamics
Easy to construct.
Can be animated at rates not possible with other
techniques
Interactive and real-time simulation is possible.
Well suited to parallel computation.
Drawbacks
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The discrete model is a significant approximation of the
true physics that occurs in a continuous body.
Proper values of spring constants may not be easily
obtained.
“Stiffness” issue: numerical instability would occur.

Large spring constants to model objects that are nearly rigid.
Deformable Models in Computer
Graphics: Survey

Continuum Models

Accurate physical models treat deformable
objects as a continuum.
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bodies with mass and energies distributed
throughout.
Modeling itself can be derived based on the
assumption of continuum. But ultimately
computation is discrete.
Deformable Models in Computer
Graphics: Survey

Continuum Models
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The full continuum model of a deformable
object considers the EQUILIBRIUM of a general
body acted on by external forces.
The object deformation is a function of the
acting forces and the object’s material
properties.
The object reaches equilibrium when its total
energy is at a minimum.

П=Λ-W
Deformable Models in Computer
Graphics: Survey

Continuum Models

To determine the equilibrium shape of the
object,
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Both Λ and W are expressed in terms of the object
deformation.
Λ is the total strain energy of the deformable object
W is the work done by external forces
The total potential reaches a minimum when the
derivative of the total potential with respect to the
material displacement function is zero.

This approach leads to a continuous differential
equilibrium equation.
Deformable Models in Computer
Graphics: Survey

Continuum Models

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A closed-form analytic solution of the
differential equation is not always possible.
We instead find an approximate solution to the
equation.

FEM method.
Deformable Models in Computer
Graphics: Survey

The use of FEM in computer graphics has
been limited because of the computational
requirements.

In real-time applications, it has proven difficult
to use FEM.

The force vectors and the mass and stiffness
matrices are computed by integrating over the object,
they must, in theory, be re-evaluated as the object
deforms.

The re-evaluation is very costly.
Deformable Models in Computer
Graphics: Survey

FEM Methods
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Advantage

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Provide a more physically realistic simulation than
mass spring methods with fewer node points.
Disadvantages

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Significant pre-processing time.
If the topology of the object changes during the
simulation, or if the object shape changes beyond
small deformation limits, the mass and stiffness
matrices must be re-evaluated during the simulation.

Meshless approach???
Deformable Models in Computer
Graphics: Survey

Approximate Continuum Models

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Physically motivated, but adhere less strictly to
the laws of physics than the FEM methods.
Snakes
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One-dimensional deformable curves that are often
used to deform or define edges or contours or to
tract motion in a moving image.
Discretized deformation energy
Hybrid models
Deformable Models in Computer
Graphics: Survey

Low Degree of Freedom Models

Discretization of the physically based models
leads to systems with many degrees of
freedom.

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A large number of node points
The systems are slow to simulate, limiting their use in
interactive and real time settings.
Alternative approximate continuum models

They restrict the deformable object to many fewer
degrees of freedom, sacrificing generality for speed.
Deformable Models in Computer
Graphics: Survey

Low Degree of Freedom Models
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Modal Analysis
Dynamic Global Deformation
Minimal Energy Surfaces