Animating Speed Position and
Orientation
Presented by
Kailash Sawant
Hemanth Krishnamachari
Introduction
animate
vb
1. To impart life to, 2. To give
sprit and vigor to, 3. To make appear to move
Introduction (contd.)
Aspects of Animation
Motion Dynamics: Changes in position and
orientation of objects
Update Dynamics: Changes in shape,
structure, color and texture of objects
Changes in lighting and camera position and
lighting
Classification of Computer
Animation
Computer

assisted animation &
Computer generated animation
Low level techniques &
High level techniques
Low Level Techniques
includes techniques, such as shape
interpolation algorithms (in

betweening)
the animator usually has a fairly specific idea of
the exact motion that he or she wants.
Low Level Techniques (contd.)
Key

Framing
frames selected on the basis of importance are
called Key

Frames
each Key

Frame has a set of parameters like
position and orientation associated with the
frame
Low Level Techniques (contd.)
In

Betweening
includes drawing intermediate frames between
two Key

Frames
given initial and final frames, the computer
uses interpolation to generate intermediate
frames
Low Level Techniques (contd.)
Interpolation Example
Low Level Techniques (contd.)
Limitations of Interpolation
Rotations that achieve same change in
orientation e.g.. 0 degrees, 360 degrees
cannot be differentiated
changes in camera orientation cannot be
reflected
High Level Techniques
animator sets up the rules of the model, or
chooses an appropriate algorithm, and selects
initial values or boundary values; the system is
then set into motion
this approach requires among other things the
study of dynamics and kinematics of the object
these techniques are capable of describing
complex motions such as that of a roller
coaster or a leaf falling of a tall tree
High Level Techniques (contd.)
Governing Aspects
Dynamics
Procedural Motion
Motion Capture
Kinematics
High Level Techniques (contd.)
Dynamics
study of forces that cause motion
considers object

properties such as mass,
size, moment of inertia, velocity, etc.
Illustration of Dynamics in
Animation
Dynamics (contd.)
Rigid Body Dynamics
how things move under the influence of given
forces
governed by Lagrangian/Hamiltonian
mechanics
given set of contacts between rigid bodies,
equations determine forces, acceleration,
velocities and deformations
Dynamics (contd.)
Issues in Rigid Body Dynamics
detecting contact changes between bodies
–
collisions
–
separations
simulation and modeling collisions
–
elastic collisions
–
inelastic collisions
High Level Techniques (contd.)
Animation Example
Car Crash
Dynamics (contd.)
Roller Coaster Animation
motion governed by Euler

Lagrange
equations
equations are solved numerically
–
Gaussian elimination and Newton

Raphson
iteration for algebraic equations
–
Runge

Kutta iteration for solving differential
equations
High Level Techniques (contd.)
Animation Example
High Level Techniques (contd.)
Governing Aspects
Dynamics
Procedural Motion
Motion Capture
Kinematics
High Level Techniques (contd.)
Procedural Motion
control of motion
functions governing movement over time
attributes:

position, velocity,color, size
High Level Techniques (contd.)
Procedural Motion Example
High Level Techniques (contd.)
Governing Aspects
Dynamics
Procedural Motion
Motion Capture
Kinematics
High Level Techniques (contd.)
Motion Capture
capturing live motion
–
e.g. actor strapped with electric sensors
motion control using accumulated motion

data
–
e.g. computer generated characters
High Level Techniques (contd.)
Motion Capture Tools
Software
–
Kaydara FiLMBOX
–
Famous 3D
–
Life Forms Studio
–
Poser
Accessories
–
Datagloves
–
Cybergloves
–
Face Trackers
–
MotionCaptor
High Level Techniques (contd.)
Governing Aspects
Dynamics
Procedural Motion
Motion Capture
Kinematics
High Level Techniques (contd.)
Kinematics
study of motion independent of underlying
forces
Forward Kinematics
Inverse Kinematics
High Level Techniques (contd.)
Forward Kinematics Example
Woman Walking
High Level Techniques (contd.)
Forward Kinematics
motion of all joints specified explicitly
motion of links determined by indirect
methods
High Level Techniques (contd.)
Forward Kinematics e.g.
Base
a1
a3
a2
L3
L2
L1
Target(x,y)
x = L1*cos(a1) + L2*cos(a2) + L3*cos(a3)
y = L1*sin(a1) + L2*sin(a2) + L3*sin(a3)
High Level Techniques (contd.)
Applications of Forward Kinematics
animation films
algorithmic animations
High Level Techniques (contd.)
Softwares employing Forward
Kinematics
DE/MEC mechanism design software
VRML
High Level Techniques (contd.)
Inverse Kinematics
final position is specified
math equations used to determine position and
orientation of joints that lead to the final
position
High Level Techniques (contd.)
Inverse Kinematics e.g.
L3
L2
L1
Target(x,y)
L1
L2
L3
?
?
?
Base
x = L1*cos(a1) + L2*cos(a2) + L3*cos(a3)
y = L1*sin(a1) + L2*sin(a2) + L3*sin(a3)
High Level Techniques (contd.)
Inverse Kinematics
x = L1*cos(a1) + L2*cos(a2) + L3*cos(a3)
y = L1*sin(a1) + L2*sin(a2) + L3*sin(a3)
three variables and two equations
thus infinitely many solutions
High Level Techniques (contd.)
Solving Inverse Kinematics Equations
Non linear programming
Differential kinematics
High Level Techniques (contd.)
Non Linear Programming (NLP)
method to optimize a nonlinear function
–
e.g. x(y+1) + sin(x+y) = 0
subject to x>=0 , y>0
objective function
constraint
iterative algorithm
High Level Techniques (contd.)
Inverse Kinematics as NLP
using goal potential function
–
distance from end effector to the goal
–
function of joint angles G(a)
minimization of goal potential function
High Level Techniques (contd.)
Our Example
a1
a3
a2
L3
L2
L1
Goal
End effector
distance
Base
G(a) = (x
g
–
x)
2
+ (y
g
–
y)
2
High Level Techniques (contd.)
Computations
x = L1*cos(a1) + L2*cos(a2) + L3*cos(a3)
y = L1*sin(a1) + L2*sin(a2) + L3*sin(a3)
G(a) = (x
g
–
(L1cos(a1)+L2cos(a2)+L3cos(a3)))
2 +
(y
g
–
(L1sin(a1)+L2sin(a2)+L3sin(a3)))
2
High Level Techniques (contd.)
Nonlinear Optimization
minimize G(a)
subject to
m
t
a = b
1
m
t
a <= b
2
High Level Techniques (contd.)
Available NLP Packages
LANCELOT
MATLAB
DONLP2
High Level Techniques (contd.)
Issues with NLP
unreachable workspace
–
G(a) may not always be zero
local minima
–
solution may not be found
redundancy
–
solution may not be unique
High Level Techniques (contd.)
Differential Kinematics
uses Jacobian matrix
linearly relates end effector change to joint
angle change
High Level Techniques (contd.)
Applications of Inverse Kinematics
video games
interactive process control simulation
Summary
we have discussed and presented the fundamental aspects of
controlling speed position and orientation in animations
a terse account of various techniques for the same has been
provided
math involved with High level animation techniques is quite
intricate and beyond the scope of this document. Details can be
obtained from the enlisted references
References
Computer Animation Concepts

Len Dorfman
Inverse Kinematics Positioning Using Non Linear
Programming
–
ACM press New York

Janimin Zhao , Norman. I Badler
Kinematic Model Of Human Spine And Torso

G. Monhett , N. I. Badler
http://www.cs.vassar.edu/~ellman/old

courses/395

spring

2001/cs395

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