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 animationLow 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

L3L2L1

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 softwareVRML

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.

L3L2L1

Target(x,y)L1 L2 L3?

?

?

Basex = 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

L3L2L1

Goal

End effector

distance

Base

G(a) = (xg – x)2 + (yg – 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) = (xg – (L1cos(a1)+L2cos(a2)+L3cos(a3)))2 +

(yg – (L1sin(a1)+L2sin(a2)+L3sin(a3)))2

High Level Techniques (contd.)

Nonlinear Optimization

minimize G(a) subject to mta = b1

mta <= b2

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-lecture11.pdf