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 L3L2 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) L1L2L3 ? ? ? 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 L3L2 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 spring-2001/cs395-lecture11.pdf