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Animating Speed Position and Orientation

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

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Animating Speed Position and Orientation

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  1. Animating Speed Position and Orientation Presented by Kailash Sawant Hemanth Krishnamachari

  2. Introduction • animatevb 1. To impart life to, 2. To give sprit and vigor to, 3. To make appear to move

  3. 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

  4. Classification of Computer Animation • Computer-assisted animation & Computer generated animation • Low level techniques & High level techniques

  5. 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.

  6. 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

  7. 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

  8. Low Level Techniques (contd.) Interpolation Example

  9. 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

  10. 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

  11. High Level Techniques (contd.) Governing Aspects • Dynamics • Procedural Motion • Motion Capture • Kinematics

  12. High Level Techniques (contd.) Dynamics • study of forces that cause motion • considers object-properties such as mass, size, moment of inertia, velocity, etc.

  13. Illustration of Dynamics in Animation

  14. 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

  15. Dynamics (contd.) Issues in Rigid Body Dynamics • detecting contact changes between bodies • collisions • separations • simulation and modeling collisions • elastic collisions • inelastic collisions

  16. High Level Techniques (contd.) Animation Example Car Crash

  17. 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

  18. High Level Techniques (contd.) Animation Example

  19. High Level Techniques (contd.) Governing Aspects • Dynamics • Procedural Motion • Motion Capture • Kinematics

  20. High Level Techniques (contd.) Procedural Motion • control of motion • functions governing movement over time • attributes: - position, velocity,color, size

  21. High Level Techniques (contd.) Procedural Motion Example

  22. High Level Techniques (contd.) Governing Aspects • Dynamics • Procedural Motion • Motion Capture • Kinematics

  23. 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

  24. High Level Techniques (contd.) Motion Capture Tools • Software • Kaydara FiLMBOX • Famous 3D • Life Forms Studio • Poser • Accessories • Datagloves • Cybergloves • Face Trackers • MotionCaptor

  25. High Level Techniques (contd.) Governing Aspects • Dynamics • Procedural Motion • Motion Capture • Kinematics

  26. High Level Techniques (contd.) Kinematics study of motion independent of underlying forces • Forward Kinematics • Inverse Kinematics

  27. High Level Techniques (contd.) Forward Kinematics Example Woman Walking

  28. High Level Techniques (contd.) Forward Kinematics • motion of all joints specified explicitly • motion of links determined by indirect methods

  29. High Level Techniques (contd.) Forward Kinematics e.g. Target(x,y) a2 L1 L2 L3 a3 a1 Base x = L1*cos(a1) + L2*cos(a2) + L3*cos(a3) y = L1*sin(a1) + L2*sin(a2) + L3*sin(a3)

  30. High Level Techniques (contd.) Applications of Forward Kinematics • animation films • algorithmic animations

  31. High Level Techniques (contd.) Softwares employing Forward Kinematics • DE/MEC mechanism design software • VRML

  32. 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

  33. L2 L1 L3 High Level Techniques (contd.) Inverse Kinematics e.g. ? 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)

  34. 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

  35. High Level Techniques (contd.) Solving Inverse Kinematics Equations • Non linear programming • Differential kinematics

  36. 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

  37. 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

  38. High Level Techniques (contd.) Our Example Goal a2 L1 L2 L3 distance End effector a3 a1 Base G(a) = (xg – x)2 + (yg – y)2

  39. 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

  40. High Level Techniques (contd.) Nonlinear Optimization • minimize G(a) • subject to mta = b1 mta <= b2

  41. High Level Techniques (contd.) Available NLP Packages • LANCELOT • MATLAB • DONLP2

  42. 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

  43. High Level Techniques (contd.) Differential Kinematics • uses Jacobian matrix • linearly relates end effector change to joint angle change

  44. High Level Techniques (contd.) Applications of Inverse Kinematics • video games • interactive process control simulation

  45. 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

  46. 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

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