Animating Speed Position and Orientation

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