Haptics and Virtual Reality

1. Haptics and Virtual Reality Lecture 7: Haptic Rendering M. Zareinejad

2. How does a basic haptic interface work?

3. Haptic System Architecture

4. Haptic System Architecture • Use haptic device to physically interact with the VE – optical encoders measure position of end effector – actuators apply forces to the user – haptic rendering algorithms compute such forces given the new positions

5. Haptic System Architecture

6. Haptic System Architecture:Haptic Rendering

7. The definition of haptic rendering • “Haptic rendering is the process of computing and generating forces in response to user interaction with virtual environment” • Computing forces and torques that should be applied to the tip of the haptic display in order to represent forces of a physical phenomena or represent some data

8. Haptic Rendering: Parallels to Visual Rendering

9. Haptic Rendering

10. Haptic Rendering

11. Haptic Rendering

13. Virtual Wall Algorithm • Virtual Wall “algorithm”

15. Sampled-Data System

16. Sampled-Data System

19. Vector Field • In vector calculus, a vector field is an assignment of a vector to each point in space

20. Force field

25. Thin Objects

26. Overlapping Objects

27. God-Object Method • ‘God-object’ is an ideal interaction point. • ƒ It stays on the surface when the object penetration occurs. • ƒ It locates on the nearest surface from the HIP.

28. Haptic Device and Avatar

29. Connecting the Device to the Avatar

30. God Object Algorithm

31. God Object Algorithm

32. God Object Algorithm

33. God Object Algorithm

36. Active surface • An active surface is the surface that has the God-object on it. • ƒ To be an active surface, • The God-object must be located in positive distance from the surface. • The HIP must be located in negative distance from the surface.

37. Search of Active Surface • Draw a line from the old God-object to the new HIP. • If the line is not under three edges, the surface is not active now. • Change the active surface after a cycle.

38. Acute Concave Object Problem • To be an active surface, the HIP must located in negative distance from the surface. • ƒ On acute concave object, the God-object moves below the surface but the HIP does not.

39. Solution: Iteration • I. Find a new God-object location. • II. Using this as a HIP, check whether there is a new constraint. • III. If there is a new constraint, find “new” God-object location. • IV. Continue until no new constraint is found.

40. God-Object Computation • We find point Q with the minimal distance. • This is a new God-object location.

41. God Object Computation – Formulation • For three active plane constraints, • This can be solved using the Lagrange Multiplier Theorem.

42. God Object Computation –Solution • Set Lagrangian as By the Lagrange Multiplier Theorem

43. Complexitiy • We can compute x, y and z in at most 65 of ×and ÷operations. • ƒ Lower number of constraints make computation much faster.