Haptics and Virtual Reality Lecture 7: Haptic Rendering M. Zareinejad
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
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
Virtual Wall Algorithm • Virtual Wall “algorithm”
Vector Field • In vector calculus, a vector field is an assignment of a vector to each point in space
God-Object Method • ‘God-object’ is an ideal interaction point. • It stays on the surface when the object penetration occurs. • It locates on the nearest surface from the HIP.
Active surface • An active surface is the surface that has the God-object on it. • 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.
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.
Acute Concave Object Problem • To be an active surface, the HIP must located in negative distance from the surface. • On acute concave object, the God-object moves below the surface but the HIP does not.
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.
God-Object Computation • We find point Q with the minimal distance. • This is a new God-object location.
God Object Computation – Formulation • For three active plane constraints, • This can be solved using the Lagrange Multiplier Theorem.
God Object Computation –Solution • Set Lagrangian as By the Lagrange Multiplier Theorem
Complexitiy • We can compute x, y and z in at most 65 of ×and ÷operations. • Lower number of constraints make computation much faster.