Haptics and Virtual Reality

M. Zareinejad

Lecture 7:Haptic Rendering

How does a basic haptic interface work?

Haptic System Architecture

Use haptic device to physically interact withthe VE– optical encoders measure position of end effector– actuators apply forces to the user– haptic rendering algorithms compute such forces given the new

positions

Haptic System Architecture

Haptic System Architecture

Haptic System Architecture: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

The definition of haptic rendering

Haptic Rendering: Parallels to Visual Rendering

Haptic Rendering

Haptic Rendering

Haptic Rendering

Virtual Wall “algorithm”

Virtual Wall Algorithm

Sampled-Data System

Sampled-Data System

Vector Field In vector calculus, a vector field is an

assignment of a vector to each point in space

Force field

Thin Objects

Overlapping Objects

‘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.

God-Object Method

Haptic Device and Avatar

Connecting the Device to the Avatar

God Object Algorithm

God Object Algorithm

God Object Algorithm

God Object Algorithm

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.

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.

Search of Active Surface

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.

Acute Concave Object Problem

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.

Solution: Iteration

We find point Q with the minimal distance.

This is a new God-object location.

God-Object Computation

For three active plane constraints,

This can be solved using the Lagrange Multiplier Theorem.

God Object Computation – Formulation

Set Lagrangian as

By the Lagrange Multiplier Theorem

God Object Computation –Solution

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

Complexitiy