Haptics and Virtual Reality
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Haptics and Virtual Reality
M. Zareinejad
Lecture 7:Haptic Rendering
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How does a basic haptic interface work?
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Haptic System Architecture
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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
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Haptic System Architecture
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Haptic System Architecture:Haptic Rendering
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“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
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Haptic Rendering: Parallels to Visual Rendering
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Haptic Rendering
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Haptic Rendering
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Haptic Rendering
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Virtual Wall “algorithm”
Virtual Wall Algorithm
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Sampled-Data System
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Sampled-Data System
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Vector Field In vector calculus, a vector field is an
assignment of a vector to each point in space
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Force field
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Thin Objects
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Overlapping Objects
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‘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
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Haptic Device and Avatar
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Connecting the Device to the Avatar
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God Object Algorithm
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God Object Algorithm
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God Object Algorithm
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God Object Algorithm
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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
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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
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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
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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
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We find point Q with the minimal distance.
This is a new God-object location.
God-Object Computation
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For three active plane constraints,
This can be solved using the Lagrange Multiplier Theorem.
God Object Computation – Formulation
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Set Lagrangian as
By the Lagrange Multiplier Theorem
God Object Computation –Solution
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We can compute x, y and z in at most 65 of ×and ÷operations. Lower number of constraints make � computation much faster.
Complexitiy