Haptic Rendering
Comp 259
Jingdan Zhang
31
, Mar, 2004
Haptic Interaction
“… process of applying forces
representing a virtual environment to the
user of a haptic interface, or force

feedback device”
Goal of haptic rendering
Enable a user to touch, feel and
manipulate virtual o
b
jects
Enhance a user’s experience in a
synthetic environment
Provide a natural intuitive interface
Applications of Haptics
Entertainment
Education and training
Scientific visualization
Surgical simulation
Robot

assisted surgery
–
Tele

operation
–
Cooperative Manipulation
Human Haptics
Two complementary channels:
Tactile
•
Strictly responsible for the variation of the
cutaneous stimuli
•
Presents spatial distribution of forces
Kinesthetic
•
Refers to the human perception of one’s
own body position and motion
•
Presents only the net force information
Main components
Haptic interface
Electro

mechanical system
Graphical objects
Contain shape and other property
Haptic rendering algorithm
Joins the first two components
Haptic interface
Sensable Technologies Inc.
PHANTOM Desktop
Virtual Technologies Inc.
Cyber Force
Immersion co.
Impulse stick
Haptic rendering algorithm
Two parts:
Collision detection, collision response
Example: Hard sphere
s
u
s
u
s
u
s
u
s
u
s
u
z
z
y
y
x
x
r
r
z
z
y
y
x
x
r
r
r
R
k
R
r
F
1
ˆ
)
(
)
(
)
(
otherwise
ˆ
)
(
0
2
2
2
Collision Detection
Computationally fast collision detection:
update rate 1KHz
H

COLLIDE
[
Gregory
et al. 1999]
•
Spatial Decomposition
•
Bounding Volume Hierarchy based on OBBTrees
•
Frame

to

Frame Coherence
Sensation preserving simplification
[Oaduy &
Lin, 2003]
•
Multiresolution representation
The models of the probe
a line segment
a point
a 3D object
Handle the collision:
Penalty methods
Determine the feedback force
directly from penetration depth
Subdivide the object volume and
associate each a sub

volume with
each surface
Work well for simple objects
Limitations of penalty
methods
Lack of locality
Force discontinuity
“Pop

Thru” of thin Object
Handle the collision:
Constrained based method
Constrain a virtual proxy of the
haptic interface to ramain on the
surfaces
Gold object [Zilles et al. 1997]
Virtual Proxy [Ruspini et al. 1997]
IHIP & HIP [Ho et al. 1999]
Virtual Proxy(1)
Virtual Proxy(2)
,
ˆ
,
ˆ
,
ˆ
ubject to
minimize
3
2
2
1
1
a
x
n
a
x
n
a
x
n
s
p
x
T
m
T
T
Surface properties
Normal
Contact Impedance
Friction
Texture
Force Shading
Render object surfaces as smooth and
continuous, even when the underlying
representation is not
Analogous to Phong Shading
Contact Impedance
Happening when user contact the
surface
Perpendicular to the surface
Spring force and
viscous
damping force
Bv
Kx
f
Friction
Happening when user stroke the
surface
The lateral force, opposite to motion
The function of the coefficient of
friction and normal force
Coulomb friction: static and dynamic
friction
Texture
Varied ways to represent and
display texture
Deterministic textures
Stochastic Models
Haptic recordings
Lateral

force gradient
algorithm(1)
Minsky’s PhD thesis 1995
Texture is represented as 2D height
field
2 DOF, render the texture as
tangential vibration force
Assume the surface is frictionless
Lateral

force gradient
algorithm(2)
Moving from
x
1
to
x
2
:
Δ
PE = work = F*D
At the same time:
Δ
PE = PE
2

PE
1
= (l
1
–
l
2
)mg
So:
F = mgtan
θ
What new?
Haptic rendering of interaction
between textured objects
[Otaduy,
Jain, Sud, Lin 2004]
Use texture (height field) to encode
surface details
A new force model
Fast calculation of directional
penetration depth( Implement on GPU)
Preprocessing
Rendering pipeline
Step1: Perform collision detection at
each step. Determine pairs of
contact points and penetration
directions based on coarse model.
Step2: Calculate the force and
torque for each contact based on
texture.
Step 3: Compute the net force and
torque.
Penetration depth
Intersection
of A & B
Global penetration
depth
Directional
penetration
depth
n
along
n
Penetration depth of height
field
))
,
(
)
,
(
(
max
)
(
)
,
(
v
u
h
v
u
h
B
A
D
D
v
u
n
B
A
Calculate height function on
surface
u
v
n
Flatten
Approximate
Height Function
The force model(1)
Penalty

based force, defined as
elastic potential field
2
2
1
k
U
Define force
F
and torque
T
as
)
(
k
U
T
F
)
,
,
,
,
,
(
z
y
x
z
y
x
The force model(2)
In the local reference system
{
u
,
v
,
n
}
T
n
n
v
n
u
n
n
n
n
T
n
v
u
n
v
u
v
u
k
T
T
T
F
F
F
)
,
,
,
1
,
,
(
)
,
,
,
,
,
(
In the global reference system
F
c
p
T
T
T
n
v
u
T
F
F
F
n
v
u
F
T
n
v
u
T
n
v
u
)
(
)
,
,
)(
,
,
(
)
,
,
)(
,
,
(
The force model(3)
The partial derivatives
u
n
v
u
u
n
v
u
u
u
n
v
u
n
n
v
u
n
n
2
)
,
,
,
,
,
(
)
,
,
,
,
,
(
,
can be obtained by
translating the object
Δ
u along the
u
axis and computing the directional
penetration depth
,...)
(
u
u
n
Experiment result
Textured blocks
File and CAD part
Hammer and torus
Block and gear
Stochastic models(1)
What is texture?
From observation
•
an image that looks approximately the
same, to humans, from neighborhood to
neighborhood
From stochastic view
•
multidimensional signal obeying some
statistical properties
Stochastic models(2)
Basic assumption:
the feedback forces from texture can
be represented as stochastic models
Several models:
Gaussian distributions
Markov random field
Stochastic input parameters derived
by analyzing actual force data
The Gaussian distribution
The roughness of many surface can
be approximated as Gaussian:
)
,
(
2
Normal
A Stochastic Approach(1)
Siira & Pai 1996
For texture rendering, it is suffice to
give the correct psychological
illustration
Two assumptions
Normal force is proportional to the
height of the asperities
Lateral texture forces is proportional to
the normal force
A Stochastic Approach(2)
If user is in contact and moving
tangential to the surface, calculate
texture output
otherwise
1
for
0
)
,
(
~
2
texture
texture
friction
constraint
contact
texture
texture
v
u
uNormal
F
F
F
F
F
F
F
Haptic recordings
Analogous to image

based rendering
Pre

sampling the forces occurring at different
location
Play them back in the simulation
Two sources
From off

line physical

simulation
•
To reduce the real time computation burden
From real world texture
•
To avoid the modeling complexity
Challenge
How to parameterize the recorded forces
Conclusion
Haptic rendering is cool. You can
not see, but you can feel.
It is the next frontier for CG
research.
References
Allison Okamura. "Haptics for Virtual Reality." Course note.
http://www.me.jhu.edu/~allisono/courses/
530.651/lectures/lecture09.pdf
Basdogan, C., Srinivasan, M.A. "Haptic rendering in virtual
environments." network.ku.edu.tr/~cbasdogan/
Tutorials/VRbookChapter.pdf
Gregory A., Lin M., Gottschalk S. and Taylor R. "H

Collide:
A Framework for Fast and Accurate Collision Detection for
Haptic Interaction." In the Proceedings of IEEE Virtual
Reality Conference 1999.
Ho,C.H., Basdogan,C., and Srinivasan, M. A. 1999.
"Efficient point

based rendering techniques for haptic
display of virtual objects." Presence 8, 5, pp.477

491.
Juhani Siira, Dinesh K. Pai, "Haptic Texturing

A
Stochastic Approach
.
", IEEE International Conference on
Robotics and Automation, 557

562, Minnesota, 1996.
Max Smolens. "Haptic Rendering." Course Note.
http://www.cs.unc.edu/~lin/COMP259

S03/LEC/20a.ppt
References(2)
Miguel A. Otaduy and Ming C. Lin, "Sensation Preserving
Simplification for Haptic Rendering." In Proceedings of ACM
SIGGRAPH 2003 / ACM Transactions on Graphics, Vol. 22. pp.
543

553. San Diego, Ca. 2003.
Miguel A. Otaduy
, Jian, Sud
and Ming C. Lin, "Haptic Rendering
of Interaction between Textured Models." Submitted to ACM
SIGGRAPH 2004.
Minsky, M. 1995. "Computational Haptics: The sandpaper
system for synthesizing texture for a force

feedback display."
PhD thesis, Ph.D. Dissertation, Program in Media Arts and
Sciences, MIT.
Ruspini, Kolarov and Khatib. “The haptic display of complex
graphical environments.” Proc. ACM SIGGRAPH 1997.
Zilles, C.B. and Salisbury, J.K. “A constraint

based god

object
method for haptic display.” Proc. IEE/RSJ International
Conference on IntelligentRobots and Systems, Human Robot
Interaction, and Cooperative Robots, Vol. 3, p. 146

151, 1995.
Salisbury, J.K. et al. “Haptic rendering: programming touch
interaction with virtual objects.” Proc. ACM SIGGRAPH 1995.
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