Content uploaded by Cagatay Basdogan
Author content
All content in this area was uploaded by Cagatay Basdogan on Jul 08, 2013
Content may be subject to copyright.
Haptic Rendering in Virtual Environments
Cagatay Basdogan
1, 2
, Mandayam A. Srinivasan
2
1
Jet Propulsion Laboratory
California Institute of Technology
Pasadena, CA 91101
Cagatay.Basdogan@jpl.nasa.gov
2
Laboratory for Human and Machine Haptics
Massachusetts Institute of Technology
Cambridge, MA 02139
basdogan, srini @mit.edu
1. Introduction
The goal of haptic rendering is to enable a user to touch, feel, and manipulate virtual objects through a
haptic interface. With the introduction of high fidelity haptic devices (ref. **Biggs and Srinivasan
Chapter**), it is now possible to simulate the feel of even fine surface textures on rigid complex shapes
under dynamic conditions. Starting from the early nineties, significant progress has occurred in our ability
to model and simulate haptic interactions with 3D virtual objects in real-time (Salisbury and Srinivasan,
1997; Srinivasan and Basdogan, 1997). The rapid increase in the number workshops, conference sessions,
community web pages, and electronic journals on haptic displays and rendering techniques
1
indicates
growing interest in this exciting new area of research, which we call computer haptics. Just as computer
graphics is concerned with synthesizing and rendering visual images, computer haptics is the art and science
of developing software algorithms that synthesize computer generated forces to be displayed to the user for
perception and manipulation of virtual objects through touch. We have already seen various applications of
computer haptics in the areas of medicine (surgical simulation, tele-medicine, haptic user interfaces for blind
people, rehabilitation of patients with neurological disorders) entertainment (3D painting, character
animation, morphing and sculpting), mechanical design (path planning and assembly sequencing), and
scientific visualization (geophysical data analysis, molecular manipulation). We anticipate that more
applications are on the way as the devices and rendering techniques improve and the computational power
increases. This chapter will primarily focus on the fundamental concepts of haptic rendering with some
discussion of implementation details. Although, it is impossible to cite all the relevant work within the
constraints of this chapter, we have made attempts to cover the major references. Given that the current
technology is mature for net force and torque feedback (as in tool usage in the real world) and not tactile
feedback (as in actual distribution of force fields on the skin during contact with real objects), we restrict
ourselves to techniques concerning the former. In general, the concepts discussed in the chapter include: (1)
1
See the proceedings of Phantom Users Group Workshops starting from 1996 (http://www.ai.mit.edu/conferences/),
ASME Dynamics Systems and Control (DSC) Division starting from 1993, IEEE International Conference on Robotics
and Automation, and IEEE Virtual Reality Conference. Also visit the haptic community pages at
http://www.sensable.com/community/index.htm and http://haptic.mech.nwu.edu/
and the haptics-e journal at
http://www.haptics-e.org/.
haptic interaction paradigms that define the nature of the “haptic cursor” and its interaction with virtual
objects and (2) object property display algorithms that enable us to render surface and material properties of
objects and their behavior through repeated use of the haptic interaction paradigm.
2. Principles of Haptic Rendering: Object Shape
Typically, a haptic rendering algorithm is made of two parts: (a) collision detection and (b) collision
response (see Figure 1). As the user manipulates the probe of the haptic device, the new position and
orientation of the haptic probe are acquired, collisions with the virtual objects are detected (i.e. collision
detection). If a collision is detected, the interaction forces are computed using preprogrammed rules for
collision response, and conveyed to the user through the haptic device to provide him/her with the tactual
representation of 3D objects and their surface details. Hence, a haptic loop, which updates forces around 1
kHz (otherwise, virtual surfaces feel softer, or, at worst, instead of a surface it feels as if the haptic device is
vibrating), includes at least the following function calls:
…
get_position (Vector &position); // position and/or orientation of the end-effector
calculate_force (Vector &force); // user-defined function to calculate forces
send_force (Vector force); // calculate joint torques and reflect forces back to the user
…
Collision
Detection
Collision
Response
Geometry
Material
Object
Database
Position
Orientation
Contact
Information
Force
Torque
Figure 1.
A haptic interaction algorithm
is typically made of two parts: (a)
collision detection and (b) collision
response. Thehaptic loop seen in the
figure requires an update rate of around
1 kHz for stable force interactions.
Computationally fast collision detection
and response techniques are required to
accommodate this requirement.
To describe the basic concepts of haptic rendering, let us consider a simple example: haptic rendering of a
3D frictionless sphere, located at the origin of a 3D virtual space (see Figure 2). Let us assume that the user
can only interact with the virtual sphere through a single point which is the end point of the haptic probe,
also known as the Haptic Interaction Point (HIP). In the real world, this is analogous to feeling the sphere
with the tip of a stick. As we freely explore the 3D space with the haptic probe, the haptic device will be
passive and will not reflect any force to the user until a contact occurs. Since our virtual sphere has a finite
stiffness, HIP will penetrate into the sphere at the contact point. Once the penetration into the virtual sphere
is detected and appropriate forces to be reflected back to the user are computed, the device will become
active and reflect opposing forces to our hand to resist further penetration. We can easily compute the
magnitude of the reaction force by assuming that it is proportional to the depth of penetration. Assuming no
friction, the direction of this force will be along the surface normal as shown in Figure 2.
F
R
distance
HIP
Hand
void calculate_force (Vector &force)
{
float X, Y, Z, distance;
float R = 20.0;
X = HIP[0]; Y = HIP[1]; Z = HIP[2];
distance = sqrt(X*X + Y*Y + Z*Z);
if(distance < R) //collision check
{
force[0] = X/distance * (R-distance);
force[1] = Y/distance * (R-distance);
force[2] = Z/distance * (R-distance);
}
}
Figure 2. Haptic rendering of a 3D sphere in virtual environments. The software code presented on the
right-hand side calculates the direction and the magnitude of the reaction force for the sphere discussed in
the example. The sphere has a radius of 20 units and located at the origin.
As it can be seen from the example given above, a rigid virtual surface can be modeled as an elastic element.
Then, the opposing force acting on the user during the interaction will be:
xkF ∆=
where, k is the stiffness coefficient and || x∆ is the depth of penetration. While keeping the stiffness
coefficient low would make the surface perceived soft, setting a high value would make the interactions
unstable by causing undesirable vibrations. Figure 3 depicts the changes in force profile with respect to
position for real and virtual walls. Since the position of the probe tip is sampled digitally with certain
frequency during the simulation of a virtual wall, a “staircase” effect is observed. This staircase effect leads
to energy generation (see the discussions and suggested solutions in Colgate and Brown, 1994 and Ellis et
al., 1996).
F
x
wall
k
1
k
2
Figure 3
. Force-displacement curves for touch interactions
with real and virtual walls. In the case of real wall, the force-
displacement curve is continuous. However, we see
“staircase” effect when simulating touch interactions with a
virtual wall. This is due to the fact that haptic device can only
sample position information with a finite frequency. The
difference in the areas enclosed by the curves that correspond
to penetrating
into
and
out of
the virtual wall is a manifestation
of energy gain. This energy gain leads to instabilities as the
stiffness coefficient is increased (compare the energy gains for
stiffness coefficients
2
k
and
1
k
). On the other hand, a low
value of stiffness coefficient generates a soft virtual wall,
which is not desirable either.
Although the basic recipe for haptic rendering of virtual objects seems easy to follow, rendering of complex
3D surfaces and volumetric objects requires more sophisticated algorithms than the one presented for the
sphere. The stringent requirement of updating forces around 1 kHz leaves us very little CPU time for
computing the collisions and reflecting the forces back to the user in real-time when interacting with
complex shaped objects. In addition, the algorithm given above for rendering of a sphere considered only
“point-based” interactions (as if interacting with objects through the tip of a stick in real world), which is far
from what our hands are capable of in real world. However, several haptic rendering techniques have been
developed recently to simulate complex touch interactions in virtual environments (reviewed in Salisbury
and Srinivasan, 1997; Srinivasan and Basdogan, 1997; Hollerbach and Johnson, 2001). The existing
techniques for haptic rendering with force display can be distinguished based on the way the probing object
is modeled: (1) a point (Zilles and Salisbury, 1995; Adachi et al., 1995; Avila and Sobierajski, 1996; Ruspini
et al., 1997; Ho et al., 1999), (2) a line segment (Basdogan, et al., 1997; Ho et al., 2000), or (3) a 3D object
made of group of points, line segments and polygons (McNeely et al., 1999). The type of interaction method
used in simulations depends on the application.
In point-based haptic interactions, only the end point of the haptic device, also known as the haptic interface
point (HIP), interacts with virtual objects (Figure 4b). Each time the user moves the generic probe of the
haptic device, the collision detection algorithm checks to see if the end point is inside the virtual object. If
so, the depth of indentation is calculated as the distance between the current HIP and the corresponding
surface point, also known as the Ideal Haptic Interface Point (IHIP; also called god-object, proxy point, or
surface contact point; see Figure 5). For exploring the shape and surface properties of objects in VEs, point-
based methods are probably sufficient and could provide the users with similar force feedback as what they
would feel when exploring the objects in real environments with the tip of a stick. Using a point-based
rendering technique, polyhedrons (Zilles and Salisbury, 1995; Ruspini et al., 1997; Ho et al., 1999), NURBS
(Thompson et al., 1997; Stewart et al., 1997), implicit surfaces (Salisbury and Tarr, 1997), and volumetric
objects (Avila and Sobierajski, 1996) have been successfully rendered. Point-based methods, however, are
not capable of simulating more general tool-object interactions that involve single or multiple objects in
contact with the tool at arbitrary locations of the tool. In such a context, both forces and torques displayed to
the user need to be independently computed.
In ray-based interactions, the generic probe of the haptic device is modeled as a line-segment whose
orientation is taken into account, and the collisions are checked between the finite line and the objects. This
approach enables the user to touch multiple objects simultaneously. In addition to forces, torque interactions
can be simulated, which is not possible with the point-based approaches (see Figure 4c). Ray-based
rendering can be considered as an approximation to long tools and as an intermediate stage in progress
towards the full interaction between 3D cursor and 3D objects. Also, if the geometric model of the probing
object can be simplified to a set of connected line segments, then ray-based rendering technique can be used
and will be faster than simulation of full 3D object interactions. For example, we have successfully
simulated the haptic interactions between a mechanical shaft and an engine block (Ho et al., 2000) as well as
the interactions between laparoscopic surgical instruments and deformable objects (Basdogan, et al. 1998;
Basdogan et al., 2001) using multiple line segments and the ray-based rendering technique. However, if the
probing object has a complex geometry and cannot be easily modeled using a set of line segments,
simulation of six degree of freedom (dof) object-object interactions has to be considered.
The simulation of haptic interactions between two 3D polyhedra is desirable for many applications, but this
is computationally more expensive than the point-based and ray-based interactions (see Figure 4d).
Although a single point is not sufficient for simulating the force and torque interactions between two 3D
virtual objects, a group of points, distributed over the surface of probing object, has been shown to be a
feasible solution. For example, McNeely et al. (1999) simulated the touch interactions between 3D model of
a teapot and a mechanical assembly.
Force
Force
Torque
b
c
a
Force
Torque
d
Figure 4. The existing interaction methods for haptic rendering with force display can be distinguished
based on the way the probing object is modeled: b) a point, c) a line segment, and d) a 3D object.
Irrespective of the interaction method used, a haptic rendering algorithm must include both collision
detection and collision response computations (see Figure 1). Although collision detection has been
extensively studied in computer graphics (Lin, 1993; Hubbard, 1995; Gottschalk et al., 1996; Cohen et al.,
1995), the existing algorithms are not designed to work directly with haptic devices to simulate touch
interactions in virtual environments. Moreover, merely detecting collisions between 3D objects is not
enough for simulating haptic interactions. How the collision occurs and how it evolves over time (i.e.
contact history) are crucial factors (see the discussion in Figure 5 on contact history) in haptic rendering to
accurately compute the interaction forces that will be reflected to the user through the haptic device (Ho et
al., 1999; 2000).
F
1
F
2
F
3
F
3
HIP
1
HIP
2
HIP
3
Although the collision detection algorithms developed in computer graphics cannot be used in haptics
directly, several concepts developed for fast collision detection can be ported to haptics. For example, haptic
rendering algorithms can easily take advantage of (a) space partitioning techniques (i.e. partitioning the
space that encloses the object into smaller sub-spaces in advance for faster detection of first contact), (b)
local search approaches (i.e. searching only the neighboring primitives for possible new contacts), and (c)
hierarchical data structures (i.e. constructing hierarchical links between the primitives that make up the
object for faster access to the contacted primitive). In addition to these improvements, a client-server model
has to be considered to synchronize visual and haptic displays for achieving faster update rates. Using multi-
threading techniques, for example, one can calculate the forces at 1 kHz in one thread while updating the
visual images at 30 Hz in another thread (Ho et al., 1999). If the forces cannot be computed at 1 kHz, a
numerical scheme can be developed to extrapolate the new forces based on the previously computed ones to
maintain the constant update rate of 1 kHz for stable interaction (Ellis et al., 1996; Basdogan, 2000).
3. Rendering of Surface Details: Smooth Shapes, Friction and Texture
Quite frequently, it is desirable to display object surfaces as smooth and continuous, even when an
underlying polyhedral representation is employed. In computer graphics, for example, illumination models
are used to compute the surface color at a given point of a 3D object (Foley et al., 1995). Then, shading
algorithms are applied to shade each polygon by interpolating the light intensities (Gourand shading) or
surface normals (Phong shading). Shading algorithms make the shared edges of the adjacent polygons
invisible and provide the user with the display of visually smooth surfaces (Watt and Watt, 1992). One can
integrate a similar approach into the study of haptics to convey the feel of haptically smooth object surfaces
(Morgenbesser and Srinivasan, 1996, Fukui, 1996; Basdogan et al, 1997; Ruspini et al, 1997). By using
force-shading technique suggested by Morgenbesser and Srinivasan (1996), we can reduce the force
discontinuities and make the edges of polyhedral object feel smoother. To implement the force shading with
polygonal surfaces (Basdogan et al., 1997), we pre-compute the surface normal at each vertex by averaging
the surface normals of neighboring polygons, weighted by their neighboring angles. During the real-time
computations, we first detect the collision point that divides the contacted triangle into three sub-triangles.
Then the surface normal (
N
s
) can be calculated at the collision point by averaging the normals of the
vertices (
i
N ) of the contacted polygon, weighted by the areas A
i
of the three sub-triangles:
Figure 5. A haptic rendering algorithm that is based on
Point interactions must calculate the IHIP for a given
HIP at each rendering cycle. IHIP, (also known as the
god-object, surface contact point, or proxy point),
can be considered as the surface point of the object
in which the tool or finger would be in contact. The
computation of this point relies on the contact history. In the
figure, for example, ignoring contact history and
always choosing the closest point on the object surface
as our new IHIP for a given HIP would make the user feel as
if he is pushed out of the object as HIP moves from
point 2 to point 3.
∑
∑
=
3
3
.
i
i
i
ii
s
A
NA
N
Haptic simulation of surface details such as friction and texture significantly improves the realism of virtual
worlds. For example, friction is almost impossible to avoid in real life and virtual surfaces without friction
feel “icy-smooth” when they are explored with a haptic device. Similarly, most of the surfaces in nature are
covered with some type of texture that is sensed and distinguished quite well by our tactile system
(Srinivasan et al, 1990). Haptic texture is a combination of small-scale variations in surface geometry and its
adhesive and frictional characteristics. However, displaying the detailed geometry of textures would be
computationally too expensive. Instead, both friction and texture can be simulated by appropriate
perturbations of the reaction force vector computed using nominal object geometry and material properties.
The major difference between the friction and the texture simulation via a haptic device is that the friction
model creates only forces tangential to the nominal surface in a direction opposite to the probe motion, while
the texture model can generate both tangential and normal forces in any direction (see Figure 6).
Di
r
e
c
t
i
o
n
o
f
m
o
v
e
m
e
n
t
F
n
F
f
F
t
F
user
Figure 6. Forces acting on the user
(
)
f
tnuser
FFFF
++=
during the haptic simulation
of friction and textures. The normal force can be
computed using a simple physics-based model such
as Hooke’s law (
x
kF
n
∆=
, where
x
∆
is the depth
of penetration of the haptic probe into the virtual
surface). To simulate coulomb friction,
we need to create a force (
n
f
FF
µ
=
,
where
µ
is the coefficient of friction) that is
opposite to the direction of the movement. To
simulate textures, we change the magnitude and
direction of the normal force vector using the gradient
vector of the texture field at the contact point.
Salcudean and Vlaar (1994) and Salisbury et al. (1995) simulated static and dynamic friction such that the
user feels the stick-slip phenomenon when the stylus of a haptic device is stroked over the object surface. By
changing the mean value of friction coefficient and its variation, more sophisticated frictional surfaces such
as periodic ones (Ho et al., 1999) and various grades of sandpaper (Green and Salisbury, 1997) can be
simulated as well.
Haptic perception and display of textures in virtual environments require a thorough investigation, primarily
because the textures in nature come in various forms. Luckily, graphics texturing has been studied
extensively and we can draw from that experience to simulate haptic textures in virtual environments. For
example, bump mapping is a well-known technique in graphics for generating the appearance of a non-
smooth surface by perturbing the surface normals. Blinn (1978) initially proposed this technique as a method
of graphically rendering 3D bumps for modeling clouds. His formulation depends on parameterization of the
surface. Although the surface parameterization techniques have some advantages, they may generate uneven
bump textures on the surface of complex shapes. Max and Becker (1994) suggested a direct method of
mapping that does not require a transformation from global to parametric space. They developed a
formulation that is purely based on the original surface normal and the local gradient of the height field that
generates bumps on the surface of the object. Max and Becker utilized this technique to generate bumps on
cloud contour surfaces. We used the same approach and perturbed the direction and magnitude of the surface
normal (
N
s
) to generate bumpy or textured surfaces that can be sensed tactually by the user in virtual
environments (Basdogan et al., 1997). The perturbed surface normals (
M ) can be computed using the
following formulation:
sss
NNhhNM ).(∇+∇−=
k
z
h
j
y
h
i
x
h
h
ˆ
ˆˆ
∂
∂
∂
∂
∂
∂
++=∇
where, h(x,y,z) represents the texture field function and ∇h is the local gradient vector. One of the earliest
methods of texture rendering that uses the force perturbation concept with a 2-dof haptic device was
developed by Minsky et al. (1990). The formulation given above extends this concept to 3D surfaces.
In general, the haptic texturing techniques can be classified into two parts: (a) image-based and (b)
procedural.
Image-based haptic texturing: This class of haptic texturing deals with constructing a texture field from a 2D
image data. In computer graphics, digital images are wrapped around 3D objects to make them look more
realistic. While a graphical texture consists of 2D texels with only color or gray scale intensities, a haptic
texture should consist of texels with a height value. To display image-based haptic textures, the two-stage
texture mapping technique of computer graphics (Bier and Sloan, 1986; Watt and Watt, 1992) can be
followed. The first stage in this technique is to map the 2D image to a simple intermediate surface such as
plane, cube, cylinder, or sphere. The second stage maps the texels from the intermediate surface to the object
surface. Following this stage, one can easily access the height value at any point on the object surface. In
addition, the gradient vector at any point can be estimated using a finite difference technique and
interpolation scheme. Then, the force perturbation concept described above can be used to display image-
based haptic textures (see Ho et al., 1999 for implementation details).
Procedural haptic texturing: The goal of procedural haptic texturing is to generate synthetic textures using
mathematical functions. The function usually takes the coordinate (x,y,z) as the input and returns the height
value and its gradient as the outputs. For example, several investigators have implemented the well-known
noise texture (Perlin, 1985; Ebert et al. 1994) to generate stochastic haptic textures (Siira and Pai, 1996;
Fritz and Barner, 1996; Basdogan et al., 1997). Fractals are also appropriate for modeling natural textures
since many objects seem to exhibit self-similarity (Mandelbrot, 1982). We have used the fractal concept in
combination with the other texturing functions such as Fourier series and pink noise in various frequency
and amplitude scales to generate more sophisticated surface details (Ho et al., 1999). Similarly, several types
of other graphical textures can be converted to haptic textures. For example, we (Ho et al., 1999) have
implemented haptic versions of reaction-diffusion textures (Turk, 1991, Witkin and Kass, 1991), the spot
noise (Wijk, 1991), and cellular texture (Worley, 1996).
4. Rendering of Deformable Objects
Graphical display of deformable objects has been extensively studied in computer graphics. With the
addition of haptic feedback, the deformable objects have gained a new characteristic. Now, our deformable
models need to estimate not only the direction and the amount of deformation of each node of object but also
the magnitude and direction of interaction forces that will be reflected to the user via a haptic device.
One way to categorize the deformation techniques is according to the approach followed by the researchers
to deform the surfaces: geometry- or physics-based deformations. In geometry-based deformations, the
object or the surrounding space is deformed, based purely on geometric manipulations. In general, the user
manipulates vertices or control points that surround the 3D object to modify the shape of the object. In
contrast, physics-based deformation techniques aim to model the physics involved in the motion and
dynamics of interactions. These models simulate physical behavior of objects under the effect of external
and internal forces. Geometry-based deformation techniques are faster, and are relatively easier to
implement, but they do not necessarily simulate the underlying mechanics of deformation. Hence, the
emphasis is on visual display and the goal is to make deformations more easily controllable and appear
smooth to the user. Physics-based approaches, although necessary for simulating realistic behavior of
deformable objects, are computationally expensive and not always suitable for real-time applications due to
current limitations in computational power. In general, hybrid approaches that take advantage of both worlds
seem to work well for many real-time applications.
Geometry- and physics-based deformation techniques used to render force-reflecting deformable objects can
be further sub-grouped as follows (see Basdogan, 1999 and 2000 for more details):
A. Geometry-based Deformation Models
• Vertex-based: The vertices of the object are manipulated to display the visual deformations.
The reaction force can be modeled using the Hooke’s law, where the depth of penetration can
be computed based on the current and home positions of the vertex that is closest to the contact
point. For example, in displaying soft tissue deformations graphically, the polynomial functions
that fit experimental data on fingerpad deformation (Srinivasan, 1989) were used to remap the
vertices of other organs (Basdogan, et al., 1998).
• Spline-based: Instead of directly transforming the vertices of the object, control points are
assigned to a group of vertices and are manipulated to achieve smoother deformations. The
concept of free form deformation was originally suggested by Sederberg and Parry (1986) and
extended by Hsu et al. (1992) to direct free form manipulation. The extension of this technique
to haptic display of deformable objects with applications in medical simulation (Basdogan et
al., 1998) and computer-aided design (CAD) and haptic sculpting (Edwards and Luecke, 1996;
Dachille et al., 1999) can be found in the literature. Here, the key advantages of using force
feedback are to increase intuition, to control deformations, and to support the implementation of
various constraints.
B Physics-based Deformation Models
In comparison to geometry-based models, the interaction forces are always part of the computation in
physics-based models and the developer does not need to consider a separate model for computing
forces.
• Particle-based: Particle systems consists of a set of point masses, connected to each other
through a network of springs and dampers, moving under the influence of internal and external
forces (see Witkin et al., 1998 for implementation details). In this model, each particle is
represented by its own mass, position, velocity, and acceleration. This technique has been used
extensively by computer graphics researchers in simulation of soft tissue and cloth behavior
(Cover et al., 1993; Lee et al., 1995; Ng and Grimsdale, 1996). Swarup (1995) demonstrated the
implementation of this technique to haptic simulation of deformable objects.
• Finite Element based: The volume occupied by 3D object is divided into finite elements,
properties of each element is formulated and the elements are assembled together to study the
deformation states for the given loads (Bathe, 1996). Due to the limited computational power
that is available today, modeling simplifications have to be made to implement real-time FEM
with haptic displays (see Cotin et al., 1999 and James and Pai, 1999 for static computations,
Basdogan et al., 2001 for dynamic computations). For example, De and Srinivasan (1999) have
proposed a modeling approach in which organs are viewed as thin walled structures enclosing a
fluid, thereby converting the 3D problem into an effectively 2D one (see also Belaniuk and
Costa, 2000). In Basdogan, et al, (2001), to compute the dynamical deformations and the
interaction forces, we implemented a modal analysis approach such that only the most
significant vibration modes of the object were selected. . In this paper, we have also
incorporated interactions between two deformable objects, one finite element based and the
other particle based. Basdogan (2001) has recently proposed the spectral Lanczos
decomposition method to obtain explicit solutions of the finite element equations that govern
the dynamics of deformations. Both methods (modal analysis and spectral Lanczos
decomposition) rely on modeling approximations, but generate dynamical solutions that are
computationally much faster than the ones obtained through direct numerical integration
techniques.
• Meshless methods: Because of the complexities of mesh generation and consequent constraints
imposed on the computations, a meshless numerical technique called the method of finite
spheres has recently been applied to physics-based soft tissue simulation (De, et al., 2001).
In our earlier studies, we have proposed a loose coupling between the force and displacement computations
to take advantage of the human perceptual limitations (Basdogan et al., 1998). In this approach, we used the
vertex-based or spline-based approaches to generate smooth visual deformations, while the interaction forces
were computed and reflected to the user based on a simple spring and a damper model between the new and
the home positions of the contact point. Since the human perception of position and motion is dominantly
influenced by visual cues in interacting with objects (Srinivasan, et al, 1996), the loose coupling between the
force and displacement computations was not readily sensed by the users during our simulations (see Model
A in Figure 7). However, this architecture is limited to the simulation of geometric-based deformations (e.g.
sculpting and animation). Since force and displacement computations are usually tightly coupled in more
physically-based systems, a closed loop architecture has to be developed to solve the equations that govern
the physics of deformable behavior (see Model B in Figure 7). In this architecture, forces and displacements
computed in the previous cycle are continuously supplied back to the physics-based model to generate the
new values in the next cycle.
Geometric
Model
Position/
Orientation
Displacement
Penetration
Displacement
Model
Force
Model
Force
Model A
Model B
Physics-
Based
Model
Geometric
Model
Position/
Orientation
Displacement
Force
Penetration
Figure 7. The computational
architectures for simulating force-
reflectingdeformable objects inVEs. In
model A, the force and displacement
computations are loosely coupled. In
model B, the physics-based model
generates forces and displacements
simultaneously, which are then fed back
to the model to generate the new values.
Although this architecture is
computationally expensive to implement,
it is more comprehensive than the
architecture A (Basdogan, 1999).
5. Rendering of Dynamic Objects
Simulating haptic interactions with 3D objects that translate and rotate over time is another challenge, which
becomes computationally quite intensive if the objects collide with each other as well as with the haptic
probe in real-time. Dynamic equations have to be solved and the state of each object has to be updated at
each iteration (see Figure 8). Techniques to calculate forces and torques based on the principles of rigid
body dynamics (Baraff, 1994) and impulse mechanics (Mirtich and Canny, 1995 and Mirtich, 1996) have
been developed for the graphical simulation of floating multiple objects. Latimer (1997) discusses the
extension of these techniques to haptics domain while Colgate and Brown (1994) and Adams and Hannaford
(1998) address the stability issues.
To describe the basic concepts of haptic interaction with dynamic objects, let us consider an example (see
Figure 8a). Let us assume that the interactions are point-based again such that the user controls the dynamics
of a floating object via only the tip point of the haptic probe. The new position and orientation of the object
can be calculated using the equations that govern the dynamics of rigid body motion. These equations can be
solved in real-time using a numerical integration method, such as Euler integration, to update the state of the
object at each cycle of the haptic loop:
ttttt
ttttt
totaltt
ttttt
ttttt
totaltt
t
t
TI
vtpp
atvv
FMa
∆+∆+
∆+∆+
−
∆+
∆+∆+
∆+∆+
−
∆+
∆+=
∆+=
=
∆+=
∆+=
=
ωθθ
αωω
α
.
.
1
1
where,
total
F and
total
T represent the total force and torque acting along a line passing through the center of
mass of the object,
pva ,, and
θωα
,, represent the linear and angular acceleration, velocity and position
vectors. In addition,
M and I are the mass and inertia matrices of the object and t∆ is the sampling time
(e.g.
t∆ = 0.001 seconds if the haptic loop is updated at 1 kHz). In this formulation, the linear quantities
can be computed either in object or global coordinate frames whereas the angular quantities need to be
computed only in the object coordinate frame. When a force is applied to the object, if there are no
constraints, the object will move to a new position defined by
tt
p
∆+
vector while rotating by a total amount
of
||
tt ∆+
θ
degrees. The total force acting on the object (
total
F ) is calculated based on the depth of
penetration of the haptic probe into the object. The torque acting on the object will be the cross product of
r
and
total
F vectors (see Figure 8). The details on computation of mass and inertia matrices for polygonal
objects can be found in Baraff (1997).
Since the position and orientation of the object change at each time step, the updated coordinates of the
object should be used to detect collisions with the new coordinates of the HIP. However, it would be
computationally too expensive to update the object database at each time step to detect collisions with the
new HIP. A better strategy is to compute everything relative to the original coordinates and then apply the
effects of transformation later (see the description in the legend for Figure 8).
T
3x3
1
2
T
1
2
HIP
T
-1
1
2
H
2
= H
1
T
V
2
= V
1
T
F
2
F
2
F
1
X
Y
(HIP) T
-1
b)
c)
H
2
= H
1
V
2
= V
1
T
F
2
= F
1
T
r
IHIP
F
total
a)
Figure 8. Modeling point-based haptic interactions with a floating rigid object in virtual environments. In
the figure, T is the transformation matrix,
2
F represents the force acting on the user through a haptic
display, H and V represent the haptic and visual coordinates of the object respectively. Here, we discuss two
different methods for computing the interaction forces when the object is transformed from state 1 to state 2.
Figure (b) describes a method in which both haptic and visual coordinates are updated and collisions are
detected with the new haptic coordinates of the object to compute the new interaction force (
2
F ) at state 2.
In Figure (c), only the visual coordinates are updated. First, HIP is multiplied with the inverse of the
transformation matrix and the collisions are detected with the original haptic coordinates. Then, the reaction
force (
1
F ) is computed relative to the original coordinates and then multiplied with the T matrix
(
TFF .
12
= ) to include the effects of transformation. Although both methods (b and c) are valid and return
the same interaction force (
2
F ) at the end, the method described in Figure (c) is computationally less
expensive than the one described in Figure (b) since the haptic coordinates of the object are not required to
be updated at each iteration when the object is transformed to a new state.
6. Recording and Playing-Back Haptic Stimuli
The concept of recording and playing back haptic stimuli (MacLean, 1996) to the user has some interesting
applications. For example, the user equipped with a desktop haptic device may touch and feel the pre-
recorded textures of a car seat that is advertised by a car company over the Internet (this concept is similar to
downloading a movie file and playing it on your screen). In another application, pre-programmed haptic
devices can be used in neuro-rehabilitation to improve the motor-control skills of patients with neurological
disorders by displaying pre-recorded haptic trajectories (Krebs et al., 1998). In both of these examples, the
user will be a passive participant of the system though he/she may have some control over the device. As the
user holds the end-effector of the device gently, the device guides his/her hand along pre-recorded shapes or
paths.
To describe the concept of haptic “play-back”, let us consider a simple example. Let us assume that our goal
is to program a haptic device such that it will display a square shaped frame to a passive user. Here, we can
consider the programming of a haptic device as a typical closed-loop control problem Although this is a
well-studied problem in robotics, the following practical issues appear when it is implemented with haptic
devices:
• Haptic devices are typically “open loop” systems. The user manipulates the end-effector of the robot to
control the end position, but the dynamics of interactions are not governed by the principles of closed
loop control systems. In other words, you need to design your own controller to command your haptic
device to play back pre-recorded haptic stimuli.
• Unless you build your own haptic device and do not purchase from a manufacturer, you most likely do
not know the kinematics (e.g. mass and length of each link) and dynamic properties (e.g. friction,
performance of motors) of your device exactly. Haptic devices, sold by a manufacturer, usually come
with a library that includes function calls for acquiring position and orientation of the end-effector and
for sending force commands to the motors (see Section 2 of this chapter). Hence, your goal is to use
these function calls to control the movements of your haptic device and navigate from one point to
another in 3D space while compensating for positional errors. One can design a controller to achieve this
goal (see Figure 9; we use a PD controller to track the desired profile).
Digital Controller
e(nT)
F(nT)
send_forces (F(nT))
P(nT)
P
d
(nT)
Desired
Profile
Haptic Library
get_position (P([n+1]T))
Σ
+
-
K
d
*{e(nT)-e([n-1]T)}/T
K
p
*{e(nT)}
Σ
+
+
Desired
Profile
Figure 9. The digital servo loop for commanding the haptic device to play pre-recorded haptic stimuli (a
frame in this example). P, e, F represent position, error, and force vectors respectively.
d
K and
p
K are
derivative and proportional control gains.
It is however possible to play back pre-recorded forces to the user even when the user is actively interacting
with the environment by using visual cues. Dang, et al (2001) have developed an epidural injection
simulator in which a training feature is the capability to display an expert’s path and forces to the novice in
two ways. The expert’s path is displayed visually either as a “tunnel” through which the novice could
traverse or as a cursor moving along the prerecorded path which the trainee needs to follow closely to feel
the pre-recorded forces continuously.
7. Shared Haptics: Haptic Interaction between Networked Users
Another potentially promising area is haptic interaction among a group of users sharing the same VE over a
network. Since the haptic loop requires a high update rate of around 1 kHz for stable interactions and
changes in the visual scene will require frequent update of the haptic database, developing a network
protocol that can provide sufficient bandwidth with minimum latency to a group of distributed users is a
quite challenging problem. For shared environments to be effective in performing collaborative tasks that
involve haptic feedback, several network architectures have been proposed (Buttolo et al., 1997; Wilsonet
al., 1999) and physics-based models that simulate the haptic interactions among the users have begun to be
developed (Basdogan et al., 2001). Because of network time delays, the difficult nature of some
collaborative tasks, and our lack of knowledge on user abilities and behaviors, the problem of developing a
universal model for shared haptics could be too complex. For example, it is obvious that time delays during
the transfer and processing of data may easily result in unstable forces and can be harmful to the user.
Similarly, participants could follow several different strategies to manipulate the virtual objects during the
execution of the task if an interaction model is established. For example, we could talk about ‘sequential’
versus ‘simultaneous’ types of haptic manipulations. It is even possible to make one user ‘stronger’ than the
other (see Basdogan, 2000). Since our limited knowledge in this area makes it almost impossible to integrate
all these features into a single interaction model, the type of model selected to simulate haptic interactions
between participants in shared environments depend, at this stage, on the collaborative task itself. For
example, we have developed a simple physics-based model to simulate the haptic interactions between
participants (Basdogan et al, 2000). In our model, each subject manipulates his/her own cursor through a
stylus attached to the force feedback device placed next to his/her seat. When the subject manipulates the
stylus of the haptic device with his/her dominant hand, the cursor moves in 3D space, so that the
manipulated object translates or rotates depending on the task. In our experiments, a spring-damper model
(
pbpkF ∆+∆= , where F is the force exerted by the user on the ring that is felt by his/her remote partner, k
and b are the spring and the damping coefficients, and
p∆ is the displacement of the subject’s cursor) was
used to control the impedance of interactions between the participants and between the subject’s cursor and
the ring in the scene (see Figure 10). This model simply simulates the translational movements of the ring on
a wire and pulling and pushing forces between the subjects. Hence, if a subject pulls or pushes his own
cursor, the remote partner feels the forces. Visually, however the ring remained rigid (i.e. no deformation of
the ring was displayed graphically). The rotation of the ring due to unbalanced forces applied by the
participants was prevented to make the task easier. Moreover only the ‘simultaneous’ haptic interactions
were supported such that the ring did not move if both subjects did not apply sufficient forces to the ring at
the same time.
Figure 10. We developed a shared VR set-up that enables two people, at remote locations, to interact with
each other through visual and haptic displays. We also designed an experiment to investigate the role of
haptics in collaborative manipulation. In our experiment, subjects were asked to hold and move a ring on a
wire in a collaborative manner as depicted in this figure. To eliminate time delays due to network
connections, we bifurcated the signals from a single host and displayed it on two separate monitors and
haptic interfaces.
8. Summary and Future
Computer haptics is concerned with the development of software algorithms that enable a user to touch, feel,
and manipulate objects in virtual environments through a haptic interface. It primarily deals with the
computation of forces to be displayed to the user in response to user’s actions. The demands placed on it
depend on the capabilities and limitations of the interface hardware, computational engine, and the user,
together with the needs of the task to be accomplished. The current haptic interface technology is mature for
net force and torque feedback, as in tool usage in the real world. Consequently, current haptic rendering
algorithms have been developed mainly for simulating the net forces and torques of interaction and give the
user the feeling of touching and manipulating objects through a stick or a rigid thimble. Point-based
rendering that views the haptic cursor as a point in computing point-object interaction forces was developed
first and is widely used. This was followed by ray-based rendering that computes line-object interaction
forces and torques. More recently, limited success has been achieved in simulating 3D object-object
interactions where one of the objects is viewed as a collection of points. Using these haptic interaction
paradigms, real-time haptic display of shapes, textures, and friction of rigid and deformable objects has been
achieved. Haptic rendering of dynamics of rigid objects, and to a lesser extent, linear dynamics of
deformable objects has also been accomplished. Methods for recording and playing back haptic stimuli as
well as algorithms for haptic interactions between multiple users in shared virtual environments are
beginning to emerge.
In the future, the capabilities of haptic interface devices are expected to improve primarily in two ways: (1)
improvements in both desktop and wearable interface devices in terms of factors such as inertia, friction,
workspace volume, resolution, force range, and bandwidth; (2) development of tactile displays to simulate
direct contact with objects, including temperature patterns. These are expected to result in multifinger,
multihand, and even whole body displays, with heterogeneous devices connected across networks. Even
with the current rapid expansion of the capabilities of affordable computers, the needs of haptic rendering
with more complex interface devices will continue to stretch computational resources. Currently, even with
point-based rendering, the computational complexity of simulating the nonlinear dynamics of physical
contact between an organ and a surgical tool as well as surrounding tissues is very high. Thus there will be
continued demand for efficient algorithms, especially when the haptic display needs to be synchronized with
the display of visual, auditory, and other modalities. Similar to graphics accelerator cards used today, it is
quite likely that much of the repetitive computations will need to be done through specialized electronic
hardware perhaps through parallel processing. Given all the complexity and need for efficiency, in any given
application the central question will be how good does the simulation needs to be to achieve a desired goal.
References
1. Adachi, Y., Kumano, T., Ogino, K. 1995, March 11-15, Intermediate Representation for Stiff Virtual
Objects. Proc. IEEE Virtual Reality Annual Intl. Symposium, Research Triangle Park, N. Carolina, pp.
203-210.
2. Adams, R., Hannaford, B., 1998, A Two-Port Framework for the Design of Unconditionally Stable
Haptic Interfaces, IEEE/RSJ International Conference on Intelligent Robots and Systems, Victoria,
B.C., Canada.
3. Avila, R. S. and Sobierajski, L. M., 1996, A Haptic Interaction Method for Volume Visualization, IEEE
Proceedings of Visualization, pp. 197-204.
4. Balniuk, R. and Costa, I. F., 2000, LEM – An Approach for Physically Based Soft Tissue Simulation
Suitable for Haptic Interaction, Proceedings of the Fifth Phantom Users Group Workshop.
5. Baraff, D., 1997, “An Introduction to Physically Based Modeling: Rigid Body Simulation I-
Unconstrained Rigid Body Dynamics”, SIGGRAPH’97 Tutorial Notes.
6. Baraff, D. (1994) Fast Contact Force Computation for Nonpenetrating Rigid Bodies. ACM (Proceedings
of SIGGRAPH), 28, 23-34.
7. Basdogan, C., Ho, C., and Srinivasan, M.A. (1997) A Ray-Based Haptic Rendering Technique for
Displaying Shape and Texture of 3D Objects in Virtual Environments. ASME Winter Annual Meeting,
Dallas, TX, 61, 77-84.
8. Basdogan C., Ho, C., Srinivasan, M.A., Small, S., Dawson, S., 1998, "Force interactions in laparoscopic
simulations: haptic rendering of soft tissues" Medicine Meets Virtual Reality (MMVR’6) Conference, pp.
385-391, San Diego, CA, January 19-22.
9. Basdogan C., 1999, “ Force Reflecting Deformable Objects for Virtual Environments” in Haptics: From
Basic Principles to Advanced Applications, SIGGRAPH’ 99, 26 th International Conference on
Computer Graphics and Interactive Techniques, Course No: 38, August 8-13, Los Angeles.
10. Basdogan C., 2000, Course Name: Simulating Minimally Invasive Surgical Procedures in Virtual
Environments: from Tissue Mechanics to Simulation and Training, Medicine Meets Virtual Reality
(MMVR’2000), Jan. 27-30, Irvine, CA, http://www.amainc.com/MMVR/MMVR2000pro.html
11. Basdogan, C., Ho, C., Srinivasan, M.A., 2001, “Virtual Environments for Medical Training: Graphical
and Haptic Simulation of Common Bile Duct Exploration”, submitted to the IEEE/ASME Transactions
on Mechatronics.
12. Basdogan C., Ho, C., Srinivasan, M.A., Small, S., Dawson, S. (1998). Force interactions in laparoscopic
simulations: haptic rendering of soft tissues. Proceedings of the Medicine Meets Virtual Reality VI
Conference, San Diego, CA, January 19-22, 385-391.
13. Basdogan, C., 2001, Real-time Simulation of Dynamically Deformable Finite Element Models Using
Modal Analysis and Spectral Lanczos Decomposition Methods, Medicine Meets Virtual Reality (in
press).
14. Basdogan, C., Ho, C., Srinivasan, M.A., Slater, M., 2000, “An Experimental Study on the Role of Touch
in Shared Virtual Environments” to appear in ACM Human Computer Interactions ”.
15. Bathe, K., (1996), “Finite Element Procedures”, Prentice Hall, New Jersey.
16. Bier, E.A., Sloan K.R. (1986). Two-Part Texture Mapping. IEEE Computer Graphics and Applications,
40-53.
17. Blinn, J.F. (1978). Simulation of Wrinkled Surfaces. ACM (Proceedings of SIGGRAPH), 12(3), 286-
292.
18. Buttolo, P., Oboe, R., Hannaford, B., 1997 ’Architectures for Shared Haptic Virtual Environments,’
Computers and Graphics, vol. 21, pp. 421-9, July-Aug 1997.
19. Cohen, J., Lin, M., Manocha, D., Ponamgi, K. (1995). I-COLLIDE: An Interactive and Exact Collision
Detection System for Large-Scaled Environments. Proceedings of ACM Interactive 3D Graphics
Conference, 189-196.
20. Colgate, J.E., Brown, J.M., 1994, Factors affecting the z-width of a haptic display”, Proceedings of
IEEE Int. Conference on Robotics and Automation, 3205-3210.
21. Cotin, S., Delingette, H., Ayache, N., 1999, “Real-time Elastic Deformations of Soft Tissues for Surgery
Simulation”, IEEE Transactions on Visualization and Computer Graphics, Vol. 5, No. 1, pp. 62-73.
22. Cover S.A., Ezquerra N.F., O’Brien J., Rowe R., Gadacz T., Palm E., 1993, “Interactively Deformable
Models for Surgery Simulation”, IEEE Computer Graphic and Applications, November, pp. 65-78.
23. Dachille, F., Qin, H., Kaufman, A., El-sana J., 1999, “Haptic sculpting of dynamic surfaces”, ACM
Symposium on Interactive 3D Graphics.
24. Dang, T., Annaswamy, T. M., and Srinivasan, M. A., 2001, Development and Evaluation of an Epidural
Injection Simulator with Force Feedback for Medical Training, Medicine Meets Virtual Reality (in
press).
25. De, S. and Srinivasan, M. A., 1999, Thin Walled Models for Haptic and Graphical Rendering of Soft
Tissues in Surgical Simulations, Medicine Meets Virtual Reality (Eds: Westwood, et al.), IOS Press.
26. De, S. Kim, J. and Srinivasan, M. A., 2001, A Meshless Numerical Technique for Physically Based Real
Time Medical Simulations, Medicine Meets Virtual Reality (in press).
27. Ellis, R.E., Sarkar, N. and Jenkins, M.A., 1996, "Numerical Methods For the Haptic Presentation of
Contact: Theory, Simulations, and Experiments", Proceedings of the ASME Dynamic Systems and
Control Division, DSC-Vol. 58, pp. 413-420.
28. Ebert, D.S., Musgrave F.K., Peachey D., Perlin K., Worley S. (1994). Texturing and Modeling. AP
Professional, Cambridge, MA.
29. Edwards, J., Luecke, G., 1996, “Physically based models for use in a force feedback virtual
environment”, Japan/USA Symposium on Flexible Automation, ASME, pp. 221-228.
30. Foley, J.D., van Dam, A., Feiner, S. K., Hughes, J.F. (1995). Computer Graphics: Principles and
Practice. Addison-Wesley.
31. Fritz and Barner (1996). Haptic Scientific Visualization. Proceedings of the First PHANToM Users
Group Workshop, Eds: Salisbury J.K. and Srinivasan M.A. MIT-AI TR-1596 and RLE TR-612.
32. Fukui, Y. (1996) Bump mapping for a force display, Proc. of the First PHANToM User Group
Workshop (PUG 96), Dedham, http://www.ai.mit.edu/conferences/pug/pug-proceedings.html
33. Gottschalk, S., Lin, M., and Manocha, D. (1996). OBB-Tree: A hierarchical Structure for Rapid
Interference Detection. ACM (Proceedings of SIGGRAPH), August.
34. Green, D. F. and Salisbury, J. K. (1997). Texture Sensing and Simulation Using the PHANToM:
Towards Remote Sensing of Soil Properties. Proceedings of the Second PHANToM Users Group
Workshop, Oct. 19-22.
35. Ho, C., Basdogan, C., Srinivasan, M.A., 2000, Modeling of Force and Torque Interactions Between a
Line Segment and Triangular Surfaces for Haptic Display of 3D Convex Objects in Virtual and
Teleoperated Environments, “International Journal of Robotics” (special issue on Tactile Perception),
Vol. 19, No. 7, pp. 668-684.
36. Ho, C., Basdogan, C., Srinivasan, M.A., 1999, “An Efficient Haptic Rendering Technique for
Displaying 3D Polyhedral Objects and Their Surface Details in Virtual Environments”, October’99 Vol.
8, No. 5, pp. 477-491, Presence: Teleoperators and Virtual Environments.
37. Hollerbach J. and Johnson, D., 2001, to appear in “Human and Machine Haptics” (Eds: Srinivasan,
Cutkosky, Howe, and Salisbury).
38. Hubbard, P. (1995). Collision Detection for Interactive Graphics Applications. IEEE Transactions on
Visualization and Computer Graphics, 1(3), 219-230.
39. Hsu W.M. Hughes J.F., Kaufman H., 1992, “Direct Manipulation of Free-Form Deformations”,
Computer Graphics (Proceedings of the SIGGRAPH), Vol. 26, No.2, pp. 177-184.
40. James, D., Pai, D., 1999, ARTDEFO: Accurate Real Time Deformable Objects, In Computer Graphics
(SIGGRAPH 99 Conference Proceedings).
41. Krebs, H. I., Hogan, N., Aisen, M. L.,and Volpe, B. T. (1998) Robot-Aided Neurorehabilitation. IEEE
Transactions on Rehabilitation Engineering, 6(1): 75-86.
42. Latimar, C., 1997, “Haptic Interaction with Rigid Objects Using Real-time Dynamic Simulation”, M.S.
Thesis, Massachusetts Institute of Technology, Mechanical Engineering.
43. Lee, Y., Terzopoulos, D., Waters, K., 1995, “Realistic Modeling for Facial Animation”, (Proceedings of
the SIGGRAPH), pp. 55-62.
44. Lin, M. (1993). Efficient Collision Detection for Animation and Robotics. Ph.D. thesis, University of
California, Berkeley.
45. MacLean, K., 1996, The "haptic camera": A technique for characterizing and playing back haptic
properties of real environments, Proceedings of ASME Dynamic Systems and Control Division, Vol. 58
of DSC, pages 459-467.
46. Mandelbrot, B. (1982). The Fractal Geometry of Nature. W.H. Freeman.
47. Mark, W., Randolph S., Finch, M., Van Verth, J., Taylor, R.M. (1996). Adding Force Feedback to
Graphics Systems: Issues and Solutions. Computer Graphics: Proceedings of SIGGRAPH’96, August,
447-452.
48. Max, N.L., Becker, B.G. (1994). Bump Shading for Volume Textures. IEEE Computer Graphics and
App., 4, 18-20.
49. McNeely, W.A., Puterbaugh K.D., Troy, J.J., 1999, Six Degree-of-Freedom Haptic Rendering Using
Voxel Sampling, Proceedings of SIGGRAPH, pp. 401-408.
50. Minsky, M., Ming, O., Steele, F., Brook, F.P., and Behensky, M. (1990). Feeling and seeing: issues in
force display. Proceedings of the symposium on 3D Real-Time Interactive Graphics, 24, 235-243.
51. Mirtich, B. (1996). Impulse-based Dynamic Simulation of Rigid Body Systems. Ph.D. thesis, University
of California, Berkeley.
52. Mirtich, B., Canny, J. (1995). Impulse-based Simulation of Rigid Bodies. Proceedings of Symposium on
Interactive 3D Graphics, April.
53. Morgenbesser, H.B., Srinivasan, M.A. (1996). Force Shading for Haptic Shape Perception. Proceedings
of the ASME Dynamic Systems and Control Division, 58, 407-412.
54. Ng, H., Grimsdale, R., 1996, “Computer Graphics Techniques for Modeling Cloth”, IEEE Computer
Graphic and Applications, September, pp. 28-41.
55. Perlin, K. (1985). An Image Synthesizer. ACM SIGGRAPH, 19(3), 287-296.
56.
Ruspini, D.C., Kolarov, K., Khatib O. (1996). Robust Haptic Display of Graphical Environments.
Proceedings of the First PHANToM Users Group Workshop, Eds: Salisbury J.K. and Srinivasan M.A.
MIT-AI TR-1596 and RLE TR-612.
57. Ruspini, D.C., Kolarov, K., Khatib O. (1997). The Haptic Display of Complex Graphical Environments.
ACM (Proceedings of SIGGRAPH), July, 345-352.
58. Salcudean, S. E. and Vlaar, T. D. (1994). On the Emulation of Stiff Walls and Static Friction with a
Magnetically Levitated Input/Output Device. ASME DSC, 55(1), 303 - 309.
59. Salisbury, J.K., Brock, D., Massie, T., Swarup, N., Zilles C. (1995). Haptic Rendering: Programming
touch interaction with virtual objects. Proceedings of the ACM Symposium on Interactive 3D Graphics,
Monterey, California.
60. Salisbury, J. K., Srinivasan, M. A. (1997). Phantom-Based Haptic Interaction with Virtual Objects.
IEEE Computer Graphics and Applications, 17(5).
61. Salisbury, J.K., and Tarr, C., 1997, Haptic Rendering of Surfaces Defined by Implicit Functions,
Proceedings of the ASME, DSC-61, pp. 61-67.
62. Sederberg, T.W., Parry S.R., 1986, “Free-form Deformation of Solid Geometric Models”, SIGGRAPH
Proceedings on Computer Graphics, Vol. 20, No. 4, pp. 151-160.
63. Siira, J., Pai D. K. (1996). Haptic Texturing - A Stochastic Approach. Proceedings of the IEEE
International Conference on Robotics and Automation, Minneapolis, Minnesota, 557-562.
64. Srinivasan MA, Whitehouse JM and LaMotte RH, 1990, Tactile detection of slip: Surface
microgeometry and peripheral neural codes, J. Neurophysiology, Vol. 63, No. 6, pp.1323-1332.
65. Srinivasan MA, Beauregard GL, and Brock, DL, 1996, The impact of visual information on haptic
perception of stiffness in virtual environments, Proceedings of the ASME Dynamic Systems and Control
Division, DSC-Vol. 58, pp. 555-559.
66. Srinivasan, M.A., and Basdogan, C. (1997). Haptics in Virtual Environments: Taxonomy, Research
Status, and Challenges. Computers and Graphics, 21(4), 393 – 404.
67. Stewart, P., Chen, Y., Buttolo, P., 1997, “Direct Integration of haptic user interface in CAD systems,
Proceedings of ASME, DSC-Vol. 61, pp. 93-99.
68. Swarup, N., 1995, “Haptic Interaction with Deformable Objects Using Real-Time Dynamic
Simulation”, M.S. Thesis, Mechanical Engineering Department, Massachusetts Institute of Technology.
69. Thompson, T.V., Johnson, D.E. and Cohen, E., 1997, Direct haptic rendering of sculptured models,
Proc. Sym. Interactive 3D Graphics, Providence, RI, pp. 1-10.
70. Turk, G. (1991). Generating Textures on Arbitrary Surfaces Using Reaction-Diffusion. ACM
(Proceedings of SIGGRAPH), 25(4), 289-298.
71. Watt, A., Watt, M. (1992). Advanced Animation and Rendering Techniques. Addison-Wesley, NY.
72. Wilson J., Kline-Schoder, Kenton, M.A., Hogan, N. 1999, Algorithms for Network-Based Force
Feedback, Proceedings of the Fourth PHANTOM Users Group Workshop, Salisbury, J.K. and
Srinivasan, M.A. (Eds), AI Lab Technical Report No. 1675 and RLE Technical Report No. 633, MIT.
73. Wijk, J. J. V. (1991). Spot Noise. ACM (Proceedings of SIGGRAPH), 25(4), 309-318.
74. Witkin, A., and Kass, M. (1991). Reaction-Diffusion Textures. ACM (Proceedings of SIGGRAPH),
25(4), 299-308.
75. Witkin A., Barraff D., Kass M., Tutorial notes on “ An Introduction to Physically-Based Modeling”,
SIGGRAPH’98.
76. Worley, S. (1996). A Cellular Texture Basis Function. ACM (Proceedings of SIGGRAPH), August, 291-
294.
77. Zilles, C.B., and Salisbury, J.K. (1995). A Constraint-Based God-Object Method for Haptic Display.
IEEE International Conference on Intelligent Robots and System, Human Robot Interaction, and Co-
operative Robots, IROS, 3, 146-151.
