A polygonal method for haptic force generation Page: 4 of 10
This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
The algorithm first focuses on determining
if the user point, or cursor, has touched an object,
which requires a collision detection algorithm.
Then forces must be created based on penetration
depth and surface position, including interpolation
for smooth corners.
Graphically, a Bendable Polygon technique
is used along with springs and dampers for
deformations, which are slave to the haptic
process. This makes the graphical deformations
happen naturally and easily as opposed to a
method in which the graphical and haptic data sets
are separate, yet overlap. In addition, this method
allows for relatively easy dynamics modeling such
as motion or permanent deformations. These
algorithms are presented below, and an
implementation of them is described together with
results and suggestions for further research.
2. Background Methods
Much of the previous haptic rendering
research has used methods that work well with
either continuous vector fields or simple geometric
objecfs.
Continuous vector fields, for example
electric potential, can be modeled by mapping the
electric force vector directly to the mechanical
force felt by the user. In this way, a user can 'feel
around' through the space permeated by the
electrical (or other vector) field.
Massie [3] has modeled the forces
associated with touching simple geometric
surfaces (a wall, for example) by using a force
function, F = kX, where F is the force vector, k
is.a constant, and X is a vector normal to the
surface, with a magnitude proportional to the
depth of penetration into a virtual surface. The
surface can be made to feel stiffer by adding a
viscous damping term to the force equation so that
F = kX + bV [2], where V is a velocity vector
associated with the user point, and b is another
empirical constant.
A box felt from outside its boundaries
(Figure 2) presents a slightly more difficult
problem. The direction of the force is dependent
on the entry path as shown in Figure 2a. One
solution for the problem [3] is shown in figure
2b, where the rectangle is split into four different
areas, each with an associated direction.F
F
/F
0 o F
(a) (b)
Figure 2: Vector field approach to
modeling forces on a square. (a) It is not
clear which of the forces is appropriate.
The force is path dependent. (b) A vector
field solution. By splitting the square up
into fourths (in 3D there are eight
pyramid shaped pieces) an appropriate
force is always presented.
Spheres can be modeled so that the force is
always in a direction away from the center, with a
magnitude determined by the distance from the
center.
All of the above vector field approaches
have limitations in that they are specific to
particular situations or apply to relatively simple
geometric shapes. Also, thin objects can be
unintentionally penetrated through with such
methods. It is conceivable that one might take
geometric primitives, and add them to make more
complex shapes, but in general this does not
always lead to the correct force [6].
Thus, there is a great need for a more
coherent approach to haptic rendering and
modeling interactions with complex objects [2], in
which a larger base of haptically renderable
objects can be obtained. Although one might take
a volumetric approach, surface approaches take
advantage of a large database of objects that
already exist.
Zilles and Salisbury [6] use such an
approach. They have modeled rigid polygonal
surfaces using a technique known as the "god-
object" method after Dworkin and Zeltzer. The
constraint-based god object method of Zilles
allows a user to intuitively control a point probing
a virtual object while preventing the point from
penetrating the object. However, the forces and
surface deformations associated with just such
penetrations in non-rigid objects are the subject of
this research and are described below.
In general, the haptic forces will be the
result of a combination of heuristics coupled with
Upcoming Pages
Here’s what’s next.
Search Inside
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
Anderson, T. A polygonal method for haptic force generation, article, December 31, 1996; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc674206/m1/4/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.